From cdc3612672cfc9916fad6636860441c1b6f8e038 Mon Sep 17 00:00:00 2001 From: Miriam Zusin Date: Sat, 16 Mar 2024 12:30:27 +0200 Subject: [PATCH] Series --- README.md | 2 + dist/index.d.ts | 2 + dist/mz-math.esm.js | 6 +- dist/mz-math.esm.js.map | 8 +- dist/mz-math.min.js | 6 +- dist/mz-math.min.js.map | 8 +- dist/mz-math.node.cjs | 6 +- dist/mz-math.node.cjs.map | 8 +- ...494664434.css => styles.1710585004234.css} | 0 docs/index.html | 6 +- ...710494664434.js => index.1710585004234.js} | 2 +- ...4434.js.map => index.1710585004234.js.map} | 0 docs/pages/Check-if-value-is-number.html | 8 +- docs/pages/adjugate-matrix.html | 8 +- docs/pages/angle-between-vectors.html | 8 +- docs/pages/angles-distance.html | 8 +- docs/pages/animation.html | 8 +- docs/pages/append-or-prepend-column.html | 8 +- docs/pages/append-or-prepend-row.html | 8 +- docs/pages/arithmetic-sequence-sum.html | 8 +- docs/pages/bezier-curves.html | 8 +- docs/pages/bounding-box.html | 8 +- docs/pages/browser-usage.html | 8 +- docs/pages/check-if-ranges-overlap.html | 8 +- docs/pages/circle-movement.html | 8 +- docs/pages/circles-collision.html | 8 +- docs/pages/circumference.html | 8 +- docs/pages/color.html | 8 +- docs/pages/convert-colors.html | 8 +- docs/pages/convert-range.html | 8 +- docs/pages/convert-string-to-number.html | 8 +- docs/pages/convex-polygons-collision.html | 8 +- docs/pages/cross-product.html | 8 +- docs/pages/degrees-and-radians.html | 8 +- docs/pages/distance-between-vectors.html | 8 +- docs/pages/divide-by-scalar.html | 8 +- docs/pages/divide-vector-by-scalar.html | 8 +- docs/pages/dot-product.html | 8 +- docs/pages/ellipse-movement.html | 8 +- docs/pages/extrema.html | 8 +- docs/pages/general-case.html | 8 +- docs/pages/get-animation-data.html | 8 +- docs/pages/get-column.html | 8 +- .../get-linear-equation-by-2-points.html | 8 +- docs/pages/get-matrix-minor.html | 8 +- docs/pages/get-normal.html | 8 +- .../get-point-on-cubic-bezier-curve.html | 8 +- .../get-point-on-quadratic-bezier-curve.html | 8 +- docs/pages/get-random-boolean.html | 8 +- docs/pages/get-random-integer.html | 8 +- docs/pages/get-random-item-from-array.html | 8 +- docs/pages/get-random-number-in-range.html | 8 +- docs/pages/inverse-matrix.html | 8 +- docs/pages/is-angle-between.html | 8 +- docs/pages/is-angle-in-circle-arc.html | 8 +- docs/pages/is-clockwise.html | 8 +- docs/pages/lerp.html | 8 +- docs/pages/linear-equation.html | 8 +- docs/pages/lissajous-curve.html | 8 +- docs/pages/matrix-deep-copy.html | 8 +- docs/pages/matrix-determinant.html | 8 +- docs/pages/matrix-equality.html | 8 +- docs/pages/matrix-initialization.html | 8 +- docs/pages/matrix-multiplication.html | 8 +- docs/pages/matrix-singularity.html | 8 +- docs/pages/matrix-subtraction.html | 8 +- docs/pages/matrix-sum.html | 8 +- docs/pages/matrix-to-CSS-transform.html | 8 +- docs/pages/matrix-transposition.html | 8 +- docs/pages/matrix.html | 8 +- docs/pages/modulo.html | 8 +- docs/pages/multiply-by-scalar.html | 8 +- docs/pages/multiply-matrix-by-vector.html | 8 +- docs/pages/multiply-vector-by-scalar.html | 8 +- docs/pages/natural-numbers-sequence-sum.html | 8 +- docs/pages/nodejs-usage.html | 8 +- docs/pages/normal.html | 8 +- docs/pages/normalize-vector.html | 8 +- docs/pages/percent-to-angle.html | 8 +- docs/pages/polar-to-cartesian.html | 8 +- docs/pages/polynomial.html | 8 +- docs/pages/quadratic-equation.html | 8 +- docs/pages/random-color.html | 8 +- docs/pages/random-id-or-GUID.html | 8 +- docs/pages/rectangles-collision.html | 8 +- docs/pages/reflection-matrix.html | 8 +- docs/pages/remove-row-or-column.html | 8 +- docs/pages/reset-matrix.html | 8 +- docs/pages/rotate-around-point.html | 8 +- docs/pages/rotation-matrix.html | 8 +- docs/pages/scale-and-stretch-matrix.html | 8 +- docs/pages/scale-around-point.html | 8 +- docs/pages/series.html | 275 ++++++++++++++++++ docs/pages/set-decimal-places.html | 8 +- docs/pages/shearing-matrix.html | 8 +- docs/pages/shift-colors.html | 8 +- docs/pages/similar-colors.html | 8 +- docs/pages/sine-wave-movement.html | 8 +- docs/pages/square-in-circle.html | 8 +- docs/pages/system-of-linear-equations.html | 8 +- docs/pages/tangent.html | 8 +- docs/pages/temperature-conversion.html | 25 +- docs/pages/translation-matrix.html | 8 +- docs/pages/trigonometric-functions.html | 8 +- docs/pages/typescript-usage.html | 8 +- docs/pages/vector-angle.html | 8 +- docs/pages/vector-initialization.html | 8 +- docs/pages/vector-length.html | 8 +- docs/pages/vectors-equality.html | 8 +- docs/pages/vectors-subtraction.html | 8 +- docs/pages/vectors-sum.html | 8 +- docs/pages/vectors.html | 8 +- docs/sitemap.txt | 1 + package.json | 2 +- src/docs/data/pages/1000-other/10-series.md | 15 + src/index-esm.ts | 3 +- src/index.ts | 5 +- src/main/series.ts | 14 + test/series.test.ts | 31 ++ 119 files changed, 784 insertions(+), 425 deletions(-) rename docs/css/{styles.1710494664434.css => styles.1710585004234.css} (100%) rename docs/js/{index.1710494664434.js => index.1710585004234.js} (99%) rename docs/js/{index.1710494664434.js.map => index.1710585004234.js.map} (100%) create mode 100644 docs/pages/series.html create mode 100644 src/docs/data/pages/1000-other/10-series.md create mode 100644 src/main/series.ts create mode 100644 test/series.test.ts diff --git a/README.md b/README.md index fa693a11..4571bc92 100644 --- a/README.md +++ b/README.md @@ -123,6 +123,7 @@ This project is a collection of TypeScript math helpers and utilities for the br - [Check If Value Is Number](https://math.mzsoft.org/pages/check-if-value-is-number.html) - [Polar To Cartesian](https://math.mzsoft.org/pages/polar-to-cartesian.html) - [Temperature Conversion](https://math.mzsoft.org/pages/temperature-conversion.html) +- [Series](https://math.mzsoft.org/pages/series.html) ------------------------------ @@ -701,6 +702,7 @@ This project is a collection of TypeScript math helpers and utilities for the br + ``` diff --git a/dist/index.d.ts b/dist/index.d.ts index b487ef85..99d1c7d2 100644 --- a/dist/index.d.ts +++ b/dist/index.d.ts @@ -370,4 +370,6 @@ declare module 'mz-math' { export const kelvinToCelsius: (kelvin: number, decimalPlaces?: number) => number; export const kelvinToFahrenheit: (kelvin: number, decimalPlaces?: number) => number; + export const naturalNumbersSum1ToN: (n: number) => number; + export const naturalNumbersSumMToN: (m: number, n: number) => number; } \ No newline at end of file diff --git a/dist/mz-math.esm.js b/dist/mz-math.esm.js index 2766f18f..44fc778a 100644 --- a/dist/mz-math.esm.js +++ b/dist/mz-math.esm.js @@ -1,14 +1,14 @@ /* -mzMath v3.0.24 +mzMath v3.0.25 A collection of TypeScript-based math helpers. https://github.com/mzusin/mz-math Licensed GPLv3 for open source use, or Commercial License for commercial use - https://github.com/mzusin/index/blob/main/LICENSE.md Copyright (c) 2023-present, Miriam Zusin */ -var h=Math.pow;var s=(t,r=1/0)=>{if(r===1/0)return 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m2Reset,Oe as m2RotateAroundPointH,Xt as m2Rotation,Yt as m2RotationAroundPointH,lt as m2RotationH,Ft as m2Scale,Ke as m2ScaleAtPointH,kt as m2ScaleAtPointHMatrix,Qt as m2ScaleH,rn as m2ScaleX,en as m2ScaleXH,mn as m2ScaleY,an as m2ScaleYH,Hn as m2ShearingX,zn as m2ShearingY,Kr as m2Sub,Wr as m2Sum,Ae as m2ToCSS,Xe as m2Translation,G as m2TranslationH,ee as m2Transpose,Ne as m2hToCSS,Ce as m2hToCSS3d,ce as m2x2,Te as m3Adjugate,le as m3AppendRow,xt as m3DeepCopy,He as m3Determinant,re as m3DivideScalar,Vt as m3Inverse,te as m3MulScalar,de as m3PrependRow,Mn as m3ReflectionOrigin,bn as m3ReflectionOriginH,Rn as m3ReflectionXY,wn as m3ReflectionXYH,gn as m3ReflectionXZ,Sn as m3ReflectionXZH,dn as m3ReflectionYZ,vn as m3ReflectionYZH,ie as m3Reset,Gt as m3RotationX,Fe as m3RotationXH,Ot as m3RotationY,Ze as m3RotationYH,jt as m3RotationZ,We as m3RotationZH,Zt as m3Scale,Pe as m3ScaleH,nn as m3ScaleX,on as m3ScaleXH,cn as m3ScaleY,sn as m3ScaleYH,un as m3ScaleZ,xn as m3ScaleZH,Jr as m3Sub,Ur as m3Sum,Ye as m3Translation,Ge as m3TranslationH,ne as m3Transpose,De as m3hToCSS3d,se as m3x3,ue as m4x4,bt as mAdjugate,Me as mAppendCol,he as mAppendRow,I as mDeepCopy,Se as mDelFirstColumn,ge as mDelFirstRow,mt as mDelLastColumn,ve as mDelLastRow,Y as mDeterminant,Q as mDivideScalar,ze as mEqual,we as mGetColumn,Re as mGetFirstColumn,at as mGetLastColumn,Z as mInverse,ft as mMinor,E as mMul,ct as mMulScalar,h as mMulVector,xe as mNxM,be as mPrependCol,ye as mPrependRow,st as mReset,it as mSub,ot as mSum,X as mTranspose,Tt as mlNormalizeArray,Ri as mlNormalizeTestData,wi as mlNormalizeUnseenData,xr as mlNormalizeValue,Bt as mlStandardizeArray,zi as mlStandardizeTestData,Hi as mlStandardizeUnseenData,mr as mlStandardizeValue,y as mod,pi as naturalNumbersSequenceSum,Bi as naturalNumbersSum1ToN,Li as naturalNumbersSumMToN,Uo as newId,zr as percentToAngle,hr as polarToCartesian,vr as radiansToDegrees,ti as rectCollide,Go as rgbToHex,Yo as rgbToHsl,gt as rgbToLab,s as setDecimalPlaces,K as setV2Angle,zo as sineWaveMovement,qn as stringToNumber,jr as v2,yo as v2CubicBezierBBox,Ut as v2CubicBezierCurve,tr as v2CubicBezierCurveExtrema,Vo as v2CubicBezierCurveNormal,Jt as v2CubicBezierCurveTangent,Xr as v2Distance,Ar as v2DivideScalar,tt as v2DotProduct,Qr as v2FromPolarCoords,nt as v2GetNormal,P as v2Length,qr as v2MulScalar,$ as v2Normalize,lo as v2QuadraticBezierBBox,Wt as v2QuadraticBezierCurve,Pt as v2QuadraticBezierCurveExtrema,ho as v2QuadraticBezierCurveNormal,Kt as v2QuadraticBezierCurveTangent,je as v2Rotate,ke as v2RotateH,Je as v2Scale,Nt as v2SetLength,w as v2Sub,Lr as v2Sum,kr as v3,Or as v3CrossProduct,po as v3CubicBezierCurve,bo as v3CubicBezierCurveTangent,Yr as v3Distance,Nr as v3DivideScalar,Gr as v3DotProduct,Cr as v3Length,F as v3MulScalar,g as v3Normalize,fo as v3QuadraticBezierCurve,Mo as v3QuadraticBezierCurveTangent,Qe as v3RotateX,_e as v3RotateY,Ue as v3RotateZ,tn as v3Scale,Er as v3Sub,$r as v3Sum,Fr as v4,Dr as vDistance,D as vDivideScalar,S as vDotProduct,et as vEqual,z as vLength,C as vMulScalar,rt as vN,B as vNormalize,d as vSub,N as vSum}; //# sourceMappingURL=mz-math.esm.js.map diff --git a/dist/mz-math.esm.js.map b/dist/mz-math.esm.js.map index 24df80aa..c1d04eb8 100644 --- a/dist/mz-math.esm.js.map +++ b/dist/mz-math.esm.js.map @@ -1,7 +1,7 @@ { "version": 3, - "sources": ["../src/main/format.ts", "../src/main/other.ts", "../src/main/angle.ts", "../src/main/linear-algebra/vector.ts", "../src/main/linear-algebra/matrix.ts", "../src/main/linear-algebra/matrix-transformations.ts", "../src/main/random.ts", "../src/main/convert.ts", "../src/main/derivative.ts", "../src/main/equations/linear-equations.ts", "../src/main/equations/quadratic-equations.ts", "../src/main/bezier-curves/bezier-curve.ts", "../src/main/path-movement.ts", "../src/main/color.ts", "../src/main/id.ts", "../src/main/collision-detection.ts", "../src/main/animation.ts", "../src/main/circle-ellipse.ts", "../src/main/sequence.ts", "../src/main/statistics.ts", "../src/main/ml.ts"], - "sourcesContent": ["export const setDecimalPlaces = (num: number, decimalPlaces: number | undefined = Infinity) => {\n if(decimalPlaces === Infinity) return num;\n\n if(decimalPlaces < 0){\n decimalPlaces = 0;\n }\n\n const coefficient = 10 ** decimalPlaces;\n return Math.round(num * coefficient) / coefficient;\n};", "import { Vector2 } from '../types';\nimport { setDecimalPlaces } from './format';\n\nexport const mod = (n: number, m: number) => {\n return ((n % m) + m) % m;\n};\n\n/**\n * Convert range [a, b] to [c, d].\n * f(x) = (d - c) * (x - a) / (b - a) + c\n */\nexport const convertRange = (x: number, a: number, b: number, c: number, d: number) => {\n return (d - c) * (x - a) / (b - a) + c;\n};\n\n/**\n * Check if 2 ranges [a,b] and [c,d] overlap.\n */\nexport const doRangesOverlap = (a: number, b: number, c: number, d: number) => {\n return Math.max(a, c) <= Math.min(b, d) ;\n};\n\n// eslint-disable-next-line\nexport const isNumber = (value: any) => {\n return !isNaN(parseFloat(value)) && isFinite(value);\n};\n\n/**\n * Convert polar coordinates to cartesian coordinates.\n */\nexport const polarToCartesian = (center: Vector2, radii: Vector2, angleInRad: number, decimalPlaces = Infinity) : Vector2 => {\n const [cx, cy] = center;\n const [rx, ry] = radii;\n\n return [\n setDecimalPlaces(cx + (rx * Math.cos(angleInRad)), decimalPlaces),\n setDecimalPlaces(cy + (ry * Math.sin(angleInRad)), decimalPlaces),\n ];\n};", "import { Vector, Vector2, Vector3 } from '../types';\nimport { setDecimalPlaces } from './format';\nimport { v2Length, vNormalize, vDotProduct, vSub } from './linear-algebra/vector';\nimport { mod } from './other';\n\nexport const getV2Angle = (v2: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1], v2[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleInEllipse = (v2: Vector2, radii: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1]/radii[1], v2[0]/radii[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const setV2Angle = (v2: Vector2, newAngleRad: number, decimalPlaces = Infinity): Vector2 => {\n const length = v2Length(v2);\n return [\n setDecimalPlaces(Math.cos(newAngleRad) * length, decimalPlaces),\n setDecimalPlaces(Math.sin(newAngleRad) * length, decimalPlaces),\n ];\n};\n\nexport const radiansToDegrees = (radians: number, decimalPlaces = Infinity) => {\n const res = radians * (180 / Math.PI);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\nexport const degreesToRadians = (degrees: number, decimalPlaces = Infinity) => {\n const res = degrees * (Math.PI / 180);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\n/**\n * Returns the range [0, Math.PI]\n * A = Math.acos( dot(v1, v2)/(v1.length()*v2.length()) );\n */\nexport const getVNAngleBetween = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n const unitVector1 = vNormalize(vector1);\n const unitVector2 = vNormalize(vector2);\n const dotProduct = vDotProduct(unitVector1, unitVector2);\n const angle = Math.acos(dotProduct);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleBetween = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) : number => {\n // return getVNAngleBetween(vector1, vector2, decimalPlaces);\n const diff = vSub(vector1, vector2);\n const angle = Math.atan2(diff[1], diff[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV3AngleBetween = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return getVNAngleBetween(vector1, vector2, decimalPlaces);\n};\n\nexport const isAngleBetween = (angleDegrees: number, startAngleDegrees: number, endAngleDegrees: number) : boolean => {\n const distance = getAnglesSub(startAngleDegrees, endAngleDegrees);\n const distance1 = getAnglesSub(startAngleDegrees, angleDegrees);\n const distance2 = getAnglesSub(endAngleDegrees, angleDegrees);\n const totalDistance = distance1 + distance2;\n\n // Use a small threshold for floating point errors\n return Math.abs(totalDistance - distance) <= 0.001;\n}\n\nexport const isClockwise = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n return angle2Deg >= angle1Deg;\n};\n\n/**\n * Shortest distance (angular) between two angles.\n */\nexport const getAnglesSub = (angleDegrees1: number, angleDegrees2: number, decimalPlaces = Infinity) : number => {\n const angleDistance = Math.abs(mod(angleDegrees1, 360) - mod(angleDegrees2, 360));\n return setDecimalPlaces(angleDistance <= 180 ? angleDistance : 360 - angleDistance, decimalPlaces);\n};\n\nexport const getAnglesDistance = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0, decimalPlaces = Infinity) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n if(isClockwise(angle1Deg, angle2Deg, startAngleDeg)) {\n return setDecimalPlaces((angle2Deg - angle1Deg + 360) % 360, decimalPlaces);\n }\n else{\n return setDecimalPlaces((angle1Deg - angle2Deg + 360) % 360, decimalPlaces);\n }\n};\n\nexport const percentToAngle = (percent: number, startAngleDeg: number, endAngleDeg: number, circleStartAngle = 0) => {\n if(percent < 0) {\n percent = 0;\n }\n\n if(percent > 100) {\n percent = 100;\n }\n\n const distance = getAnglesDistance(startAngleDeg, endAngleDeg, circleStartAngle);\n\n const clockwise = isClockwise(startAngleDeg, endAngleDeg, circleStartAngle);\n if(clockwise) {\n return mod(circleStartAngle + (percent * distance / 100), 360);\n }\n else {\n return mod(circleStartAngle - (percent * distance / 100), 360);\n }\n};", "import { Vector, Vector2, Vector3, Vector4 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { getV2Angle, setV2Angle } from '../angle';\n\n// ------------ SUM ------------------------\n\nexport const vSum = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSum(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sum = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSum(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ SUB ------------------------\n\nexport const vSub = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSub(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sub = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSub(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ MUL SCALAR ------------------------\n\nexport const vMulScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n const vector: Vector = [];\n\n for(let i=0; i {\n return vMulScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3MulScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vMulScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ DIVIDE ------------------------\n\nexport const vDivideScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vDivideScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3DivideScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vDivideScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ LENGTH ------------------------\n\nexport const vLength = (vector: Vector, decimalPlaces = Infinity) => {\n let sum = 0;\n\n for(let i=0; i {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v3Length = (vector: Vector3, decimalPlaces = Infinity) => {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v2SetLength = (v2: Vector2, newLength: number, decimalPlaces = Infinity): Vector2 => {\n const angle = getV2Angle(v2);\n return [\n setDecimalPlaces(Math.cos(angle) * newLength, decimalPlaces),\n setDecimalPlaces(Math.sin(angle) * newLength, decimalPlaces),\n ];\n};\n\n// ----------- DISTANCE ------------------------\n\nexport const vDistance = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v2Distance = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v3Distance = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\n// ------------ NORMALIZE ------------------------\n\n/**\n * Normalization creates a unit vector, which is a vector of length 1.\n */\nexport const vNormalize = (v: Vector, decimalPlaces = Infinity) : Vector => {\n const length = vLength(v);\n const unitVector: Vector = [];\n\n for(let i=0; i {\n return vNormalize(v2, decimalPlaces) as Vector2;\n};\n\nexport const v3Normalize = (v3: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vNormalize(v3, decimalPlaces) as Vector3;\n};\n\n// ------------ DOT PRODUCT ------------------------\n\nexport const vDotProduct = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n let sum = 0;\n\n for(let i=0; i {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\nexport const v3DotProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\n// ------------ CROSS PRODUCT ------------------------\n\n/**\n * Cross product is possible on 3D vectors only.\n * The cross product a \u00D7 b is defined as a vector c that is perpendicular (orthogonal) to both a and b.\n */\nexport const v3CrossProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity): Vector3 => {\n return [\n setDecimalPlaces(vector1[1] * vector2[2] - vector1[2] * vector2[1], decimalPlaces),\n setDecimalPlaces(vector1[2] * vector2[0] - vector1[0] * vector2[2], decimalPlaces),\n setDecimalPlaces(vector1[0] * vector2[1] - vector1[1] * vector2[0], decimalPlaces),\n ];\n};\n\n// --------------- INIT VECTOR HELPER -----------------\n\nexport const v2 = (defaultValue = 0): Vector2 => {\n return [defaultValue, defaultValue];\n};\n\nexport const v3 = (defaultValue = 0): Vector3 => {\n return [defaultValue, defaultValue, defaultValue];\n};\n\nexport const v4 = (defaultValue = 0): Vector4 => {\n return [defaultValue, defaultValue, defaultValue, defaultValue];\n};\n\nexport const vN = (N: number, defaultValue = 0): Vector => {\n\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n const vector: Vector = [];\n for(let i=0; i {\n let vector: Vector2 = [0, 0];\n vector = v2SetLength(vector, distance);\n return setV2Angle(vector, angleRad);\n};\n\n// --------------- EQUALITY -------------------------\n\nexport const vEqual = (vector1: Vector, vector2: Vector): boolean => {\n if(vector1.length !== vector2.length) return false;\n\n for(let i=0; i {\n const sub = v2Sub(vector2, vector1);\n return [\n -setDecimalPlaces(sub[1], decimalPlaces),\n setDecimalPlaces(sub[0], decimalPlaces)\n ];\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector, Vector2, Vector3 } from '../../types';\nimport { vMulScalar, vSum, vSub, vDotProduct, vN, vEqual, vDivideScalar } from './vector';\n\n// --------------- SUM ----------------------\n\nexport const mSum = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sum = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- SUB ----------------------\n\nexport const mSub = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sub = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- MUL SCALAR ----------------------\n\nexport const mMulScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vMulScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2MulScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mMulScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3MulScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mMulScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n// --------------- DIVIDE SCALAR ----------------------\n\nexport const mDivideScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vDivideScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2DivideScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mDivideScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3DivideScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mDivideScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n\n// --------------- TRANSPOSE ----------------------\n\nexport const mTranspose = (m: Matrix): Matrix => {\n\n const vectorsCount = m.length;\n if(vectorsCount <= 0) return m;\n\n const vectorLength = m[0].length;\n if(vectorLength <= 0) return m;\n\n const matrix: Matrix = [];\n for(let i=0; i {\n return mTranspose(m2);\n};\n\nexport const m3Transpose = (m3: Matrix3): Matrix => {\n return mTranspose(m3);\n};\n\n// ----------------- RESET ----------------------\n\nexport const mReset = (m: Matrix, defaultValue = 0): Matrix => {\n\n if(m.length <= 0) return [];\n\n const res: Matrix = [];\n\n for(let i=0; i {\n return mReset(m2, defaultValue) as Matrix2;\n};\n\nexport const m3Reset = (m3: Matrix3, defaultValue = 0): Matrix3 => {\n return mReset(m3, defaultValue) as Matrix3;\n};\n\n// --------------- MATRIX INIT HELPERS -----------------\n\nexport const m2x2 = (defaultValue = 0): Matrix2 => {\n return [\n [defaultValue, defaultValue],\n [defaultValue, defaultValue],\n ];\n};\n\nexport const m3x3 = (defaultValue = 0): Matrix3 => {\n return [\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const m4x4 = (defaultValue = 0): Matrix4 => {\n return [\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const mNxM = (N: number, M: number, defaultValue = 0): Matrix => {\n if(N <= 0 || M <= 0){\n throw new Error('M and N must be positive numbers.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return [\n [1, 0],\n [0, 1],\n ];\n};\n\nexport const identity3 = (): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\nexport const identity4 = (): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Identity Matrix (I).\n * M x I = I x M = M for any matrix M.\n * Identity Matrix is a special case of scale matrix.\n */\nexport const identityN = (N: number): Matrix => {\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n if(N === 0) return [];\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mDeepCopy(m2) as Matrix2;\n};\n\nexport const m3DeepCopy = (m3: Matrix3): Matrix3 => {\n return mDeepCopy(m3) as Matrix3;\n};\n\n// -------------- APPEND / PREPEND ROW OR COLUMN ---------------\n\nexport const mAppendCol = (m: Matrix, col: Vector): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n const copy = mDeepCopy(m);\n copy.push(row);\n return copy;\n};\n\nexport const m2AppendRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.push(row);\n return copy;\n};\n\nexport const m3AppendRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.push(row);\n return copy;\n};\n\nexport const mPrependRow = (m: Matrix, row: Vector) : Matrix => {\n const copy = mDeepCopy(m);\n copy.unshift(row);\n return copy;\n};\n\nexport const m2PrependRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.unshift(row);\n return copy;\n};\n\nexport const m3PrependRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.unshift(row);\n return copy;\n};\n\n// ------------ DELETE ROW OR COLUMN ----------------------------\n\nexport const mDelLastRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.pop();\n return copy;\n};\n\nexport const mDelFirstRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.shift();\n return copy;\n};\n\nexport const mDelLastColumn = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const size = m[0].length;\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n\n const matrix: Matrix = [];\n for(let i=0; i {\n\n if(matrix.length < 0) return [];\n\n if(matrix[0].length !== vector.length){\n throw new Error('The number of columns in the matrix must be equal to the length of the vector.');\n }\n\n const res: Vector = [];\n\n for(let i=0; i {\n if(matrix1.length !== matrix2.length) return false;\n\n for(let i=0; i returns matrix N (m-1 x m-1)\n * The matrix must be square.\n */\nconst mMinorHelper = (m: Matrix, row: number, col: number) => {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // prepare the matrix without provided row and column\n const matrix = mMinorHelper(m, row, col);\n\n // calculate the matrix determinant\n return mDeterminant(matrix);\n};\n\n/**\n * Calculate determinant for NxN matrix.\n * Matrix should be square.\n */\nexport const mDeterminant = (matrix: Matrix): number => {\n const size = matrix.length;\n if(size === 0) return 1;\n\n if(size !== matrix[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return matrix[0][0];\n if(size === 2) return m2Determinant(matrix as Matrix2);\n\n let d = 0;\n\n for(let i=0; i {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return m2[0][0] * m2[1][1] - m2[1][0] * m2[0][1];\n};\n\n/**\n * Calculate determinant for 3x3 matrix.\n * Matrix should be square.\n */\nexport const m3Determinant = (m3: Matrix3): number => {\n if(m3.length !== m3[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return mDeterminant(m3);\n};\n\n// ------------------ INVERSE -----------------------\n\nexport const m2Adjugate = (m2: Matrix2): Matrix2|null => {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return [\n [m2[1][1], -m2[0][1]],\n [-m2[1][0], m2[0][0]],\n ];\n};\n\nexport const m3Adjugate = (m3: Matrix3) : Matrix3|null => {\n return mAdjugate(m3) as (Matrix3|null);\n};\n\n/**\n * Adjugate is a transpose of a cofactor matrix\n */\nexport const mAdjugate = (m: Matrix): Matrix|null => {\n\n const size = m.length;\n if(size <= 0) return null;\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return m;\n\n if(size === 2) return m2Adjugate(m as Matrix2);\n\n // build a cofactor matrix ----------------\n const cofactors: Matrix = [];\n\n for(let i=0; i {\n if(m.length > 0 && m.length !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = mDeterminant(m);\n return d === 0;\n};\n\n/**\n * Square matrix A (nxn) is invertible is there is another square matrix B (nxn) so AxB = BxA = I\n * For A (2x2) matrix, the inverse is:\n * (1 / (determinant(A))) * adj(A)\n */\nexport const m2Inverse = (m2: Matrix2, decimalPlaces = Infinity): (Matrix2 | null) => {\n if(m2.length > 0 && m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = m2Determinant(m2);\n if(d === 0) return null;\n\n const adj = m2Adjugate(m2);\n if(adj === null) return null;\n\n return m2DivideScalar(adj, d, decimalPlaces);\n};\n\nexport const m3Inverse = (m3: Matrix3, decimalPlaces = Infinity): (Matrix3 | null) => {\n return mInverse(m3, decimalPlaces) as (Matrix3|null);\n};\n\nexport const mInverse = (m: Matrix, decimalPlaces = Infinity): (Matrix | null) => {\n const size = m.length;\n\n if(size > 0 && size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // find a determinant ----------------------\n const d = mDeterminant(m);\n\n // find an Adjugate - a transpose of a cofactor matrix\n const adj = mAdjugate(m);\n if(adj === null) return null;\n\n return mDivideScalar(adj, d, decimalPlaces);\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector2, Vector3, Vector4 } from '../../types';\nimport { v2Normalize, v3MulScalar, v3Normalize } from './vector';\nimport { mMulVector, mMul } from './matrix';\nimport { setDecimalPlaces } from '../format';\n\n/*\nAny 2D affine transformation can be decomposed\ninto a rotation, followed by a scaling, followed by a\nshearing, and followed by a translation.\n---------------------------------------------------------\nAffine matrix = translation x shearing x scaling x rotation\n */\n\n// ----------------- CSS -------------------------------------\n\n/**\n * Matrix 2D in non-homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2ToCSS = (m: Matrix2) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, 0, 0)`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2hToCSS = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, ${ tx }, ${ ty })`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m2hToCSS3d = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix3d(${ a }, ${ b }, 0, 0, ${ c }, ${ d }, 0, 0, 0, 0, 1, 0, ${ tx }, ${ ty }, 0, 1)`;\n};\n\n/**\n * Matrix 3D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m3hToCSS3d = (m: Matrix4) : string => {\n\n return `matrix3d(\n ${ m[0][0] }, ${ m[0][1] }, ${ m[0][2] }, ${ m[0][3] },\n ${ m[1][0] }, ${ m[1][1] }, ${ m[1][2] }, ${ m[1][3] },\n ${ m[2][0] }, ${ m[2][1] }, ${ m[2][2] }, ${ m[2][3] },\n ${ m[3][0] }, ${ m[3][1] }, ${ m[3][2] }, ${ m[3][3] }\n )`;\n};\n\n// ---------------- TRANSLATION MATRICES ----------------------\n\nexport const m2Translation = (position: Vector2, decimalPlaces = Infinity): Matrix2 => {\n\n return [\n [1, 0],\n [0, 1],\n [setDecimalPlaces(position[0], decimalPlaces), setDecimalPlaces(position[1], decimalPlaces)],\n ];\n};\n\nexport const m3Translation = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n [\n setDecimalPlaces(position[0], decimalPlaces),\n setDecimalPlaces(position[1], decimalPlaces),\n setDecimalPlaces(position[2], decimalPlaces)\n ],\n ];\n};\n\n/**\n * 2D Translation matrix in homogeneous coordinates.\n */\nexport const m2TranslationH = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1],\n ];\n};\n\n/**\n * 3D Translation matrix in homogeneous coordinates.\n */\nexport const m3TranslationH = (position: Vector4, decimalPlaces = Infinity): Matrix4 => {\n\n return [\n [1, 0, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, 0, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1, setDecimalPlaces(position[2], decimalPlaces)],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- ROTATION MATRICES -------------------------\n\n/**\n * Rotation of an angle about the origin.\n */\nexport const m2Rotation = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix2 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin],\n [sin, cos],\n ] :\n [\n [cos, sin],\n [-sin, cos],\n ];\n};\n\n/**\n * Rotation of an angle about the origin in homogeneous coordinates (clockwise).\n */\nexport const m2RotationH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ]:\n [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation of an angle \"angleRad\" around the given point (transformOrigin) in homogeneous coordinates (clockwise).\n * result_vector = TranslationMatrix(x, y) * RotationMatrix() * TranslationMatrix(-x, -y) * position_vector\n */\nexport const m2RotationAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const rotation = m2RotationH(angleRad, isClockwise, decimalPlaces);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, rotation);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2RotateAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n position: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2RotationAroundPointH(angleRad, transformOrigin, isClockwise, decimalPlaces);\n return mMulVector(mat3h, position) as Vector3;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2Rotate = (angleRad: number, vector: Vector2, isClockwise = true, decimalPlaces = Infinity): Vector2 => {\n const unitVector = v2Normalize(vector);\n return mMulVector(m2Rotation(angleRad, isClockwise, decimalPlaces), unitVector) as Vector2;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2RotateH = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m2RotationH(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the X axis (clockwise).\n */\nexport const m3RotationX = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0],\n [0, cos, -sin],\n [0, sin, cos],\n ] :\n [\n [1, 0, 0],\n [0, cos, sin],\n [0, -sin, cos],\n ];\n};\n\n/**\n * Rotation around the X axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationXH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0, 0],\n [0, cos, -sin, 0],\n [0, sin, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [1, 0, 0, 0],\n [0, cos, sin, 0],\n [0, -sin, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateX = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationX(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Y axis (clockwise).\n */\nexport const m3RotationY = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin],\n [0, 1, 0],\n [-sin, 0, cos],\n ] :\n [\n [cos, 0, -sin],\n [0, 1, 0],\n [sin, 0, cos],\n ];\n};\n\n/**\n * Rotation around the Y axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationYH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin, 0],\n [0, 1, 0, 0],\n [-sin, 0, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [cos, 0, -sin, 0],\n [0, 1, 0, 0],\n [sin, 0, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateY = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationY(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Z axis (clockwise).\n */\nexport const m3RotationZ = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ] : [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation around the Z axis (clockwise)- in homogeneous coordinates\n */\nexport const m3RotationZH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0, 0],\n [sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ] : [\n [cos, sin, 0, 0],\n [-sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateZ = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationZ(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n// ---------------- SCALE MATRICES -------------\n\n/**\n * Get matrix for arbitrary scaling pivot point.\n * result_vector = TranslationMatrix(x, y) * ScaleMatrix() * TranslationMatrix(-x, -y) * scale_vector\n */\nexport const m2ScaleAtPointHMatrix = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const scale = m2ScaleH(scaleVector);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, scale);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2ScaleAtPointH = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n point: Vector3,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2ScaleAtPointHMatrix(scaleVector, transformOrigin, decimalPlaces);\n return mMulVector(mat3h, point) as Vector3;\n};\n\nexport const m2Scale = (scaleVector: Vector2): Matrix2 => {\n return [\n [scaleVector[0], 0],\n [0, scaleVector[1]],\n ];\n};\n\nexport const v2Scale = (scaleVector: Vector2, vector: Vector2): Vector2 => {\n return mMulVector(m2Scale(scaleVector), vector) as Vector2;\n};\n\n/**\n * homogeneous coordinates\n */\nexport const m2ScaleH = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, 1],\n ];\n};\n\nexport const m3Scale = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, scaleVector[2]],\n ];\n};\n\nexport const m3ScaleH = (scaleVector: Vector4): Matrix4 => {\n return [\n [scaleVector[0], 0, 0, 0],\n [0, scaleVector[1], 0, 0],\n [0, 0, scaleVector[2], 0],\n [0, 0, 0, 1]\n ];\n};\n\nexport const v3Scale = (scaleVector: Vector3, vector: Vector3): Vector3 => {\n return mMulVector(m3Scale(scaleVector), vector) as Vector3;\n};\n\n/**\n * Stretch, parallel to the x-axis.\n */\nexport const m2ScaleX = (scale: number): Matrix2 => {\n return [\n [scale, 0],\n [0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the x-axis - homogeneous coordinates\n */\nexport const m2ScaleXH = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleX = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleXH = (scale: number): Matrix4 => {\n return [\n [scale, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleY = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleYH = (scale: number): Matrix => {\n return [\n [1, 0, 0, 0],\n [0, scale, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZ = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, scale],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZH = (scale: number): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, scale, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis.\n */\nexport const m2ScaleY = (scale: number): Matrix2 => {\n return [\n [1, 0],\n [0, scale],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis - homogeneous coordinates\n */\nexport const m2ScaleYH = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n// ---------------- REFLECTION MATRICES -------------------------\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOrigin = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOriginH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection about the origin in non-homogeneous coordinates\n */\nexport const m3ReflectionOrigin = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection about the origin in homogeneous coordinates\n */\nexport const m3ReflectionOriginH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection about y=-x\n */\nexport const m2ReflectionYmX = (): Matrix2 => {\n\n return [\n [0, -1],\n [-1, 0],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionX = (): Matrix2 => {\n\n return [\n [1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionXH = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection in the y-axis.\n */\nexport const m2ReflectionY = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, 1],\n ];\n};\n\nexport const m2ReflectionYH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionYZ = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in homogeneous coordinates\n */\nexport const m3ReflectionYZH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXZ = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in homogeneous coordinates\n */\nexport const m3ReflectionXZH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXY = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in homogeneous coordinates\n */\nexport const m3ReflectionXYH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- SHEARING MATRICES -------------------------\n\n\n/**\n * Shearing in y-axis, with x-axis fixed with (0,1) moving to (factor, 1)\n */\nexport const m2ShearingY = (factor: number): Matrix2 => {\n\n return [\n [1, factor],\n [0, 1],\n ];\n};\n\n/**\n * Shearing in x-axis, with y-axis fixed with (1,0) moving to (1, factor)\n */\nexport const m2ShearingX = (factor: number): Matrix2 => {\n\n return [\n [1, 0],\n [factor, 1],\n ];\n};", "import { setDecimalPlaces } from './format';\n\n/**\n * Returns a random number in the [min,max] range.\n */\nexport const getRandom = (min: number, max: number, decimalPlaces = Infinity): number => {\n return setDecimalPlaces(Math.random() * (max - min) + min, decimalPlaces);\n};\n\n/**\n * Returns a random integer number in the [min,max] range.\n */\nexport const getRandomInt = (min: number, max: number): number => {\n return Math.floor(Math.random() * (max - min + 1) + min);\n};\n\nexport const getRandomBoolean = () => Math.random() < 0.5;\n\n/* eslint-disable @typescript-eslint/no-explicit-any */\nexport const getRandomItemFromArray = (array: any[]) => {\n const randomIndex = getRandomInt(0, array.length - 1);\n return array[randomIndex];\n};", "export const stringToNumber = (value: string|undefined|null|number, defaultNumber: number) => {\n if(value === undefined || value === null) return defaultNumber;\n const res = Number(value) ?? defaultNumber;\n return isNaN(res) ? defaultNumber : res;\n};", "import { setDecimalPlaces } from './format';\nimport { Vector2, Vector3 } from '../types';\n\n/**\n * u(x) and v(x) are functions ---------->\n *\n * dx(u + v) = dx(u) + dx(v)\n * dx(u - v) = dx(u) - dx(v)\n * dx(u * v) = dx(u) * v + u * dx(v)\n * dx(u / v) = (dx(u) * v - u * dx(v)) / (v ^ 2), when v(x) != 0\n */\n\n// ------------------ Derivatives of Polynomial ---------------------------\n\n/**\n * y = 3x+2\n * dxPolynomial(10, [[3, 1], [2, 0]])\n */\nexport const dxPolynomial = (x: number, polynomial: number[][], decimalPlaces = Infinity) => {\n let res = 0;\n\n for(const part of polynomial){\n if(part.length !== 2) return NaN;\n\n const coeff = part[0];\n const power = part[1];\n res += coeff * power * Math.pow(x, power - 1);\n }\n\n return setDecimalPlaces(res, decimalPlaces);\n}\n\n// ---------------------- Bezier Curves ---------------------------\n\n/**\n * Derivative of Bezier Curve is another Bezier Curve.\n * t must min in range [0, 1]\n */\nexport const dxV2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n // The derivative: P1 * (2t-2) + (2*P3-4*P2) * t + 2 * P2\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\nexport const dxV2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n\n// ----------------- Derivatives of trigonometry functions ---------------------------\n\nexport const dxSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(Math.cos(x), decimalPlaces);\n};\n\nexport const dxCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-Math.sin(x), decimalPlaces);\n};\n\nexport const dxTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.cos(x) ** 2), decimalPlaces);\n};\n\n/**\n * x != Math.PI * n, where n is an integer\n */\nexport const dxCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sin(x) ** 2), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\nexport const dxArcTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (1 + x ** 2), decimalPlaces);\n};\n\nexport const dxArcCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (1 + x ** 2), decimalPlaces);\n};\n", "import { Matrix, Matrix2, Matrix3, Vector, Vector2, Vector3 } from '../../types';\nimport { m2Inverse, m3Inverse, mInverse, mMulVector, mDelLastColumn, mGetLastColumn } from '../linear-algebra/matrix';\nimport { setDecimalPlaces } from '../format';\nimport { v2Sub } from '../linear-algebra/vector';\n\n/**\n * Linear equation\n * ax + b = c\n * x = (c - b) / a; a != 0\n */\nexport const linearEquation = (equation: Vector3, decimalPlaces = Infinity) : number => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n\n const diff = c - b;\n\n if(a === 0 && diff === 0) return Infinity; // any number is a solution\n if(a === 0) return NaN; // no solution\n\n return setDecimalPlaces(diff / a, decimalPlaces);\n};\n\n/**\n * System of 2 linear equations.\n * [x, y] = inverse(Matrix of equation parameters) x (vector of equation results)\n * ---------------\n * 3x + 2y = 7\n * -6x + 6y = 6\n */\nexport const linearEquationSystem2 = (equation1: Vector3, equation2: Vector3, decimalPlaces = Infinity) : Vector2 | null => {\n const equationParams: Matrix2 = [\n [equation1[0], equation1[1]],\n [equation2[0], equation2[1]],\n ];\n\n const inversed = m2Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector2 = [\n equation1[2],\n equation2[2]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector2;\n};\n\n/**\n * System of 3 linear equations.\n * ---------------------------------------\n * 3x + 2y + 5z = 7\n * -6x + 6y + 6z = 6\n * 2x + 7y - z = 4\n */\nexport const linearEquationSystem3 = (\n equation1: Vector,\n equation2: Vector,\n equation3: Vector,\n decimalPlaces = Infinity) : Vector3 | null => {\n const equationParams: Matrix3 = [\n [equation1[0], equation1[1], equation1[2]],\n [equation2[0], equation2[1], equation2[2]],\n [equation3[0], equation3[1], equation3[2]],\n ];\n\n const inversed = m3Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector3 = [\n equation1[3],\n equation2[3],\n equation3[3]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector3;\n};\n\n/**\n * System of N linear equations.\n */\nexport const linearEquationSystemN = (equations: Matrix, decimalPlaces = Infinity) : Vector | null => {\n if(equations.length <= 0) return null;\n\n const equationParams = mDelLastColumn(equations);\n\n const inversed = mInverse(equationParams);\n if(inversed === null) return null; // no results\n\n // the last column of the equations matrix\n const equationResults = mGetLastColumn(equations);\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector;\n};\n\n/**\n * Calculate the equation of a line given two points in a 2D space.\n * y = ax + b\n * y - y1 = m(x - x1)\n * m = (y2 - y1) / (x2 - x1)\n */\nexport const getLinearEquationBy2Points = (point1: Vector2, point2: Vector2) : {\n slope: number|undefined,\n yIntercept: number|undefined,\n xIntercept: number|undefined,\n formula: string,\n} => {\n const [deltaX, deltaY] = v2Sub(point2, point1);\n const [x, y] = point1;\n\n if(deltaX === 0) {\n return {\n slope: undefined,\n xIntercept: x,\n yIntercept: undefined,\n formula: `x = ${ x }`,\n };\n }\n\n const m = deltaY / deltaX;\n const b = y - m * x;\n let formula = '';\n\n if(m === 0) {\n formula = `y = ${ b }`;\n }\n else{\n formula = `y = ${ m === 1 ? '' : m }x`;\n\n if(b !== 0) {\n formula += ` ${ b < 0 ? '-' : '+' } ${ Math.abs(b) }`;\n }\n }\n\n return {\n slope: m,\n xIntercept: undefined,\n yIntercept: b,\n formula,\n };\n};", "import { Vector } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { linearEquation } from './linear-equations';\nimport { isNumber } from '../other';\n\n/**\n * Quadratic Equation.\n * ax^2 + bx + c = d\n */\nexport const quadraticEquation = (equation: Vector, decimalPlaces = Infinity) : Vector => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n const d = equation[3];\n\n if(a === 0){\n // it's a linear equation -------------------------------------------\n const res = linearEquation([b, c, d], decimalPlaces);\n if(isNumber(res)) return [res];\n return [];\n }\n\n const diff = c - d;\n\n const discriminant = b * b - (4 * a * diff);\n\n if(discriminant < 0){\n return []; // no results\n }\n\n if(discriminant === 0){\n return [ setDecimalPlaces(-b / (2 * a), decimalPlaces) ]; // 1 result\n }\n\n // if(determinant > 0) ---> 2 results\n const t1 = 2 * a;\n const t2 = Math.sqrt(discriminant);\n\n return [\n setDecimalPlaces((-b + t2) / t1, decimalPlaces),\n setDecimalPlaces((-b - t2) / t1, decimalPlaces),\n ];\n};", "import { IBBox, Vector, Vector2, Vector3 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport {\n dxV2CubicBezierCurve,\n dxV2QuadraticBezierCurve,\n dxV3CubicBezierCurve,\n dxV3QuadraticBezierCurve\n} from '../derivative';\nimport { v2Normalize, v3Normalize } from '../linear-algebra/vector';\nimport { linearEquation } from '../equations/linear-equations';\nimport { quadraticEquation } from '../equations/quadratic-equations';\nimport { isNumber } from '../other';\n\n/**\n * B\u00E9zier Curves\n * quadratic: y = P1 * (1-t)\u00B2 + P2 * 2 * (1-t)t + P3 * t\u00B2\n * t in range [0, 1]\n */\n\n// -------------------- GET POINT ON CURVE --------------------------\n\n/**\n * Get a point on a quadratic B\u00E9zier curve as a function of time.\n */\nexport const v2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n/**\n * Get a point on a cubic B\u00E9zier curve as a function of time.\n */\nexport const v2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n// -------------------- TANGENT --------------------------\n\n/**\n * Tangent indicates the direction of travel at specific points along the B\u00E9zier curve,\n * and is literally just the first derivative of our curve.\n */\nexport const v2QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\nexport const v2CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\n// -------------------- NORMAL --------------------------\n\n/**\n * Normal is a vector that runs at a right angle to the direction of the curve, and is typically of length 1.\n * To find it, we take the normalised tangent vector, and then rotate it by a 90 degrees.\n */\nexport const v2QuadraticBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2QuadraticBezierCurveTangent(t, startControlPoint, centerControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\nexport const v2CubicBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2CubicBezierCurveTangent(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\n// -------------------- EXTREMA --------------------------\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2QuadraticBezierCurveExtrema = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector => {\n\n /*\n (-2 * (1 - t)) * startControlPoint[0] + (2 - 4 * t) * centerControlPoint[0] + (2 * t) * endControlPoint[0]\n 2 * t * startControlPoint[0] - 4 * t * centerControlPoint[0] + 2 * t * endControlPoint[0] - 2 * startControlPoint[0] + 2 * centerControlPoint[0]\n t * (2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0]) + (- 2 * startControlPoint[0] + 2 * centerControlPoint[0])\n */\n\n const a1 = 2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0];\n const b1 = -2 * startControlPoint[0] + 2 * centerControlPoint[0];\n const equation1: Vector3 = [a1, b1, 0];\n const res1 = linearEquation(equation1, decimalPlaces);\n\n const a2 = 2 * startControlPoint[1] - 4 * centerControlPoint[1] + 2 * endControlPoint[1];\n const b2 = -2 * startControlPoint[1] + 2 * centerControlPoint[1];\n const equation2: Vector3 = [a2, b2, 0];\n const res2 = linearEquation(equation2, decimalPlaces);\n\n const res: Vector = [];\n\n if(isNumber(res1)){\n res.push(res1);\n }\n\n if(isNumber(res2)){\n res.push(res2);\n }\n\n return res;\n};\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2CubicBezierCurveExtrema = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2|null => {\n\n const a1 = -3 * startControlPoint[0] + 9 * center1ControlPoint[0] - 9 * center2ControlPoint[0] + 3 * endControlPoint[0];\n const b1 = 6 * startControlPoint[0] - 12 * center1ControlPoint[0] + 6 * center2ControlPoint[0];\n const c1 = -3 * startControlPoint[0] + 3 * center1ControlPoint[0];\n const equation1: Vector = [a1, b1, c1, 0];\n\n const a2 = -3 * startControlPoint[1] + 9 * center1ControlPoint[1] - 9 * center2ControlPoint[1] + 3 * endControlPoint[1];\n const b2 = 6 * startControlPoint[1] - 12 * center1ControlPoint[1] + 6 * center2ControlPoint[1];\n const c2 = -3 * startControlPoint[1] + 3 * center1ControlPoint[1];\n const equation2: Vector = [a2, b2, c2, 0];\n\n // Any value between 0 and 1 is a root that matters for B\u00E9zier curves, anything below or above that is irrelevant (because B\u00E9zier curves are only defined over the interval [0,1]).\n const res1 = quadraticEquation(equation1, decimalPlaces).filter(num => num >= 0 && num <= 1);\n const res2 = quadraticEquation(equation2, decimalPlaces).filter(num => num >= 0 && num <= 1);\n\n const res = [...res1, ...res2];\n if(res.length === 2){\n return [...res1, ...res2] as Vector2;\n }\n\n return null;\n};\n\n// -------------------- BOUNDING BOX --------------------------\n\nexport const v2QuadraticBezierBBox = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2QuadraticBezierCurveExtrema(startControlPoint, centerControlPoint, endControlPoint);\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2QuadraticBezierCurve(percent, startControlPoint, centerControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x);\n maxX = Math.max(maxX, x);\n\n minY = Math.min(minY, y);\n maxY = Math.max(maxY, y);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\nexport const v2CubicBezierBBox = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2CubicBezierCurveExtrema(startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint) || [];\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2CubicBezierCurve(percent, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x ?? Infinity);\n maxX = Math.max(maxX, x ?? -Infinity);\n\n minY = Math.min(minY, y ?? Infinity);\n maxY = Math.max(maxY, y ?? -Infinity);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\n\n", "import { Vector2 } from '../types';\nimport { v2Sub } from './linear-algebra/vector';\nimport { getV2Angle } from './angle';\nimport { convertRange } from './other';\n\n/**\n * Circle Equation\n * x^2 + y^2 = radius^2\n * ----------------------\n * Circle Parametric Equation\n * x(t) = radius * cos(t)\n * y(t) = radius * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const circleMovement = (center: Vector2, angle: number, radius: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius,\n center[1] + Math.sin(angle) * radius\n ];\n};\n\n/**\n * Circle Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const circleMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radius: number\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return circleMovement(center, angle, radius);\n};\n\n/**\n * Ellipse Equation\n * (x - centerX)^2 / (radius1^2) + (y - centerY)^2 / (radius2^2) = 1\n * -----------------------------------------------------------------\n * Ellipse Parametric Equation\n * x(t) = radius1 * cos(t)\n * y(t) = radius2 * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const ellipseMovement = (center: Vector2, angle: number, radius1: number, radius2: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius1,\n center[1] + Math.sin(angle) * radius2\n ];\n};\n\n/**\n * Ellipse Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const ellipseMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radii: Vector2\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return ellipseMovement(center, angle, radii[0], radii[1]);\n};\n\n/**\n * Sine Wave Equation (Sinusoid)\n * -----------------------------\n * const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n * amplitude = the peak deviation of the function from zero\n * frequency = number of cycles\n * phase = specifies (in radians) where in its cycle the oscillation is at t = 0.\n * think of it as \"shifting\" the starting point of the function to the right (positive p) or left (negative)\n */\nexport const sineWaveMovement = (x: number, amplitude: number, frequency: number, phase: number) : Vector2 => {\n /*\n example values:\n const amplitude = 50;\n const frequency = 0.005;\n const phase = 0;\n x: [0, 1000]\n */\n const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n\n return [x, y];\n};\n\n/**\n * Lissajous curve (Lissajous figure or Bowditch curve)\n * Parametric equation #1\n * f(t) = A * sin(k * t + m)\n * f(t) = B * sin(n * t)\n * 0 <= m <= PI/2\n * k, n >= 1\n * -----------------------\n * Parametric equation #2\n * f(t) = A * cos(k * t - m)\n * f(t) = B * cos(n * t - p)\n * -----------------------------\n * Shapes:\n * k = 1, n = 1, m = 0, p = 0 ---> line\n * A = B, k = 1, n = 1, m = PI/2, p = PI/2 ----> circle\n * A != B, k = 1, n = 1, m = PI/2, p = PI/2 ----> ellipse\n * k = 2, n = 2, m = PI/2, p = PI/2 ----> section of a parabola\n */\nexport const lissajousCurve = (\n width: number,\n height: number,\n t: number,\n k: number,\n n: number,\n m: number,\n p: number\n) :Vector2 => {\n return [\n width * Math.cos(k * t - m),\n height * Math.cos(n * t - p),\n ];\n};\n", "import { getRandom } from './random';\nimport { HSLColor, LABColor, RGBColor } from '../types';\nimport { mod } from './other';\nimport { setDecimalPlaces } from './format';\n\n// ------------------------ RANDOM COLOR -------------------------------------\n\nexport const getRandomRGBColor = () : RGBColor => {\n const hslColor = getRandomHSLColor();\n return hslToRgb(hslColor);\n};\n\nexport const getRandomHexColor = () : string => {\n const hslColor = getRandomHSLColor();\n return hslToHex(hslColor);\n};\n\nexport const getRandomHSLColor = () : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given hue\n */\nexport const getRandomHSLColorWithHue = (h: number) : HSLColor => {\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given saturation\n */\nexport const getRandomHSLColorWithSaturation = (s: number) : HSLColor => {\n const h = getRandom(1, 360);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given lightness\n */\nexport const getRandomHSLColorWithLightness = (l: number) : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n return [h, s, l];\n};\n\nexport const getRandomGrayscaleHSLColor = () : HSLColor => {\n const l = getRandom(0, 100);\n return [0, 0, l];\n};\n\nexport const getRandomHSLColorWithinRanges = (\n hueStart = 1, hueEnd = 360,\n saturationStart = 0, saturationEnd = 100,\n lightStart = 0, lightEnd = 100\n) : HSLColor => {\n const h = getRandom(hueStart, hueEnd);\n const s = getRandom(saturationStart, saturationEnd);\n const l = getRandom(lightStart, lightEnd);\n return [h, s, l];\n};\n\n// ----------------------- CONVERT COLORS --------------------------------------\n\n/**\n * helper: convert hue value to degrees.\n * @param {number} h\n * @return {number} [0, 360] degrees\n */\nconst convertHueToDegrees = (h : number) : number => {\n\n // the hue value needs to be multiplied by 60 to convert it to degrees\n h *= 60;\n\n // if hue becomes negative, you need to add 360 to, because a circle has 360 degrees\n if(h < 0){\n h += 360;\n }\n\n return h;\n // convert huw to %\n // return h * 100 / 360;\n};\n\n/**\n * get hue from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] % - we use here % instead of [0, 359] degrees\n */\nconst getHue = (r : number, g : number, b : number, min : number | undefined = undefined, max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (max === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no hue, as it's gray\n if(min === max) return 0;\n\n const diff = max - min;\n\n let h = 0;\n\n // if red is max\n if(max === r){\n h = (g - b) / diff + (g < b ? 6 : 0);\n }\n\n // if green is max\n if(max === g){\n h = 2 + (b - r) / diff;\n }\n\n // if blue is max\n if(max === b){\n h = 4 + (r - g) / diff;\n }\n\n return convertHueToDegrees(h);\n};\n\n/**\n * get luminance from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] %\n */\nconst getLuminance = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // calculate the luminance value\n // @ts-ignore\n const l = (min + max) / 2; // [0, 1]\n\n // return l value in %\n return l * 100;\n};\n\n/**\n * get saturation from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @param {number|undefined=} l - luminance in [0, 100] %\n * @return {number} [0, 100] %\n */\nconst getSaturation = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined,\n l : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no saturation, as it's gray\n if(min === max) return 0;\n\n // calculate luminance if it's not provided\n l = (l === undefined) ? getLuminance(r, g, b) : l;\n\n // check the level of luminance\n const s = (l <= 50) ?\n // @ts-ignore\n ((max - min) / (max + min)) : // this formula is used when luminance <= 50%\n // @ts-ignore\n (max - min) / (2.0 - max - min); // this formula is used when luminance > 50%\n\n // return saturation in %\n return s * 100;\n};\n\nexport const rgbToHsl = (rgb: RGBColor, decimalPlaces = Infinity): HSLColor => {\n\n // convert rgb values to the range [0, 1]\n const r = rgb[0] / 255;\n const g = rgb[1] / 255;\n const b = rgb[2] / 255;\n\n // find the minimum and maximum values of r, g, and b\n const min = Math.min(r, g, b);\n const max = Math.max(r, g, b);\n\n // calculate the luminance value in %\n const l = getLuminance(r, g, b, min, max);\n\n // calculate the saturation in %\n const s = getSaturation(r, g, b, min, max, l);\n\n // calculate the hue in % (not in degrees!)\n const h = getHue(r, g, b, min, max);\n\n if(h > 360 || s > 100 || l > 100){\n return [0, 0, 100];\n }\n\n if(h < 0 || s < 0 || l < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(h, decimalPlaces),\n setDecimalPlaces(s, decimalPlaces),\n setDecimalPlaces(l, decimalPlaces),\n ];\n};\n\n/**\n * helper: HSL to RGB\n */\nconst hslToRgbHelper = (helper1 : number, helper2 : number, colorHelper : number) : number => {\n\n // all values need to be between 0 and 1\n // if you get a negative value you need to add 1 to it\n if(colorHelper < 0) colorHelper += 1;\n\n // if you get a value above 1 you need to subtract 1 from it.\n if(colorHelper > 1) colorHelper -= 1;\n\n if(colorHelper * 6 < 1) return helper2 + (helper1 - helper2) * 6 * colorHelper;\n\n if(colorHelper * 2 < 1) return helper1;\n\n if(colorHelper * 3 < 2){\n return helper2 + (helper1 - helper2) * (0.666 - colorHelper) * 6;\n }\n else{\n return helper2;\n }\n};\n\nexport const hslToRgb = (hsl: HSLColor, decimalPlaces = Infinity): RGBColor => {\n\n // convert all values to [0, 1] from %\n const h = hsl[0] / 100;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n // if there is no saturation -> it\u2019s grey\n if(s === 0){\n // convert the luminance from [0, 1] to [0, 255]\n const gray = l * 255;\n return [gray, gray, gray];\n }\n\n // check the level of luminance\n const helper1 = (l < 0.5) ?\n (l * (1.0 + s)) :\n (l + s - l * s);\n\n const helper2 = 2 * l - helper1;\n\n const rHelper = h + 0.333;\n const gHelper = h;\n const bHelper = h - 0.333;\n\n let r = hslToRgbHelper(helper1, helper2, rHelper);\n let g = hslToRgbHelper(helper1, helper2, gHelper);\n let b = hslToRgbHelper(helper1, helper2, bHelper);\n\n // convert rgb to [0, 255]\n r *= 255;\n g *= 255;\n b *= 255;\n\n if(r > 255 || g > 255 || b > 255){\n return [255, 255, 255];\n }\n\n if(r < 0 || g < 0 || b < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(r, decimalPlaces),\n setDecimalPlaces(g, decimalPlaces),\n setDecimalPlaces(b, decimalPlaces),\n ];\n};\n\n/**\n * HSL to hex\n * hslToHex(360, 100, 50) // [360, 100, 5] ==> \"#ff0000\" (red)\n */\nexport const hslToHex = (hsl: HSLColor) => {\n\n if(hsl[0] > 360 || hsl[1] > 100 || hsl[2] > 100){\n return '#ffffff';\n }\n\n if(hsl[0] < 0 || hsl[1] < 0 || hsl[2] < 0){\n return '#000000';\n }\n\n const h = hsl[0] / 360;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n let r, g, b;\n if (s === 0) {\n r = g = b = l; // achromatic\n } else {\n const hue2rgb = (p: number, q: number, t: number) => {\n if (t < 0) t += 1;\n if (t > 1) t -= 1;\n if (t < 1 / 6) return p + (q - p) * 6 * t;\n if (t < 1 / 2) return q;\n if (t < 2 / 3) return p + (q - p) * (2 / 3 - t) * 6;\n return p;\n };\n const q = l < 0.5 ? l * (1 + s) : l + s - l * s;\n const p = 2 * l - q;\n r = hue2rgb(p, q, h + 1 / 3);\n g = hue2rgb(p, q, h);\n b = hue2rgb(p, q, h - 1 / 3);\n }\n const toHex = (x: number) => {\n const hex = Math.round(x * 255).toString(16);\n return hex.length === 1 ? '0' + hex : hex;\n };\n\n return `#${toHex(r)}${toHex(g)}${toHex(b)}`;\n};\n\n/**\n * RGB to HEX\n * rgbToHex([235, 64, 52]) // #eb4034\n */\nexport const rgbToHex = (rgb: RGBColor) => {\n const [r, g, b] = rgb;\n return '#' + (1 << 24 | r << 16 | g << 8 | b).toString(16).slice(1);\n};\n\nexport const hexToRgb = (hex: string) : RGBColor | null => {\n\n const shorthandRegex = /^#?([a-f\\d])([a-f\\d])([a-f\\d])$/i;\n const _hex = hex.replace(shorthandRegex, (_m, r, g, b) => {\n return r + r + g + g + b + b;\n });\n\n const result = /^#?([a-f\\d]{2})([a-f\\d]{2})([a-f\\d]{2})$/i.exec(_hex);\n if(!result) return null;\n\n const r = parseInt(result[1], 16);\n const g = parseInt(result[2], 16);\n const b = parseInt(result[3], 16);\n\n return [r, g, b];\n};\n\nexport const rgbToLab = (rgb: RGBColor, decimalPlaces = Infinity) : LABColor => {\n\n let r = rgb[0] / 255;\n let g = rgb[1] / 255;\n let b = rgb[2] / 255;\n\n r = (r > 0.04045) ? Math.pow((r + 0.055) / 1.055, 2.4) : r / 12.92;\n g = (g > 0.04045) ? Math.pow((g + 0.055) / 1.055, 2.4) : g / 12.92;\n b = (b > 0.04045) ? Math.pow((b + 0.055) / 1.055, 2.4) : b / 12.92;\n\n let x = (r * 0.4124 + g * 0.3576 + b * 0.1805) / 0.95047;\n let y = (r * 0.2126 + g * 0.7152 + b * 0.0722) / 1.00000;\n let z = (r * 0.0193 + g * 0.1192 + b * 0.9505) / 1.08883;\n\n x = (x > 0.008856) ? Math.pow(x, 1/3) : (7.787 * x) + 16/116;\n y = (y > 0.008856) ? Math.pow(y, 1/3) : (7.787 * y) + 16/116;\n z = (z > 0.008856) ? Math.pow(z, 1/3) : (7.787 * z) + 16/116;\n\n return [\n setDecimalPlaces((116 * y) - 16, decimalPlaces),\n setDecimalPlaces(500 * (x - y), decimalPlaces),\n setDecimalPlaces(200 * (y - z), decimalPlaces),\n ];\n};\n\nexport const labToRgb = (lab: LABColor, decimalPlaces = Infinity) : RGBColor => {\n let y = (lab[0] + 16) / 116;\n let x = lab[1] / 500 + y;\n let z = y - lab[2] / 200;\n\n x = 0.95047 * ((x * x * x > 0.008856) ? x * x * x : (x - 16/116) / 7.787);\n y = 1.00000 * ((y * y * y > 0.008856) ? y * y * y : (y - 16/116) / 7.787);\n z = 1.08883 * ((z * z * z > 0.008856) ? z * z * z : (z - 16/116) / 7.787);\n\n let r = x * 3.2406 + y * -1.5372 + z * -0.4986;\n let g = x * -0.9689 + y * 1.8758 + z * 0.0415;\n let b = x * 0.0557 + y * -0.2040 + z * 1.0570;\n\n r = (r > 0.0031308) ? (1.055 * Math.pow(r, 1/2.4) - 0.055) : 12.92 * r;\n g = (g > 0.0031308) ? (1.055 * Math.pow(g, 1/2.4) - 0.055) : 12.92 * g;\n b = (b > 0.0031308) ? (1.055 * Math.pow(b, 1/2.4) - 0.055) : 12.92 * b;\n\n return [\n setDecimalPlaces(Math.max(0, Math.min(1, r)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, g)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, b)) * 255, decimalPlaces),\n ];\n};\n\n// ----------------------- GET SHIFTED COLORS --------------------------------------\n\nexport const getShiftedHue = (color: HSLColor, shift = 180) : HSLColor => {\n let hue = color[0];\n hue += shift;\n\n if (hue > 360 || hue < 0) {\n hue = mod(hue, 360);\n }\n\n return [hue, color[1], color[2]];\n};\n\nexport const getShiftedLightness = (color: HSLColor, shift = 10) : HSLColor => {\n let lightness = color[2];\n lightness += shift;\n\n if (lightness > 100 || lightness < 0) {\n lightness = mod(lightness, 100);\n }\n\n return [color[0], color[1], lightness];\n};\n\nexport const getShiftedSaturation = (color: HSLColor, shift = 10) : HSLColor => {\n let saturation = color[1];\n saturation += shift;\n\n if (saturation > 100) {\n saturation -= 100;\n }\n\n if(saturation < 0){\n saturation += 100;\n }\n\n return [color[0], saturation, color[2]];\n};\n\n// ----------------------- SIMILAR COLORS --------------------------------------\n\n/**\n * Measure the perceptual difference between two RGB colors using the CIE76 color difference formula:\n * delta = Math.sqrt((L2 - L1)^2 + (a2 - a1)^2 + (b2 - b1)^2)\n * https://en.wikipedia.org/wiki/Color_difference\n * https://stackoverflow.com/questions/13586999/color-difference-similarity-between-two-values-with-js\n * <= 1.0 Not perceptible by human eyes.\n * 1 - 2 Perceptible through close observation.\n * 2 - 10 Perceptible at a glance.\n * 11 - 49 Colors are more similar than opposite\n * 100 Colors are exact opposite\n */\nexport const getColorsDelta = (rgbA: RGBColor, rgbB: RGBColor, decimalPlaces = Infinity) => {\n const labA = rgbToLab(rgbA, decimalPlaces);\n const labB = rgbToLab(rgbB, decimalPlaces);\n\n // differences between the LAB components of the two colors\n const deltaL = labA[0] - labB[0];\n const deltaA = labA[1] - labB[1];\n const deltaB = labA[2] - labB[2];\n\n // chroma components\n const c1 = Math.sqrt(labA[1] * labA[1] + labA[2] * labA[2]);\n const c2 = Math.sqrt(labB[1] * labB[1] + labB[2] * labB[2]);\n const deltaC = c1 - c2;\n\n // difference in hue, deltaH, which takes into account both the differences\n // in the a* and b* components of LAB and the differences in chroma.\n let deltaH = deltaA * deltaA + deltaB * deltaB - deltaC * deltaC;\n deltaH = deltaH < 0 ? 0 : Math.sqrt(deltaH);\n\n const sc = 1.0 + 0.045 * c1;\n const sh = 1.0 + 0.015 * c1;\n\n // It applies weighting factors to the differences in lightness (deltaL),\n // chroma (deltaC), and hue (deltaH).\n const deltaLKlsl = deltaL / (1.0);\n const deltaCkcsc = deltaC / (sc);\n const deltaHkhsh = deltaH / (sh);\n\n // It computes the final color difference using the CIE76 formula:\n // deltaE = sqrt(deltaLKlsl^2 + deltaCkcsc^2 + deltaHkhsh^2),\n // where deltaLKlsl is the weighted lightness difference,\n // deltaCkcsc is the weighted chroma difference,\n // and deltaHkhsh is the weighted hue difference.\n const i = deltaLKlsl * deltaLKlsl + deltaCkcsc * deltaCkcsc + deltaHkhsh * deltaHkhsh;\n\n // It returns the calculated color difference,\n // optionally rounded to the specified number of decimal places.\n return i < 0 ? 0 : Math.sqrt(i);\n};\n", "/**\n * guid like '932ade5e-c515-4807-ac01-73b20ab3fb66'\n */\nexport const guid = () => {\n return 'xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx'.replace(/[xy]/g, (c) => {\n const r = Math.random() * 16 | 0;\n return (c == 'x' ? r : r & 0x3 | 0x8).toString(16);\n });\n};\n\n/**\n * id like 'df4unio1opulby2uqh4'\n */\nexport const newId = () => {\n return Math.random().toString(36).substring(2) + (new Date()).getTime().toString(36);\n};\n", "import { ICircle, IPolygon, IRect, Matrix2, Vector2 } from '../types';\nimport { mod } from './other';\nimport { v2GetNormal, v2DotProduct } from './linear-algebra/vector';\n\n/**\n * Rectangles collision detection.\n * Rectangles should not be rotated.\n * The algorithm works by ensuring there is no gap between any of the 4 sides of the rectangles.\n * Any gap means a collision does not exist.\n * Returns true if collision is detected.\n */\nexport const rectCollide = (rect1: IRect, rect2: IRect) : boolean => {\n return rect1.x <= rect2.x + rect2.w &&\n rect1.x + rect1.w >= rect2.x &&\n rect1.y <= rect2.y + rect2.h &&\n rect1.h + rect1.y >= rect2.y;\n};\n\n/**\n * Circles collision detection.\n * This algorithm works by taking the center points of the two circles\n * and ensuring the distance between the center points\n * are less than the two radii added together.\n * Returns true if collision is detected.\n */\nexport const circleCollide = (circle1: ICircle, circle2: ICircle) => {\n const dx = Math.abs(circle1.cx - circle2.cx);\n const dy = Math.abs(circle1.cy - circle2.cy);\n const distance = Math.sqrt(dx * dx + dy * dy);\n return distance <= circle1.r + circle2.r;\n};\n\n//-------------------- Separating Axis Theorem (SAT) Collision detection -------------------------\n\nconst getEdges = (poly: IPolygon) : Matrix2[] => {\n const edges: Matrix2[] = [];\n\n for(let i= 0; i {\n const edges: Matrix2[] = [];\n\n // collect polygon edges, and combine then into a single array\n edges.push(...getEdges(poly1));\n edges.push(...getEdges(poly2));\n\n // for each edge, find the normal vector and project both polygons onto it\n for (const edge of edges) {\n const normal = v2GetNormal(edge[0], edge[1]);\n const p1Proj = projectPolygon(poly1, normal);\n const p2Proj = projectPolygon(poly2, normal);\n\n // Check if the projections overlap\n const isOverlap = p1Proj.max >= p2Proj.min && p2Proj.max >= p1Proj.min;\n\n // Check if the projections overlap; if not, the polygons do not collide\n if (!isOverlap) return false;\n }\n\n // If all tests pass, the polygons overlap and collide\n return true;\n};\n\n/**\n * Project every polygon point onto the normal.\n * Then find min and max.\n */\nconst projectPolygon = (polygon: IPolygon, normal: Vector2): { min: number, max: number } => {\n let min = Infinity;\n let max = -Infinity;\n\n // Project each vertex of the polygon onto the axis\n for (const vertex of polygon) {\n const projection = v2DotProduct(vertex, normal);\n min = Math.min(min, projection);\n max = Math.max(max, projection);\n }\n\n return { min, max };\n};", "export interface IAnimationProps {\n duration?: number;\n callback: (result: IAnimationResult) => void;\n restartOnResize?: boolean;\n resizeCallback?: (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => void;\n}\n\nexport interface IAnimationResult {\n start: () => void;\n stop: () => void;\n pause: () => void;\n resume: () => void;\n restart: () => void;\n isAnimating: () => boolean;\n getStartTime: () => number|undefined;\n getElapsedTime: () => number|undefined;\n getPercent: () => number|undefined;\n getResizeObserver: () => ResizeObserver|undefined;\n}\n\nexport const animate = (props: IAnimationProps) : IAnimationResult => {\n\n const _duration = props.duration !== undefined ? props.duration : Infinity;\n\n let startTime: number|undefined = undefined; // in milliseconds\n let animationId: number|undefined = undefined;\n\n // the time elapsed since the start of the animation (in milliseconds)\n let elapsed: number|undefined = undefined;\n let previousTimeStamp: number|undefined = undefined;\n\n let animating = false;\n let observer: ResizeObserver|undefined = undefined;\n\n // -------------------- COMMANDS ---------------------\n\n const stop = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = false;\n\n /*if(observer !== undefined){\n observer.disconnect();\n observer = undefined;\n }*/\n\n if(animationId === undefined) return;\n window.cancelAnimationFrame(animationId);\n };\n\n const restart = () => {\n stop();\n start();\n };\n\n const pause = () => {\n animating = false;\n };\n\n const resume = () => {\n animating = true;\n };\n\n /**\n * Animation Step.\n * @param {number} timeStamp in milliseconds\n */\n const step = (timeStamp: DOMHighResTimeStamp) => {\n\n if (startTime === undefined) {\n startTime = timeStamp;\n }\n\n // the time elapsed since the start of the animation (in milliseconds)\n elapsed = timeStamp - startTime;\n\n if (animating && previousTimeStamp !== timeStamp && typeof props.callback === 'function') {\n\n // do the rendering .............\n props.callback(getResult());\n }\n\n if(elapsed <= _duration){\n previousTimeStamp = timeStamp;\n animationId = window.requestAnimationFrame(step);\n }\n else{\n stop();\n }\n };\n\n const observerHandler = (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => {\n restart();\n\n if(typeof props.resizeCallback === 'function'){\n props.resizeCallback(_entries, _observer);\n }\n };\n\n const start = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = true;\n\n if(props.restartOnResize && window.ResizeObserver && observer === undefined){\n observer = new ResizeObserver(observerHandler);\n observer.observe(document.body, { box: 'border-box' });\n }\n else{\n animationId = window.requestAnimationFrame(step);\n }\n };\n\n // --------------- GET INFO ----------------------\n\n /**\n * the time elapsed since the start of the animation (in milliseconds)\n */\n const getElapsedTime = () : number|undefined => {\n return elapsed;\n };\n\n const isAnimating = () => {\n return animating;\n };\n\n const getStartTime = () => {\n return startTime;\n };\n\n const getPercent = () => {\n if(_duration === Infinity || elapsed === undefined) return undefined;\n return elapsed * 100 / _duration;\n };\n\n const getResizeObserver = () => {\n return observer;\n };\n\n const getResult = () : IAnimationResult => {\n return {\n\n // commands --------------\n start,\n stop,\n pause,\n resume,\n restart,\n\n // information -------\n isAnimating,\n getElapsedTime,\n getStartTime,\n getPercent,\n getResizeObserver,\n };\n };\n\n return getResult();\n};\n", "import { setDecimalPlaces } from './format';\n\nexport const getCircleCircumference = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * radius, decimalPlaces);\n};\n\nexport const getEllipseCircumference = (radius1: number, radius2: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * Math.sqrt((radius1 ** 2 + radius2 ** 2) / 2), decimalPlaces);\n};\n\nexport const isAngleInCircleArc = (startAngleDeg: number, endAngleDeg: number, currentDegrees: number) : boolean => {\n\n if(startAngleDeg > endAngleDeg) {\n endAngleDeg += 360;\n }\n\n return currentDegrees >= startAngleDeg && currentDegrees <= endAngleDeg ||\n (currentDegrees + 360) >= startAngleDeg && (currentDegrees + 360) <= endAngleDeg;\n};\n\n/**\n * get the side of a square inscribed in a circle\n */\nexport const getSquareInCircleSide = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(radius * 2 / Math.sqrt(2), decimalPlaces);\n};\n", "/**\n * 1 + 2 + ... + n = n * (n + 1) / 2\n */\nexport const naturalNumbersSequenceSum = (n: number) => {\n return n * (n + 1) / 2;\n};\n\n/**\n * n = the number of terms to be added\n * a = the first term in the sequence\n * d = the constant value between terms\n */\nexport const arithmeticSequenceSum = (n: number, a: number, d: number) => {\n return (n / 2) * (2 * a + (n - 1) * d);\n};", "import { setDecimalPlaces } from './format';\n\n// -------------------- CENTRAL TENDENCY ----------------------------\n\n/**\n * Central tendency: Calculate the Average (mean = \u03BC)\n * Sum of all numbers divided by the array length.\n */\nexport const getArithmeticMean = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const sum = data.reduce((acc, val) => acc + val, 0);\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Frequency map: number ---> it's frequency\n */\nexport const getArithmeticMeanFromFrequency = (frequencyMap: Map, decimalPlaces = Infinity) => {\n\n let mean = 0;\n\n for(const [val, frequency] of frequencyMap) {\n mean += val * frequency;\n }\n\n return setDecimalPlaces(mean, decimalPlaces);\n};\n\n/**\n * Central tendency: What is the central number in the sorted array?\n * Good for lists like [3, 3, 3, 3, 3, 3, 100] - 100 here is called \"Outlier\"\n */\nexport const getMedian = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const copy = [...data].sort((num1, num2) => num1 - num2);\n const mid = Math.floor(copy.length / 2);\n\n if(copy.length % 2 === 0) {\n return setDecimalPlaces((copy[mid] + copy[mid - 1]) / 2, decimalPlaces);\n }\n else {\n return setDecimalPlaces(copy[mid], decimalPlaces);\n }\n};\n\n/**\n * Central tendency: What number is most common in the set.\n * If all numbers have the same frequency, there is no mode.\n */\nexport const getMode = (data: number[]) : number[]|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n // Count frequency of each number in the data array.\n const frequencyMap: Map = new Map();\n for (const num of data) {\n frequencyMap.set(num, (frequencyMap.get(num) || 0) + 1);\n }\n\n let maxFrequency = 0;\n let modes: number[] = [];\n\n // Find the maximum frequency\n for (const [num, frequency] of frequencyMap) {\n if (frequency > maxFrequency) {\n maxFrequency = frequency;\n modes = [num];\n }\n else if (frequency === maxFrequency) {\n modes.push(num);\n }\n }\n\n // If all numbers have the same frequency, there is no mode\n if (modes.length === data.length) {\n return undefined;\n }\n\n // Return the mode(s)\n return modes.length === 1 ? [modes[0]] : modes;\n};\n\n/*\nTODO:\n- geometric mean\n- harmonic mean\n */\n\n// -------------------- DISPERSION ----------------------------\n\n/**\n * Dispersion: the average square distance from the mean.\n * Sum of (x - mean)^2 / N\n */\nexport const getVariance1 = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + ((val - mean) ** 2), 0);\n\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Another formula of dispersion - the average square distance from the mean.\n * (Sum of x^2) / N - (mean ^ 2)\n */\nexport const getVariance = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + (val ** 2), 0);\n\n return setDecimalPlaces((sum / data.length) - (mean ** 2), decimalPlaces);\n};\n\n/**\n * \u03C3\n */\nexport const getStandardDeviation = (data: number[], decimalPlaces = Infinity) => {\n const variance = getVariance(data) ?? 0;\n return setDecimalPlaces(Math.sqrt(variance), decimalPlaces);\n};", "import { setDecimalPlaces } from './format';\nimport { getArithmeticMean, getStandardDeviation } from './statistics';\nimport { IMlNormalizeResult, IMlStandardizeResult } from '../types';\n\n// --------------------- NORMALIZE --------------------------------\n\n/**\n * Changes value to be in the range [0, 1].\n */\nexport const mlNormalizeValue = (value: number, min: number, max: number, decimalPlaces = Infinity) : number => {\n const diff = max - min;\n if(diff === 0) return 0;\n return setDecimalPlaces((value - min) / diff, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [0, 1].\n */\nexport const mlNormalizeArray = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n const copy = [...data];\n\n for(let i=0; i {\n const min = Math.min(...data);\n const max = Math.max(...data);\n const _data = mlNormalizeArray(data, min, max, decimalPlaces);\n\n return {\n min: setDecimalPlaces(min, decimalPlaces),\n max: setDecimalPlaces(max, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlNormalizeUnseenData = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n return mlNormalizeArray(data, min, max, decimalPlaces);\n};\n\n// --------------------- STANDARDIZE --------------------------------\n\n/**\n * Changes value to be in the range [-1, 1].\n */\nexport const mlStandardizeValue = (value: number, mean: number, stdDev: number, decimalPlaces = Infinity) : number => {\n if(stdDev === 0) return 0;\n return setDecimalPlaces((value - mean) / stdDev, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [-1, 1].\n */\nexport const mlStandardizeArray = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity) : number[] => {\n return [...data].map(value => mlStandardizeValue(value, mean, stdDev, decimalPlaces));\n};\n\nexport const mlStandardizeTestData = (data: number[], decimalPlaces = Infinity): IMlStandardizeResult => {\n const mean = getArithmeticMean(data) ?? 0;\n const stdDev = getStandardDeviation(data);\n const _data = mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n\n return {\n mean: setDecimalPlaces(mean, decimalPlaces),\n stdDev: setDecimalPlaces(stdDev, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlStandardizeUnseenData = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity): number[] => {\n return mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n};"], - "mappings": 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"decimalPlaces", "setDecimalPlaces", "m3Translation", "m2TranslationH", "m3TranslationH", "m2Rotation", "angleRad", "isClockwise", "cos", "sin", "m2RotationH", "m2RotationAroundPointH", "transformOrigin", "translation", "rotation", "translationBack", "v3MulScalar", "temp1", "mMul", "m2RotateAroundPointH", "mat3h", "mMulVector", "v2Rotate", "vector", "unitVector", "v2Normalize", "v2RotateH", "v3Normalize", "m3RotationX", "m3RotationXH", "v3RotateX", "m3RotationY", "m3RotationYH", "v3RotateY", "m3RotationZ", "m3RotationZH", "v3RotateZ", "m2ScaleAtPointHMatrix", "scaleVector", "scale", "m2ScaleH", "m2ScaleAtPointH", "point", "m2Scale", "v2Scale", "m3Scale", "m3ScaleH", "v3Scale", "m2ScaleX", "m2ScaleXH", "m3ScaleX", "m3ScaleXH", "m3ScaleY", "m3ScaleYH", "m3ScaleZ", "m3ScaleZH", "m2ScaleY", "m2ScaleYH", "m2ReflectionOrigin", "m2ReflectionOriginH", "m3ReflectionOrigin", "m3ReflectionOriginH", "m2ReflectionYmX", "m2ReflectionX", "m2ReflectionXH", "m2ReflectionY", "m2ReflectionYH", "m3ReflectionYZ", "m3ReflectionYZH", "m3ReflectionXZ", "m3ReflectionXZH", "m3ReflectionXY", "m3ReflectionXYH", "m2ShearingY", "factor", "m2ShearingX", "getRandom", "min", "max", "decimalPlaces", "setDecimalPlaces", "getRandomInt", "getRandomBoolean", "getRandomItemFromArray", "array", "randomIndex", "stringToNumber", "value", "defaultNumber", "_a", "res", "dxPolynomial", "x", "polynomial", "decimalPlaces", "res", "part", "coeff", "power", "setDecimalPlaces", "dxV2QuadraticBezierCurve", "startControlPoint", "centerControlPoint", "endControlPoint", "temp1", "temp2", "temp3", "dxV3QuadraticBezierCurve", "dxV2CubicBezierCurve", "center1ControlPoint", "center2ControlPoint", "temp4", "dxV3CubicBezierCurve", "dxSin", "dxCos", "dxTan", "__pow", "dxCot", "dxArcSin", "dxArcCos", "dxArcTan", "dxArcCot", "linearEquation", "equation", "decimalPlaces", "a", "b", "diff", "setDecimalPlaces", "linearEquationSystem2", "equation1", "equation2", "equationParams", "inversed", "m2Inverse", "equationResults", "mMulVector", "linearEquationSystem3", "equation3", "m3Inverse", "linearEquationSystemN", "equations", "mDelLastColumn", "mInverse", "mGetLastColumn", "getLinearEquationBy2Points", "point1", "point2", "deltaX", "deltaY", "v2Sub", "x", "y", "m", "formula", "quadraticEquation", "equation", "decimalPlaces", "a", "b", "c", "d", "res", "linearEquation", "isNumber", "diff", "discriminant", "setDecimalPlaces", "t1", "t2", "v2QuadraticBezierCurve", "startControlPoint", "centerControlPoint", "endControlPoint", "decimalPlaces", "temp1", "temp2", "temp3", "setDecimalPlaces", "v3QuadraticBezierCurve", "v2CubicBezierCurve", "center1ControlPoint", "center2ControlPoint", "temp4", "v3CubicBezierCurve", "v2QuadraticBezierCurveTangent", "dxVector", "dxV2QuadraticBezierCurve", "v2Normalize", "v3QuadraticBezierCurveTangent", "dxV3QuadraticBezierCurve", "v3Normalize", "v2CubicBezierCurveTangent", "dxV2CubicBezierCurve", "v3CubicBezierCurveTangent", "dxV3CubicBezierCurve", "v2QuadraticBezierCurveNormal", "tangent", "v2CubicBezierCurveNormal", "v2QuadraticBezierCurveExtrema", "a1", "b1", "res1", "linearEquation", "a2", "b2", "res2", "res", "isNumber", "v2CubicBezierCurveExtrema", "c1", "equation1", "c2", "equation2", "quadraticEquation", "num", "v2QuadraticBezierBBox", "extrema", "minX", "minY", "maxX", "maxY", "percent", "point", "x", "y", "v2CubicBezierBBox", "circleMovement", "center", "angle", "radius", "circleMovementAfterMouse", "mouse", "vector", "v2Sub", "getV2Angle", "convertRange", "ellipseMovement", "radius1", "radius2", "ellipseMovementAfterMouse", "radii", "sineWaveMovement", "x", "amplitude", "frequency", "phase", "y", "lissajousCurve", "width", "height", "t", "k", "n", "m", "p", "getRandomRGBColor", "hslColor", "getRandomHSLColor", "hslToRgb", "getRandomHexColor", "hslToHex", "h", "getRandom", "s", "l", "getRandomHSLColorWithHue", "getRandomHSLColorWithSaturation", "getRandomHSLColorWithLightness", "getRandomGrayscaleHSLColor", "getRandomHSLColorWithinRanges", "hueStart", "hueEnd", "saturationStart", "saturationEnd", "lightStart", "lightEnd", "convertHueToDegrees", "getHue", "r", "g", "b", "min", "max", "diff", "getLuminance", "getSaturation", "rgbToHsl", "rgb", "decimalPlaces", "setDecimalPlaces", "hslToRgbHelper", "helper1", "helper2", "colorHelper", "hsl", "gray", "rHelper", "gHelper", "bHelper", "hue2rgb", "q", "t", "p", "toHex", "hex", "rgbToHex", "hexToRgb", "shorthandRegex", "_hex", "_m", "result", "rgbToLab", "x", "y", "z", "labToRgb", "lab", "getShiftedHue", "color", "shift", "hue", "mod", "getShiftedLightness", "lightness", "getShiftedSaturation", "saturation", "getColorsDelta", "rgbA", "rgbB", "labA", "labB", "deltaL", "deltaA", "deltaB", "c1", "c2", "deltaC", "deltaH", "sc", "sh", "deltaLKlsl", "deltaCkcsc", "deltaHkhsh", "i", "guid", "c", "newId", "rectCollide", "rect1", "rect2", "circleCollide", "circle1", "circle2", "dx", "dy", "getEdges", "poly", "edges", "i", "nextIndex", "mod", "edge", "convexPolygonsCollide", "poly1", "poly2", "normal", "v2GetNormal", "p1Proj", "projectPolygon", "p2Proj", "polygon", "min", "max", "vertex", "projection", "v2DotProduct", "animate", "props", "_duration", "startTime", "animationId", "elapsed", "previousTimeStamp", "animating", "observer", "stop", "restart", "start", "pause", "resume", "step", "timeStamp", "getResult", "observerHandler", "_entries", "_observer", "getElapsedTime", "isAnimating", "getStartTime", "getPercent", "getResizeObserver", "getCircleCircumference", "radius", "decimalPlaces", "setDecimalPlaces", "getEllipseCircumference", "radius1", "radius2", "__pow", "isAngleInCircleArc", "startAngleDeg", "endAngleDeg", "currentDegrees", "getSquareInCircleSide", "naturalNumbersSequenceSum", "n", "arithmeticSequenceSum", "a", "d", "getArithmeticMean", "data", "decimalPlaces", "sum", "acc", "val", "setDecimalPlaces", "getArithmeticMeanFromFrequency", "frequencyMap", "mean", "frequency", "getMedian", "copy", "num1", "num2", "mid", "getMode", "num", "maxFrequency", "modes", "getVariance1", "__pow", "getVariance", "getStandardDeviation", "_a", "variance", "mlNormalizeValue", "value", "min", "max", "decimalPlaces", "diff", "setDecimalPlaces", "mlNormalizeArray", "data", "copy", "mlNormalizeTestData", "_data", "mlNormalizeUnseenData", "mlStandardizeValue", "mean", "stdDev", "mlStandardizeArray", "mlStandardizeTestData", "_a", "getArithmeticMean", "getStandardDeviation", "mlStandardizeUnseenData"] + "sources": ["../src/main/format.ts", "../src/main/other.ts", "../src/main/angle.ts", "../src/main/linear-algebra/vector.ts", "../src/main/linear-algebra/matrix.ts", "../src/main/linear-algebra/matrix-transformations.ts", "../src/main/random.ts", "../src/main/convert.ts", "../src/main/derivative.ts", "../src/main/equations/linear-equations.ts", "../src/main/equations/quadratic-equations.ts", "../src/main/bezier-curves/bezier-curve.ts", "../src/main/path-movement.ts", "../src/main/color.ts", "../src/main/id.ts", "../src/main/collision-detection.ts", "../src/main/animation.ts", "../src/main/circle-ellipse.ts", "../src/main/sequence.ts", "../src/main/statistics.ts", "../src/main/ml.ts", "../src/main/series.ts"], + "sourcesContent": ["export const setDecimalPlaces = (num: number, decimalPlaces: number | undefined = Infinity) => {\n if(decimalPlaces === Infinity) return num;\n\n if(decimalPlaces < 0){\n decimalPlaces = 0;\n }\n\n const coefficient = 10 ** decimalPlaces;\n return Math.round(num * coefficient) / coefficient;\n};", "import { Vector2 } from '../types';\nimport { setDecimalPlaces } from './format';\n\nexport const mod = (n: number, m: number) => {\n return ((n % m) + m) % m;\n};\n\n/**\n * Convert range [a, b] to [c, d].\n * f(x) = (d - c) * (x - a) / (b - a) + c\n */\nexport const convertRange = (x: number, a: number, b: number, c: number, d: number) => {\n return (d - c) * (x - a) / (b - a) + c;\n};\n\n/**\n * Check if 2 ranges [a,b] and [c,d] overlap.\n */\nexport const doRangesOverlap = (a: number, b: number, c: number, d: number) => {\n return Math.max(a, c) <= Math.min(b, d) ;\n};\n\n// eslint-disable-next-line\nexport const isNumber = (value: any) => {\n return !isNaN(parseFloat(value)) && isFinite(value);\n};\n\n/**\n * Convert polar coordinates to cartesian coordinates.\n */\nexport const polarToCartesian = (center: Vector2, radii: Vector2, angleInRad: number, decimalPlaces = Infinity) : Vector2 => {\n const [cx, cy] = center;\n const [rx, ry] = radii;\n\n return [\n setDecimalPlaces(cx + (rx * Math.cos(angleInRad)), decimalPlaces),\n setDecimalPlaces(cy + (ry * Math.sin(angleInRad)), decimalPlaces),\n ];\n};", "import { Vector, Vector2, Vector3 } from '../types';\nimport { setDecimalPlaces } from './format';\nimport { v2Length, vNormalize, vDotProduct, vSub } from './linear-algebra/vector';\nimport { mod } from './other';\n\nexport const getV2Angle = (v2: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1], v2[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleInEllipse = (v2: Vector2, radii: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1]/radii[1], v2[0]/radii[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const setV2Angle = (v2: Vector2, newAngleRad: number, decimalPlaces = Infinity): Vector2 => {\n const length = v2Length(v2);\n return [\n setDecimalPlaces(Math.cos(newAngleRad) * length, decimalPlaces),\n setDecimalPlaces(Math.sin(newAngleRad) * length, decimalPlaces),\n ];\n};\n\nexport const radiansToDegrees = (radians: number, decimalPlaces = Infinity) => {\n const res = radians * (180 / Math.PI);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\nexport const degreesToRadians = (degrees: number, decimalPlaces = Infinity) => {\n const res = degrees * (Math.PI / 180);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\n/**\n * Returns the range [0, Math.PI]\n * A = Math.acos( dot(v1, v2)/(v1.length()*v2.length()) );\n */\nexport const getVNAngleBetween = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n const unitVector1 = vNormalize(vector1);\n const unitVector2 = vNormalize(vector2);\n const dotProduct = vDotProduct(unitVector1, unitVector2);\n const angle = Math.acos(dotProduct);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleBetween = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) : number => {\n // return getVNAngleBetween(vector1, vector2, decimalPlaces);\n const diff = vSub(vector1, vector2);\n const angle = Math.atan2(diff[1], diff[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV3AngleBetween = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return getVNAngleBetween(vector1, vector2, decimalPlaces);\n};\n\nexport const isAngleBetween = (angleDegrees: number, startAngleDegrees: number, endAngleDegrees: number) : boolean => {\n const distance = getAnglesSub(startAngleDegrees, endAngleDegrees);\n const distance1 = getAnglesSub(startAngleDegrees, angleDegrees);\n const distance2 = getAnglesSub(endAngleDegrees, angleDegrees);\n const totalDistance = distance1 + distance2;\n\n // Use a small threshold for floating point errors\n return Math.abs(totalDistance - distance) <= 0.001;\n}\n\nexport const isClockwise = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n return angle2Deg >= angle1Deg;\n};\n\n/**\n * Shortest distance (angular) between two angles.\n */\nexport const getAnglesSub = (angleDegrees1: number, angleDegrees2: number, decimalPlaces = Infinity) : number => {\n const angleDistance = Math.abs(mod(angleDegrees1, 360) - mod(angleDegrees2, 360));\n return setDecimalPlaces(angleDistance <= 180 ? angleDistance : 360 - angleDistance, decimalPlaces);\n};\n\nexport const getAnglesDistance = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0, decimalPlaces = Infinity) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n if(isClockwise(angle1Deg, angle2Deg, startAngleDeg)) {\n return setDecimalPlaces((angle2Deg - angle1Deg + 360) % 360, decimalPlaces);\n }\n else{\n return setDecimalPlaces((angle1Deg - angle2Deg + 360) % 360, decimalPlaces);\n }\n};\n\nexport const percentToAngle = (percent: number, startAngleDeg: number, endAngleDeg: number, circleStartAngle = 0) => {\n if(percent < 0) {\n percent = 0;\n }\n\n if(percent > 100) {\n percent = 100;\n }\n\n const distance = getAnglesDistance(startAngleDeg, endAngleDeg, circleStartAngle);\n\n const clockwise = isClockwise(startAngleDeg, endAngleDeg, circleStartAngle);\n if(clockwise) {\n return mod(circleStartAngle + (percent * distance / 100), 360);\n }\n else {\n return mod(circleStartAngle - (percent * distance / 100), 360);\n }\n};", "import { Vector, Vector2, Vector3, Vector4 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { getV2Angle, setV2Angle } from '../angle';\n\n// ------------ SUM ------------------------\n\nexport const vSum = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSum(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sum = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSum(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ SUB ------------------------\n\nexport const vSub = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSub(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sub = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSub(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ MUL SCALAR ------------------------\n\nexport const vMulScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n const vector: Vector = [];\n\n for(let i=0; i {\n return vMulScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3MulScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vMulScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ DIVIDE ------------------------\n\nexport const vDivideScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vDivideScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3DivideScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vDivideScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ LENGTH ------------------------\n\nexport const vLength = (vector: Vector, decimalPlaces = Infinity) => {\n let sum = 0;\n\n for(let i=0; i {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v3Length = (vector: Vector3, decimalPlaces = Infinity) => {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v2SetLength = (v2: Vector2, newLength: number, decimalPlaces = Infinity): Vector2 => {\n const angle = getV2Angle(v2);\n return [\n setDecimalPlaces(Math.cos(angle) * newLength, decimalPlaces),\n setDecimalPlaces(Math.sin(angle) * newLength, decimalPlaces),\n ];\n};\n\n// ----------- DISTANCE ------------------------\n\nexport const vDistance = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v2Distance = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v3Distance = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\n// ------------ NORMALIZE ------------------------\n\n/**\n * Normalization creates a unit vector, which is a vector of length 1.\n */\nexport const vNormalize = (v: Vector, decimalPlaces = Infinity) : Vector => {\n const length = vLength(v);\n const unitVector: Vector = [];\n\n for(let i=0; i {\n return vNormalize(v2, decimalPlaces) as Vector2;\n};\n\nexport const v3Normalize = (v3: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vNormalize(v3, decimalPlaces) as Vector3;\n};\n\n// ------------ DOT PRODUCT ------------------------\n\nexport const vDotProduct = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n let sum = 0;\n\n for(let i=0; i {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\nexport const v3DotProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\n// ------------ CROSS PRODUCT ------------------------\n\n/**\n * Cross product is possible on 3D vectors only.\n * The cross product a \u00D7 b is defined as a vector c that is perpendicular (orthogonal) to both a and b.\n */\nexport const v3CrossProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity): Vector3 => {\n return [\n setDecimalPlaces(vector1[1] * vector2[2] - vector1[2] * vector2[1], decimalPlaces),\n setDecimalPlaces(vector1[2] * vector2[0] - vector1[0] * vector2[2], decimalPlaces),\n setDecimalPlaces(vector1[0] * vector2[1] - vector1[1] * vector2[0], decimalPlaces),\n ];\n};\n\n// --------------- INIT VECTOR HELPER -----------------\n\nexport const v2 = (defaultValue = 0): Vector2 => {\n return [defaultValue, defaultValue];\n};\n\nexport const v3 = (defaultValue = 0): Vector3 => {\n return [defaultValue, defaultValue, defaultValue];\n};\n\nexport const v4 = (defaultValue = 0): Vector4 => {\n return [defaultValue, defaultValue, defaultValue, defaultValue];\n};\n\nexport const vN = (N: number, defaultValue = 0): Vector => {\n\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n const vector: Vector = [];\n for(let i=0; i {\n let vector: Vector2 = [0, 0];\n vector = v2SetLength(vector, distance);\n return setV2Angle(vector, angleRad);\n};\n\n// --------------- EQUALITY -------------------------\n\nexport const vEqual = (vector1: Vector, vector2: Vector): boolean => {\n if(vector1.length !== vector2.length) return false;\n\n for(let i=0; i {\n const sub = v2Sub(vector2, vector1);\n return [\n -setDecimalPlaces(sub[1], decimalPlaces),\n setDecimalPlaces(sub[0], decimalPlaces)\n ];\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector, Vector2, Vector3 } from '../../types';\nimport { vMulScalar, vSum, vSub, vDotProduct, vN, vEqual, vDivideScalar } from './vector';\n\n// --------------- SUM ----------------------\n\nexport const mSum = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sum = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- SUB ----------------------\n\nexport const mSub = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sub = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- MUL SCALAR ----------------------\n\nexport const mMulScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vMulScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2MulScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mMulScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3MulScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mMulScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n// --------------- DIVIDE SCALAR ----------------------\n\nexport const mDivideScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vDivideScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2DivideScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mDivideScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3DivideScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mDivideScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n\n// --------------- TRANSPOSE ----------------------\n\nexport const mTranspose = (m: Matrix): Matrix => {\n\n const vectorsCount = m.length;\n if(vectorsCount <= 0) return m;\n\n const vectorLength = m[0].length;\n if(vectorLength <= 0) return m;\n\n const matrix: Matrix = [];\n for(let i=0; i {\n return mTranspose(m2);\n};\n\nexport const m3Transpose = (m3: Matrix3): Matrix => {\n return mTranspose(m3);\n};\n\n// ----------------- RESET ----------------------\n\nexport const mReset = (m: Matrix, defaultValue = 0): Matrix => {\n\n if(m.length <= 0) return [];\n\n const res: Matrix = [];\n\n for(let i=0; i {\n return mReset(m2, defaultValue) as Matrix2;\n};\n\nexport const m3Reset = (m3: Matrix3, defaultValue = 0): Matrix3 => {\n return mReset(m3, defaultValue) as Matrix3;\n};\n\n// --------------- MATRIX INIT HELPERS -----------------\n\nexport const m2x2 = (defaultValue = 0): Matrix2 => {\n return [\n [defaultValue, defaultValue],\n [defaultValue, defaultValue],\n ];\n};\n\nexport const m3x3 = (defaultValue = 0): Matrix3 => {\n return [\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const m4x4 = (defaultValue = 0): Matrix4 => {\n return [\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const mNxM = (N: number, M: number, defaultValue = 0): Matrix => {\n if(N <= 0 || M <= 0){\n throw new Error('M and N must be positive numbers.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return [\n [1, 0],\n [0, 1],\n ];\n};\n\nexport const identity3 = (): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\nexport const identity4 = (): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Identity Matrix (I).\n * M x I = I x M = M for any matrix M.\n * Identity Matrix is a special case of scale matrix.\n */\nexport const identityN = (N: number): Matrix => {\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n if(N === 0) return [];\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mDeepCopy(m2) as Matrix2;\n};\n\nexport const m3DeepCopy = (m3: Matrix3): Matrix3 => {\n return mDeepCopy(m3) as Matrix3;\n};\n\n// -------------- APPEND / PREPEND ROW OR COLUMN ---------------\n\nexport const mAppendCol = (m: Matrix, col: Vector): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n const copy = mDeepCopy(m);\n copy.push(row);\n return copy;\n};\n\nexport const m2AppendRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.push(row);\n return copy;\n};\n\nexport const m3AppendRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.push(row);\n return copy;\n};\n\nexport const mPrependRow = (m: Matrix, row: Vector) : Matrix => {\n const copy = mDeepCopy(m);\n copy.unshift(row);\n return copy;\n};\n\nexport const m2PrependRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.unshift(row);\n return copy;\n};\n\nexport const m3PrependRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.unshift(row);\n return copy;\n};\n\n// ------------ DELETE ROW OR COLUMN ----------------------------\n\nexport const mDelLastRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.pop();\n return copy;\n};\n\nexport const mDelFirstRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.shift();\n return copy;\n};\n\nexport const mDelLastColumn = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const size = m[0].length;\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n\n const matrix: Matrix = [];\n for(let i=0; i {\n\n if(matrix.length < 0) return [];\n\n if(matrix[0].length !== vector.length){\n throw new Error('The number of columns in the matrix must be equal to the length of the vector.');\n }\n\n const res: Vector = [];\n\n for(let i=0; i {\n if(matrix1.length !== matrix2.length) return false;\n\n for(let i=0; i returns matrix N (m-1 x m-1)\n * The matrix must be square.\n */\nconst mMinorHelper = (m: Matrix, row: number, col: number) => {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // prepare the matrix without provided row and column\n const matrix = mMinorHelper(m, row, col);\n\n // calculate the matrix determinant\n return mDeterminant(matrix);\n};\n\n/**\n * Calculate determinant for NxN matrix.\n * Matrix should be square.\n */\nexport const mDeterminant = (matrix: Matrix): number => {\n const size = matrix.length;\n if(size === 0) return 1;\n\n if(size !== matrix[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return matrix[0][0];\n if(size === 2) return m2Determinant(matrix as Matrix2);\n\n let d = 0;\n\n for(let i=0; i {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return m2[0][0] * m2[1][1] - m2[1][0] * m2[0][1];\n};\n\n/**\n * Calculate determinant for 3x3 matrix.\n * Matrix should be square.\n */\nexport const m3Determinant = (m3: Matrix3): number => {\n if(m3.length !== m3[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return mDeterminant(m3);\n};\n\n// ------------------ INVERSE -----------------------\n\nexport const m2Adjugate = (m2: Matrix2): Matrix2|null => {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return [\n [m2[1][1], -m2[0][1]],\n [-m2[1][0], m2[0][0]],\n ];\n};\n\nexport const m3Adjugate = (m3: Matrix3) : Matrix3|null => {\n return mAdjugate(m3) as (Matrix3|null);\n};\n\n/**\n * Adjugate is a transpose of a cofactor matrix\n */\nexport const mAdjugate = (m: Matrix): Matrix|null => {\n\n const size = m.length;\n if(size <= 0) return null;\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return m;\n\n if(size === 2) return m2Adjugate(m as Matrix2);\n\n // build a cofactor matrix ----------------\n const cofactors: Matrix = [];\n\n for(let i=0; i {\n if(m.length > 0 && m.length !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = mDeterminant(m);\n return d === 0;\n};\n\n/**\n * Square matrix A (nxn) is invertible is there is another square matrix B (nxn) so AxB = BxA = I\n * For A (2x2) matrix, the inverse is:\n * (1 / (determinant(A))) * adj(A)\n */\nexport const m2Inverse = (m2: Matrix2, decimalPlaces = Infinity): (Matrix2 | null) => {\n if(m2.length > 0 && m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = m2Determinant(m2);\n if(d === 0) return null;\n\n const adj = m2Adjugate(m2);\n if(adj === null) return null;\n\n return m2DivideScalar(adj, d, decimalPlaces);\n};\n\nexport const m3Inverse = (m3: Matrix3, decimalPlaces = Infinity): (Matrix3 | null) => {\n return mInverse(m3, decimalPlaces) as (Matrix3|null);\n};\n\nexport const mInverse = (m: Matrix, decimalPlaces = Infinity): (Matrix | null) => {\n const size = m.length;\n\n if(size > 0 && size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // find a determinant ----------------------\n const d = mDeterminant(m);\n\n // find an Adjugate - a transpose of a cofactor matrix\n const adj = mAdjugate(m);\n if(adj === null) return null;\n\n return mDivideScalar(adj, d, decimalPlaces);\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector2, Vector3, Vector4 } from '../../types';\nimport { v2Normalize, v3MulScalar, v3Normalize } from './vector';\nimport { mMulVector, mMul } from './matrix';\nimport { setDecimalPlaces } from '../format';\n\n/*\nAny 2D affine transformation can be decomposed\ninto a rotation, followed by a scaling, followed by a\nshearing, and followed by a translation.\n---------------------------------------------------------\nAffine matrix = translation x shearing x scaling x rotation\n */\n\n// ----------------- CSS -------------------------------------\n\n/**\n * Matrix 2D in non-homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2ToCSS = (m: Matrix2) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, 0, 0)`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2hToCSS = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, ${ tx }, ${ ty })`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m2hToCSS3d = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix3d(${ a }, ${ b }, 0, 0, ${ c }, ${ d }, 0, 0, 0, 0, 1, 0, ${ tx }, ${ ty }, 0, 1)`;\n};\n\n/**\n * Matrix 3D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m3hToCSS3d = (m: Matrix4) : string => {\n\n return `matrix3d(\n ${ m[0][0] }, ${ m[0][1] }, ${ m[0][2] }, ${ m[0][3] },\n ${ m[1][0] }, ${ m[1][1] }, ${ m[1][2] }, ${ m[1][3] },\n ${ m[2][0] }, ${ m[2][1] }, ${ m[2][2] }, ${ m[2][3] },\n ${ m[3][0] }, ${ m[3][1] }, ${ m[3][2] }, ${ m[3][3] }\n )`;\n};\n\n// ---------------- TRANSLATION MATRICES ----------------------\n\nexport const m2Translation = (position: Vector2, decimalPlaces = Infinity): Matrix2 => {\n\n return [\n [1, 0],\n [0, 1],\n [setDecimalPlaces(position[0], decimalPlaces), setDecimalPlaces(position[1], decimalPlaces)],\n ];\n};\n\nexport const m3Translation = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n [\n setDecimalPlaces(position[0], decimalPlaces),\n setDecimalPlaces(position[1], decimalPlaces),\n setDecimalPlaces(position[2], decimalPlaces)\n ],\n ];\n};\n\n/**\n * 2D Translation matrix in homogeneous coordinates.\n */\nexport const m2TranslationH = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1],\n ];\n};\n\n/**\n * 3D Translation matrix in homogeneous coordinates.\n */\nexport const m3TranslationH = (position: Vector4, decimalPlaces = Infinity): Matrix4 => {\n\n return [\n [1, 0, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, 0, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1, setDecimalPlaces(position[2], decimalPlaces)],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- ROTATION MATRICES -------------------------\n\n/**\n * Rotation of an angle about the origin.\n */\nexport const m2Rotation = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix2 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin],\n [sin, cos],\n ] :\n [\n [cos, sin],\n [-sin, cos],\n ];\n};\n\n/**\n * Rotation of an angle about the origin in homogeneous coordinates (clockwise).\n */\nexport const m2RotationH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ]:\n [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation of an angle \"angleRad\" around the given point (transformOrigin) in homogeneous coordinates (clockwise).\n * result_vector = TranslationMatrix(x, y) * RotationMatrix() * TranslationMatrix(-x, -y) * position_vector\n */\nexport const m2RotationAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const rotation = m2RotationH(angleRad, isClockwise, decimalPlaces);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, rotation);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2RotateAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n position: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2RotationAroundPointH(angleRad, transformOrigin, isClockwise, decimalPlaces);\n return mMulVector(mat3h, position) as Vector3;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2Rotate = (angleRad: number, vector: Vector2, isClockwise = true, decimalPlaces = Infinity): Vector2 => {\n const unitVector = v2Normalize(vector);\n return mMulVector(m2Rotation(angleRad, isClockwise, decimalPlaces), unitVector) as Vector2;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2RotateH = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m2RotationH(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the X axis (clockwise).\n */\nexport const m3RotationX = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0],\n [0, cos, -sin],\n [0, sin, cos],\n ] :\n [\n [1, 0, 0],\n [0, cos, sin],\n [0, -sin, cos],\n ];\n};\n\n/**\n * Rotation around the X axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationXH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0, 0],\n [0, cos, -sin, 0],\n [0, sin, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [1, 0, 0, 0],\n [0, cos, sin, 0],\n [0, -sin, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateX = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationX(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Y axis (clockwise).\n */\nexport const m3RotationY = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin],\n [0, 1, 0],\n [-sin, 0, cos],\n ] :\n [\n [cos, 0, -sin],\n [0, 1, 0],\n [sin, 0, cos],\n ];\n};\n\n/**\n * Rotation around the Y axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationYH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin, 0],\n [0, 1, 0, 0],\n [-sin, 0, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [cos, 0, -sin, 0],\n [0, 1, 0, 0],\n [sin, 0, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateY = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationY(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Z axis (clockwise).\n */\nexport const m3RotationZ = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ] : [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation around the Z axis (clockwise)- in homogeneous coordinates\n */\nexport const m3RotationZH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0, 0],\n [sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ] : [\n [cos, sin, 0, 0],\n [-sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateZ = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationZ(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n// ---------------- SCALE MATRICES -------------\n\n/**\n * Get matrix for arbitrary scaling pivot point.\n * result_vector = TranslationMatrix(x, y) * ScaleMatrix() * TranslationMatrix(-x, -y) * scale_vector\n */\nexport const m2ScaleAtPointHMatrix = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const scale = m2ScaleH(scaleVector);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, scale);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2ScaleAtPointH = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n point: Vector3,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2ScaleAtPointHMatrix(scaleVector, transformOrigin, decimalPlaces);\n return mMulVector(mat3h, point) as Vector3;\n};\n\nexport const m2Scale = (scaleVector: Vector2): Matrix2 => {\n return [\n [scaleVector[0], 0],\n [0, scaleVector[1]],\n ];\n};\n\nexport const v2Scale = (scaleVector: Vector2, vector: Vector2): Vector2 => {\n return mMulVector(m2Scale(scaleVector), vector) as Vector2;\n};\n\n/**\n * homogeneous coordinates\n */\nexport const m2ScaleH = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, 1],\n ];\n};\n\nexport const m3Scale = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, scaleVector[2]],\n ];\n};\n\nexport const m3ScaleH = (scaleVector: Vector4): Matrix4 => {\n return [\n [scaleVector[0], 0, 0, 0],\n [0, scaleVector[1], 0, 0],\n [0, 0, scaleVector[2], 0],\n [0, 0, 0, 1]\n ];\n};\n\nexport const v3Scale = (scaleVector: Vector3, vector: Vector3): Vector3 => {\n return mMulVector(m3Scale(scaleVector), vector) as Vector3;\n};\n\n/**\n * Stretch, parallel to the x-axis.\n */\nexport const m2ScaleX = (scale: number): Matrix2 => {\n return [\n [scale, 0],\n [0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the x-axis - homogeneous coordinates\n */\nexport const m2ScaleXH = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleX = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleXH = (scale: number): Matrix4 => {\n return [\n [scale, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleY = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleYH = (scale: number): Matrix => {\n return [\n [1, 0, 0, 0],\n [0, scale, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZ = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, scale],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZH = (scale: number): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, scale, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis.\n */\nexport const m2ScaleY = (scale: number): Matrix2 => {\n return [\n [1, 0],\n [0, scale],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis - homogeneous coordinates\n */\nexport const m2ScaleYH = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n// ---------------- REFLECTION MATRICES -------------------------\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOrigin = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOriginH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection about the origin in non-homogeneous coordinates\n */\nexport const m3ReflectionOrigin = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection about the origin in homogeneous coordinates\n */\nexport const m3ReflectionOriginH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection about y=-x\n */\nexport const m2ReflectionYmX = (): Matrix2 => {\n\n return [\n [0, -1],\n [-1, 0],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionX = (): Matrix2 => {\n\n return [\n [1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionXH = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection in the y-axis.\n */\nexport const m2ReflectionY = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, 1],\n ];\n};\n\nexport const m2ReflectionYH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionYZ = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in homogeneous coordinates\n */\nexport const m3ReflectionYZH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXZ = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in homogeneous coordinates\n */\nexport const m3ReflectionXZH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXY = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in homogeneous coordinates\n */\nexport const m3ReflectionXYH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- SHEARING MATRICES -------------------------\n\n\n/**\n * Shearing in y-axis, with x-axis fixed with (0,1) moving to (factor, 1)\n */\nexport const m2ShearingY = (factor: number): Matrix2 => {\n\n return [\n [1, factor],\n [0, 1],\n ];\n};\n\n/**\n * Shearing in x-axis, with y-axis fixed with (1,0) moving to (1, factor)\n */\nexport const m2ShearingX = (factor: number): Matrix2 => {\n\n return [\n [1, 0],\n [factor, 1],\n ];\n};", "import { setDecimalPlaces } from './format';\n\n/**\n * Returns a random number in the [min,max] range.\n */\nexport const getRandom = (min: number, max: number, decimalPlaces = Infinity): number => {\n return setDecimalPlaces(Math.random() * (max - min) + min, decimalPlaces);\n};\n\n/**\n * Returns a random integer number in the [min,max] range.\n */\nexport const getRandomInt = (min: number, max: number): number => {\n return Math.floor(Math.random() * (max - min + 1) + min);\n};\n\nexport const getRandomBoolean = () => Math.random() < 0.5;\n\n/* eslint-disable @typescript-eslint/no-explicit-any */\nexport const getRandomItemFromArray = (array: any[]) => {\n const randomIndex = getRandomInt(0, array.length - 1);\n return array[randomIndex];\n};", "export const stringToNumber = (value: string|undefined|null|number, defaultNumber: number) => {\n if(value === undefined || value === null) return defaultNumber;\n const res = Number(value) ?? defaultNumber;\n return isNaN(res) ? defaultNumber : res;\n};", "import { setDecimalPlaces } from './format';\nimport { Vector2, Vector3 } from '../types';\n\n/**\n * u(x) and v(x) are functions ---------->\n *\n * dx(u + v) = dx(u) + dx(v)\n * dx(u - v) = dx(u) - dx(v)\n * dx(u * v) = dx(u) * v + u * dx(v)\n * dx(u / v) = (dx(u) * v - u * dx(v)) / (v ^ 2), when v(x) != 0\n */\n\n// ------------------ Derivatives of Polynomial ---------------------------\n\n/**\n * y = 3x+2\n * dxPolynomial(10, [[3, 1], [2, 0]])\n */\nexport const dxPolynomial = (x: number, polynomial: number[][], decimalPlaces = Infinity) => {\n let res = 0;\n\n for(const part of polynomial){\n if(part.length !== 2) return NaN;\n\n const coeff = part[0];\n const power = part[1];\n res += coeff * power * Math.pow(x, power - 1);\n }\n\n return setDecimalPlaces(res, decimalPlaces);\n}\n\n// ---------------------- Bezier Curves ---------------------------\n\n/**\n * Derivative of Bezier Curve is another Bezier Curve.\n * t must min in range [0, 1]\n */\nexport const dxV2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n // The derivative: P1 * (2t-2) + (2*P3-4*P2) * t + 2 * P2\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\nexport const dxV2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n\n// ----------------- Derivatives of trigonometry functions ---------------------------\n\nexport const dxSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(Math.cos(x), decimalPlaces);\n};\n\nexport const dxCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-Math.sin(x), decimalPlaces);\n};\n\nexport const dxTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.cos(x) ** 2), decimalPlaces);\n};\n\n/**\n * x != Math.PI * n, where n is an integer\n */\nexport const dxCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sin(x) ** 2), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\nexport const dxArcTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (1 + x ** 2), decimalPlaces);\n};\n\nexport const dxArcCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (1 + x ** 2), decimalPlaces);\n};\n", "import { Matrix, Matrix2, Matrix3, Vector, Vector2, Vector3 } from '../../types';\nimport { m2Inverse, m3Inverse, mInverse, mMulVector, mDelLastColumn, mGetLastColumn } from '../linear-algebra/matrix';\nimport { setDecimalPlaces } from '../format';\nimport { v2Sub } from '../linear-algebra/vector';\n\n/**\n * Linear equation\n * ax + b = c\n * x = (c - b) / a; a != 0\n */\nexport const linearEquation = (equation: Vector3, decimalPlaces = Infinity) : number => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n\n const diff = c - b;\n\n if(a === 0 && diff === 0) return Infinity; // any number is a solution\n if(a === 0) return NaN; // no solution\n\n return setDecimalPlaces(diff / a, decimalPlaces);\n};\n\n/**\n * System of 2 linear equations.\n * [x, y] = inverse(Matrix of equation parameters) x (vector of equation results)\n * ---------------\n * 3x + 2y = 7\n * -6x + 6y = 6\n */\nexport const linearEquationSystem2 = (equation1: Vector3, equation2: Vector3, decimalPlaces = Infinity) : Vector2 | null => {\n const equationParams: Matrix2 = [\n [equation1[0], equation1[1]],\n [equation2[0], equation2[1]],\n ];\n\n const inversed = m2Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector2 = [\n equation1[2],\n equation2[2]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector2;\n};\n\n/**\n * System of 3 linear equations.\n * ---------------------------------------\n * 3x + 2y + 5z = 7\n * -6x + 6y + 6z = 6\n * 2x + 7y - z = 4\n */\nexport const linearEquationSystem3 = (\n equation1: Vector,\n equation2: Vector,\n equation3: Vector,\n decimalPlaces = Infinity) : Vector3 | null => {\n const equationParams: Matrix3 = [\n [equation1[0], equation1[1], equation1[2]],\n [equation2[0], equation2[1], equation2[2]],\n [equation3[0], equation3[1], equation3[2]],\n ];\n\n const inversed = m3Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector3 = [\n equation1[3],\n equation2[3],\n equation3[3]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector3;\n};\n\n/**\n * System of N linear equations.\n */\nexport const linearEquationSystemN = (equations: Matrix, decimalPlaces = Infinity) : Vector | null => {\n if(equations.length <= 0) return null;\n\n const equationParams = mDelLastColumn(equations);\n\n const inversed = mInverse(equationParams);\n if(inversed === null) return null; // no results\n\n // the last column of the equations matrix\n const equationResults = mGetLastColumn(equations);\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector;\n};\n\n/**\n * Calculate the equation of a line given two points in a 2D space.\n * y = ax + b\n * y - y1 = m(x - x1)\n * m = (y2 - y1) / (x2 - x1)\n */\nexport const getLinearEquationBy2Points = (point1: Vector2, point2: Vector2) : {\n slope: number|undefined,\n yIntercept: number|undefined,\n xIntercept: number|undefined,\n formula: string,\n} => {\n const [deltaX, deltaY] = v2Sub(point2, point1);\n const [x, y] = point1;\n\n if(deltaX === 0) {\n return {\n slope: undefined,\n xIntercept: x,\n yIntercept: undefined,\n formula: `x = ${ x }`,\n };\n }\n\n const m = deltaY / deltaX;\n const b = y - m * x;\n let formula = '';\n\n if(m === 0) {\n formula = `y = ${ b }`;\n }\n else{\n formula = `y = ${ m === 1 ? '' : m }x`;\n\n if(b !== 0) {\n formula += ` ${ b < 0 ? '-' : '+' } ${ Math.abs(b) }`;\n }\n }\n\n return {\n slope: m,\n xIntercept: undefined,\n yIntercept: b,\n formula,\n };\n};", "import { Vector } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { linearEquation } from './linear-equations';\nimport { isNumber } from '../other';\n\n/**\n * Quadratic Equation.\n * ax^2 + bx + c = d\n */\nexport const quadraticEquation = (equation: Vector, decimalPlaces = Infinity) : Vector => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n const d = equation[3];\n\n if(a === 0){\n // it's a linear equation -------------------------------------------\n const res = linearEquation([b, c, d], decimalPlaces);\n if(isNumber(res)) return [res];\n return [];\n }\n\n const diff = c - d;\n\n const discriminant = b * b - (4 * a * diff);\n\n if(discriminant < 0){\n return []; // no results\n }\n\n if(discriminant === 0){\n return [ setDecimalPlaces(-b / (2 * a), decimalPlaces) ]; // 1 result\n }\n\n // if(determinant > 0) ---> 2 results\n const t1 = 2 * a;\n const t2 = Math.sqrt(discriminant);\n\n return [\n setDecimalPlaces((-b + t2) / t1, decimalPlaces),\n setDecimalPlaces((-b - t2) / t1, decimalPlaces),\n ];\n};", "import { IBBox, Vector, Vector2, Vector3 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport {\n dxV2CubicBezierCurve,\n dxV2QuadraticBezierCurve,\n dxV3CubicBezierCurve,\n dxV3QuadraticBezierCurve\n} from '../derivative';\nimport { v2Normalize, v3Normalize } from '../linear-algebra/vector';\nimport { linearEquation } from '../equations/linear-equations';\nimport { quadraticEquation } from '../equations/quadratic-equations';\nimport { isNumber } from '../other';\n\n/**\n * B\u00E9zier Curves\n * quadratic: y = P1 * (1-t)\u00B2 + P2 * 2 * (1-t)t + P3 * t\u00B2\n * t in range [0, 1]\n */\n\n// -------------------- GET POINT ON CURVE --------------------------\n\n/**\n * Get a point on a quadratic B\u00E9zier curve as a function of time.\n */\nexport const v2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n/**\n * Get a point on a cubic B\u00E9zier curve as a function of time.\n */\nexport const v2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n// -------------------- TANGENT --------------------------\n\n/**\n * Tangent indicates the direction of travel at specific points along the B\u00E9zier curve,\n * and is literally just the first derivative of our curve.\n */\nexport const v2QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\nexport const v2CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\n// -------------------- NORMAL --------------------------\n\n/**\n * Normal is a vector that runs at a right angle to the direction of the curve, and is typically of length 1.\n * To find it, we take the normalised tangent vector, and then rotate it by a 90 degrees.\n */\nexport const v2QuadraticBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2QuadraticBezierCurveTangent(t, startControlPoint, centerControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\nexport const v2CubicBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2CubicBezierCurveTangent(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\n// -------------------- EXTREMA --------------------------\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2QuadraticBezierCurveExtrema = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector => {\n\n /*\n (-2 * (1 - t)) * startControlPoint[0] + (2 - 4 * t) * centerControlPoint[0] + (2 * t) * endControlPoint[0]\n 2 * t * startControlPoint[0] - 4 * t * centerControlPoint[0] + 2 * t * endControlPoint[0] - 2 * startControlPoint[0] + 2 * centerControlPoint[0]\n t * (2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0]) + (- 2 * startControlPoint[0] + 2 * centerControlPoint[0])\n */\n\n const a1 = 2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0];\n const b1 = -2 * startControlPoint[0] + 2 * centerControlPoint[0];\n const equation1: Vector3 = [a1, b1, 0];\n const res1 = linearEquation(equation1, decimalPlaces);\n\n const a2 = 2 * startControlPoint[1] - 4 * centerControlPoint[1] + 2 * endControlPoint[1];\n const b2 = -2 * startControlPoint[1] + 2 * centerControlPoint[1];\n const equation2: Vector3 = [a2, b2, 0];\n const res2 = linearEquation(equation2, decimalPlaces);\n\n const res: Vector = [];\n\n if(isNumber(res1)){\n res.push(res1);\n }\n\n if(isNumber(res2)){\n res.push(res2);\n }\n\n return res;\n};\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2CubicBezierCurveExtrema = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2|null => {\n\n const a1 = -3 * startControlPoint[0] + 9 * center1ControlPoint[0] - 9 * center2ControlPoint[0] + 3 * endControlPoint[0];\n const b1 = 6 * startControlPoint[0] - 12 * center1ControlPoint[0] + 6 * center2ControlPoint[0];\n const c1 = -3 * startControlPoint[0] + 3 * center1ControlPoint[0];\n const equation1: Vector = [a1, b1, c1, 0];\n\n const a2 = -3 * startControlPoint[1] + 9 * center1ControlPoint[1] - 9 * center2ControlPoint[1] + 3 * endControlPoint[1];\n const b2 = 6 * startControlPoint[1] - 12 * center1ControlPoint[1] + 6 * center2ControlPoint[1];\n const c2 = -3 * startControlPoint[1] + 3 * center1ControlPoint[1];\n const equation2: Vector = [a2, b2, c2, 0];\n\n // Any value between 0 and 1 is a root that matters for B\u00E9zier curves, anything below or above that is irrelevant (because B\u00E9zier curves are only defined over the interval [0,1]).\n const res1 = quadraticEquation(equation1, decimalPlaces).filter(num => num >= 0 && num <= 1);\n const res2 = quadraticEquation(equation2, decimalPlaces).filter(num => num >= 0 && num <= 1);\n\n const res = [...res1, ...res2];\n if(res.length === 2){\n return [...res1, ...res2] as Vector2;\n }\n\n return null;\n};\n\n// -------------------- BOUNDING BOX --------------------------\n\nexport const v2QuadraticBezierBBox = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2QuadraticBezierCurveExtrema(startControlPoint, centerControlPoint, endControlPoint);\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2QuadraticBezierCurve(percent, startControlPoint, centerControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x);\n maxX = Math.max(maxX, x);\n\n minY = Math.min(minY, y);\n maxY = Math.max(maxY, y);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\nexport const v2CubicBezierBBox = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2CubicBezierCurveExtrema(startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint) || [];\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2CubicBezierCurve(percent, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x ?? Infinity);\n maxX = Math.max(maxX, x ?? -Infinity);\n\n minY = Math.min(minY, y ?? Infinity);\n maxY = Math.max(maxY, y ?? -Infinity);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\n\n", "import { Vector2 } from '../types';\nimport { v2Sub } from './linear-algebra/vector';\nimport { getV2Angle } from './angle';\nimport { convertRange } from './other';\n\n/**\n * Circle Equation\n * x^2 + y^2 = radius^2\n * ----------------------\n * Circle Parametric Equation\n * x(t) = radius * cos(t)\n * y(t) = radius * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const circleMovement = (center: Vector2, angle: number, radius: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius,\n center[1] + Math.sin(angle) * radius\n ];\n};\n\n/**\n * Circle Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const circleMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radius: number\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return circleMovement(center, angle, radius);\n};\n\n/**\n * Ellipse Equation\n * (x - centerX)^2 / (radius1^2) + (y - centerY)^2 / (radius2^2) = 1\n * -----------------------------------------------------------------\n * Ellipse Parametric Equation\n * x(t) = radius1 * cos(t)\n * y(t) = radius2 * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const ellipseMovement = (center: Vector2, angle: number, radius1: number, radius2: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius1,\n center[1] + Math.sin(angle) * radius2\n ];\n};\n\n/**\n * Ellipse Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const ellipseMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radii: Vector2\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return ellipseMovement(center, angle, radii[0], radii[1]);\n};\n\n/**\n * Sine Wave Equation (Sinusoid)\n * -----------------------------\n * const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n * amplitude = the peak deviation of the function from zero\n * frequency = number of cycles\n * phase = specifies (in radians) where in its cycle the oscillation is at t = 0.\n * think of it as \"shifting\" the starting point of the function to the right (positive p) or left (negative)\n */\nexport const sineWaveMovement = (x: number, amplitude: number, frequency: number, phase: number) : Vector2 => {\n /*\n example values:\n const amplitude = 50;\n const frequency = 0.005;\n const phase = 0;\n x: [0, 1000]\n */\n const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n\n return [x, y];\n};\n\n/**\n * Lissajous curve (Lissajous figure or Bowditch curve)\n * Parametric equation #1\n * f(t) = A * sin(k * t + m)\n * f(t) = B * sin(n * t)\n * 0 <= m <= PI/2\n * k, n >= 1\n * -----------------------\n * Parametric equation #2\n * f(t) = A * cos(k * t - m)\n * f(t) = B * cos(n * t - p)\n * -----------------------------\n * Shapes:\n * k = 1, n = 1, m = 0, p = 0 ---> line\n * A = B, k = 1, n = 1, m = PI/2, p = PI/2 ----> circle\n * A != B, k = 1, n = 1, m = PI/2, p = PI/2 ----> ellipse\n * k = 2, n = 2, m = PI/2, p = PI/2 ----> section of a parabola\n */\nexport const lissajousCurve = (\n width: number,\n height: number,\n t: number,\n k: number,\n n: number,\n m: number,\n p: number\n) :Vector2 => {\n return [\n width * Math.cos(k * t - m),\n height * Math.cos(n * t - p),\n ];\n};\n", "import { getRandom } from './random';\nimport { HSLColor, LABColor, RGBColor } from '../types';\nimport { mod } from './other';\nimport { setDecimalPlaces } from './format';\n\n// ------------------------ RANDOM COLOR -------------------------------------\n\nexport const getRandomRGBColor = () : RGBColor => {\n const hslColor = getRandomHSLColor();\n return hslToRgb(hslColor);\n};\n\nexport const getRandomHexColor = () : string => {\n const hslColor = getRandomHSLColor();\n return hslToHex(hslColor);\n};\n\nexport const getRandomHSLColor = () : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given hue\n */\nexport const getRandomHSLColorWithHue = (h: number) : HSLColor => {\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given saturation\n */\nexport const getRandomHSLColorWithSaturation = (s: number) : HSLColor => {\n const h = getRandom(1, 360);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given lightness\n */\nexport const getRandomHSLColorWithLightness = (l: number) : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n return [h, s, l];\n};\n\nexport const getRandomGrayscaleHSLColor = () : HSLColor => {\n const l = getRandom(0, 100);\n return [0, 0, l];\n};\n\nexport const getRandomHSLColorWithinRanges = (\n hueStart = 1, hueEnd = 360,\n saturationStart = 0, saturationEnd = 100,\n lightStart = 0, lightEnd = 100\n) : HSLColor => {\n const h = getRandom(hueStart, hueEnd);\n const s = getRandom(saturationStart, saturationEnd);\n const l = getRandom(lightStart, lightEnd);\n return [h, s, l];\n};\n\n// ----------------------- CONVERT COLORS --------------------------------------\n\n/**\n * helper: convert hue value to degrees.\n * @param {number} h\n * @return {number} [0, 360] degrees\n */\nconst convertHueToDegrees = (h : number) : number => {\n\n // the hue value needs to be multiplied by 60 to convert it to degrees\n h *= 60;\n\n // if hue becomes negative, you need to add 360 to, because a circle has 360 degrees\n if(h < 0){\n h += 360;\n }\n\n return h;\n // convert huw to %\n // return h * 100 / 360;\n};\n\n/**\n * get hue from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] % - we use here % instead of [0, 359] degrees\n */\nconst getHue = (r : number, g : number, b : number, min : number | undefined = undefined, max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (max === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no hue, as it's gray\n if(min === max) return 0;\n\n const diff = max - min;\n\n let h = 0;\n\n // if red is max\n if(max === r){\n h = (g - b) / diff + (g < b ? 6 : 0);\n }\n\n // if green is max\n if(max === g){\n h = 2 + (b - r) / diff;\n }\n\n // if blue is max\n if(max === b){\n h = 4 + (r - g) / diff;\n }\n\n return convertHueToDegrees(h);\n};\n\n/**\n * get luminance from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] %\n */\nconst getLuminance = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // calculate the luminance value\n // @ts-ignore\n const l = (min + max) / 2; // [0, 1]\n\n // return l value in %\n return l * 100;\n};\n\n/**\n * get saturation from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @param {number|undefined=} l - luminance in [0, 100] %\n * @return {number} [0, 100] %\n */\nconst getSaturation = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined,\n l : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no saturation, as it's gray\n if(min === max) return 0;\n\n // calculate luminance if it's not provided\n l = (l === undefined) ? getLuminance(r, g, b) : l;\n\n // check the level of luminance\n const s = (l <= 50) ?\n // @ts-ignore\n ((max - min) / (max + min)) : // this formula is used when luminance <= 50%\n // @ts-ignore\n (max - min) / (2.0 - max - min); // this formula is used when luminance > 50%\n\n // return saturation in %\n return s * 100;\n};\n\nexport const rgbToHsl = (rgb: RGBColor, decimalPlaces = Infinity): HSLColor => {\n\n // convert rgb values to the range [0, 1]\n const r = rgb[0] / 255;\n const g = rgb[1] / 255;\n const b = rgb[2] / 255;\n\n // find the minimum and maximum values of r, g, and b\n const min = Math.min(r, g, b);\n const max = Math.max(r, g, b);\n\n // calculate the luminance value in %\n const l = getLuminance(r, g, b, min, max);\n\n // calculate the saturation in %\n const s = getSaturation(r, g, b, min, max, l);\n\n // calculate the hue in % (not in degrees!)\n const h = getHue(r, g, b, min, max);\n\n if(h > 360 || s > 100 || l > 100){\n return [0, 0, 100];\n }\n\n if(h < 0 || s < 0 || l < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(h, decimalPlaces),\n setDecimalPlaces(s, decimalPlaces),\n setDecimalPlaces(l, decimalPlaces),\n ];\n};\n\n/**\n * helper: HSL to RGB\n */\nconst hslToRgbHelper = (helper1 : number, helper2 : number, colorHelper : number) : number => {\n\n // all values need to be between 0 and 1\n // if you get a negative value you need to add 1 to it\n if(colorHelper < 0) colorHelper += 1;\n\n // if you get a value above 1 you need to subtract 1 from it.\n if(colorHelper > 1) colorHelper -= 1;\n\n if(colorHelper * 6 < 1) return helper2 + (helper1 - helper2) * 6 * colorHelper;\n\n if(colorHelper * 2 < 1) return helper1;\n\n if(colorHelper * 3 < 2){\n return helper2 + (helper1 - helper2) * (0.666 - colorHelper) * 6;\n }\n else{\n return helper2;\n }\n};\n\nexport const hslToRgb = (hsl: HSLColor, decimalPlaces = Infinity): RGBColor => {\n\n // convert all values to [0, 1] from %\n const h = hsl[0] / 100;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n // if there is no saturation -> it\u2019s grey\n if(s === 0){\n // convert the luminance from [0, 1] to [0, 255]\n const gray = l * 255;\n return [gray, gray, gray];\n }\n\n // check the level of luminance\n const helper1 = (l < 0.5) ?\n (l * (1.0 + s)) :\n (l + s - l * s);\n\n const helper2 = 2 * l - helper1;\n\n const rHelper = h + 0.333;\n const gHelper = h;\n const bHelper = h - 0.333;\n\n let r = hslToRgbHelper(helper1, helper2, rHelper);\n let g = hslToRgbHelper(helper1, helper2, gHelper);\n let b = hslToRgbHelper(helper1, helper2, bHelper);\n\n // convert rgb to [0, 255]\n r *= 255;\n g *= 255;\n b *= 255;\n\n if(r > 255 || g > 255 || b > 255){\n return [255, 255, 255];\n }\n\n if(r < 0 || g < 0 || b < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(r, decimalPlaces),\n setDecimalPlaces(g, decimalPlaces),\n setDecimalPlaces(b, decimalPlaces),\n ];\n};\n\n/**\n * HSL to hex\n * hslToHex(360, 100, 50) // [360, 100, 5] ==> \"#ff0000\" (red)\n */\nexport const hslToHex = (hsl: HSLColor) => {\n\n if(hsl[0] > 360 || hsl[1] > 100 || hsl[2] > 100){\n return '#ffffff';\n }\n\n if(hsl[0] < 0 || hsl[1] < 0 || hsl[2] < 0){\n return '#000000';\n }\n\n const h = hsl[0] / 360;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n let r, g, b;\n if (s === 0) {\n r = g = b = l; // achromatic\n } else {\n const hue2rgb = (p: number, q: number, t: number) => {\n if (t < 0) t += 1;\n if (t > 1) t -= 1;\n if (t < 1 / 6) return p + (q - p) * 6 * t;\n if (t < 1 / 2) return q;\n if (t < 2 / 3) return p + (q - p) * (2 / 3 - t) * 6;\n return p;\n };\n const q = l < 0.5 ? l * (1 + s) : l + s - l * s;\n const p = 2 * l - q;\n r = hue2rgb(p, q, h + 1 / 3);\n g = hue2rgb(p, q, h);\n b = hue2rgb(p, q, h - 1 / 3);\n }\n const toHex = (x: number) => {\n const hex = Math.round(x * 255).toString(16);\n return hex.length === 1 ? '0' + hex : hex;\n };\n\n return `#${toHex(r)}${toHex(g)}${toHex(b)}`;\n};\n\n/**\n * RGB to HEX\n * rgbToHex([235, 64, 52]) // #eb4034\n */\nexport const rgbToHex = (rgb: RGBColor) => {\n const [r, g, b] = rgb;\n return '#' + (1 << 24 | r << 16 | g << 8 | b).toString(16).slice(1);\n};\n\nexport const hexToRgb = (hex: string) : RGBColor | null => {\n\n const shorthandRegex = /^#?([a-f\\d])([a-f\\d])([a-f\\d])$/i;\n const _hex = hex.replace(shorthandRegex, (_m, r, g, b) => {\n return r + r + g + g + b + b;\n });\n\n const result = /^#?([a-f\\d]{2})([a-f\\d]{2})([a-f\\d]{2})$/i.exec(_hex);\n if(!result) return null;\n\n const r = parseInt(result[1], 16);\n const g = parseInt(result[2], 16);\n const b = parseInt(result[3], 16);\n\n return [r, g, b];\n};\n\nexport const rgbToLab = (rgb: RGBColor, decimalPlaces = Infinity) : LABColor => {\n\n let r = rgb[0] / 255;\n let g = rgb[1] / 255;\n let b = rgb[2] / 255;\n\n r = (r > 0.04045) ? Math.pow((r + 0.055) / 1.055, 2.4) : r / 12.92;\n g = (g > 0.04045) ? Math.pow((g + 0.055) / 1.055, 2.4) : g / 12.92;\n b = (b > 0.04045) ? Math.pow((b + 0.055) / 1.055, 2.4) : b / 12.92;\n\n let x = (r * 0.4124 + g * 0.3576 + b * 0.1805) / 0.95047;\n let y = (r * 0.2126 + g * 0.7152 + b * 0.0722) / 1.00000;\n let z = (r * 0.0193 + g * 0.1192 + b * 0.9505) / 1.08883;\n\n x = (x > 0.008856) ? Math.pow(x, 1/3) : (7.787 * x) + 16/116;\n y = (y > 0.008856) ? Math.pow(y, 1/3) : (7.787 * y) + 16/116;\n z = (z > 0.008856) ? Math.pow(z, 1/3) : (7.787 * z) + 16/116;\n\n return [\n setDecimalPlaces((116 * y) - 16, decimalPlaces),\n setDecimalPlaces(500 * (x - y), decimalPlaces),\n setDecimalPlaces(200 * (y - z), decimalPlaces),\n ];\n};\n\nexport const labToRgb = (lab: LABColor, decimalPlaces = Infinity) : RGBColor => {\n let y = (lab[0] + 16) / 116;\n let x = lab[1] / 500 + y;\n let z = y - lab[2] / 200;\n\n x = 0.95047 * ((x * x * x > 0.008856) ? x * x * x : (x - 16/116) / 7.787);\n y = 1.00000 * ((y * y * y > 0.008856) ? y * y * y : (y - 16/116) / 7.787);\n z = 1.08883 * ((z * z * z > 0.008856) ? z * z * z : (z - 16/116) / 7.787);\n\n let r = x * 3.2406 + y * -1.5372 + z * -0.4986;\n let g = x * -0.9689 + y * 1.8758 + z * 0.0415;\n let b = x * 0.0557 + y * -0.2040 + z * 1.0570;\n\n r = (r > 0.0031308) ? (1.055 * Math.pow(r, 1/2.4) - 0.055) : 12.92 * r;\n g = (g > 0.0031308) ? (1.055 * Math.pow(g, 1/2.4) - 0.055) : 12.92 * g;\n b = (b > 0.0031308) ? (1.055 * Math.pow(b, 1/2.4) - 0.055) : 12.92 * b;\n\n return [\n setDecimalPlaces(Math.max(0, Math.min(1, r)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, g)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, b)) * 255, decimalPlaces),\n ];\n};\n\n// ----------------------- GET SHIFTED COLORS --------------------------------------\n\nexport const getShiftedHue = (color: HSLColor, shift = 180) : HSLColor => {\n let hue = color[0];\n hue += shift;\n\n if (hue > 360 || hue < 0) {\n hue = mod(hue, 360);\n }\n\n return [hue, color[1], color[2]];\n};\n\nexport const getShiftedLightness = (color: HSLColor, shift = 10) : HSLColor => {\n let lightness = color[2];\n lightness += shift;\n\n if (lightness > 100 || lightness < 0) {\n lightness = mod(lightness, 100);\n }\n\n return [color[0], color[1], lightness];\n};\n\nexport const getShiftedSaturation = (color: HSLColor, shift = 10) : HSLColor => {\n let saturation = color[1];\n saturation += shift;\n\n if (saturation > 100) {\n saturation -= 100;\n }\n\n if(saturation < 0){\n saturation += 100;\n }\n\n return [color[0], saturation, color[2]];\n};\n\n// ----------------------- SIMILAR COLORS --------------------------------------\n\n/**\n * Measure the perceptual difference between two RGB colors using the CIE76 color difference formula:\n * delta = Math.sqrt((L2 - L1)^2 + (a2 - a1)^2 + (b2 - b1)^2)\n * https://en.wikipedia.org/wiki/Color_difference\n * https://stackoverflow.com/questions/13586999/color-difference-similarity-between-two-values-with-js\n * <= 1.0 Not perceptible by human eyes.\n * 1 - 2 Perceptible through close observation.\n * 2 - 10 Perceptible at a glance.\n * 11 - 49 Colors are more similar than opposite\n * 100 Colors are exact opposite\n */\nexport const getColorsDelta = (rgbA: RGBColor, rgbB: RGBColor, decimalPlaces = Infinity) => {\n const labA = rgbToLab(rgbA, decimalPlaces);\n const labB = rgbToLab(rgbB, decimalPlaces);\n\n // differences between the LAB components of the two colors\n const deltaL = labA[0] - labB[0];\n const deltaA = labA[1] - labB[1];\n const deltaB = labA[2] - labB[2];\n\n // chroma components\n const c1 = Math.sqrt(labA[1] * labA[1] + labA[2] * labA[2]);\n const c2 = Math.sqrt(labB[1] * labB[1] + labB[2] * labB[2]);\n const deltaC = c1 - c2;\n\n // difference in hue, deltaH, which takes into account both the differences\n // in the a* and b* components of LAB and the differences in chroma.\n let deltaH = deltaA * deltaA + deltaB * deltaB - deltaC * deltaC;\n deltaH = deltaH < 0 ? 0 : Math.sqrt(deltaH);\n\n const sc = 1.0 + 0.045 * c1;\n const sh = 1.0 + 0.015 * c1;\n\n // It applies weighting factors to the differences in lightness (deltaL),\n // chroma (deltaC), and hue (deltaH).\n const deltaLKlsl = deltaL / (1.0);\n const deltaCkcsc = deltaC / (sc);\n const deltaHkhsh = deltaH / (sh);\n\n // It computes the final color difference using the CIE76 formula:\n // deltaE = sqrt(deltaLKlsl^2 + deltaCkcsc^2 + deltaHkhsh^2),\n // where deltaLKlsl is the weighted lightness difference,\n // deltaCkcsc is the weighted chroma difference,\n // and deltaHkhsh is the weighted hue difference.\n const i = deltaLKlsl * deltaLKlsl + deltaCkcsc * deltaCkcsc + deltaHkhsh * deltaHkhsh;\n\n // It returns the calculated color difference,\n // optionally rounded to the specified number of decimal places.\n return i < 0 ? 0 : Math.sqrt(i);\n};\n", "/**\n * guid like '932ade5e-c515-4807-ac01-73b20ab3fb66'\n */\nexport const guid = () => {\n return 'xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx'.replace(/[xy]/g, (c) => {\n const r = Math.random() * 16 | 0;\n return (c == 'x' ? r : r & 0x3 | 0x8).toString(16);\n });\n};\n\n/**\n * id like 'df4unio1opulby2uqh4'\n */\nexport const newId = () => {\n return Math.random().toString(36).substring(2) + (new Date()).getTime().toString(36);\n};\n", "import { ICircle, IPolygon, IRect, Matrix2, Vector2 } from '../types';\nimport { mod } from './other';\nimport { v2GetNormal, v2DotProduct } from './linear-algebra/vector';\n\n/**\n * Rectangles collision detection.\n * Rectangles should not be rotated.\n * The algorithm works by ensuring there is no gap between any of the 4 sides of the rectangles.\n * Any gap means a collision does not exist.\n * Returns true if collision is detected.\n */\nexport const rectCollide = (rect1: IRect, rect2: IRect) : boolean => {\n return rect1.x <= rect2.x + rect2.w &&\n rect1.x + rect1.w >= rect2.x &&\n rect1.y <= rect2.y + rect2.h &&\n rect1.h + rect1.y >= rect2.y;\n};\n\n/**\n * Circles collision detection.\n * This algorithm works by taking the center points of the two circles\n * and ensuring the distance between the center points\n * are less than the two radii added together.\n * Returns true if collision is detected.\n */\nexport const circleCollide = (circle1: ICircle, circle2: ICircle) => {\n const dx = Math.abs(circle1.cx - circle2.cx);\n const dy = Math.abs(circle1.cy - circle2.cy);\n const distance = Math.sqrt(dx * dx + dy * dy);\n return distance <= circle1.r + circle2.r;\n};\n\n//-------------------- Separating Axis Theorem (SAT) Collision detection -------------------------\n\nconst getEdges = (poly: IPolygon) : Matrix2[] => {\n const edges: Matrix2[] = [];\n\n for(let i= 0; i {\n const edges: Matrix2[] = [];\n\n // collect polygon edges, and combine then into a single array\n edges.push(...getEdges(poly1));\n edges.push(...getEdges(poly2));\n\n // for each edge, find the normal vector and project both polygons onto it\n for (const edge of edges) {\n const normal = v2GetNormal(edge[0], edge[1]);\n const p1Proj = projectPolygon(poly1, normal);\n const p2Proj = projectPolygon(poly2, normal);\n\n // Check if the projections overlap\n const isOverlap = p1Proj.max >= p2Proj.min && p2Proj.max >= p1Proj.min;\n\n // Check if the projections overlap; if not, the polygons do not collide\n if (!isOverlap) return false;\n }\n\n // If all tests pass, the polygons overlap and collide\n return true;\n};\n\n/**\n * Project every polygon point onto the normal.\n * Then find min and max.\n */\nconst projectPolygon = (polygon: IPolygon, normal: Vector2): { min: number, max: number } => {\n let min = Infinity;\n let max = -Infinity;\n\n // Project each vertex of the polygon onto the axis\n for (const vertex of polygon) {\n const projection = v2DotProduct(vertex, normal);\n min = Math.min(min, projection);\n max = Math.max(max, projection);\n }\n\n return { min, max };\n};", "export interface IAnimationProps {\n duration?: number;\n callback: (result: IAnimationResult) => void;\n restartOnResize?: boolean;\n resizeCallback?: (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => void;\n}\n\nexport interface IAnimationResult {\n start: () => void;\n stop: () => void;\n pause: () => void;\n resume: () => void;\n restart: () => void;\n isAnimating: () => boolean;\n getStartTime: () => number|undefined;\n getElapsedTime: () => number|undefined;\n getPercent: () => number|undefined;\n getResizeObserver: () => ResizeObserver|undefined;\n}\n\nexport const animate = (props: IAnimationProps) : IAnimationResult => {\n\n const _duration = props.duration !== undefined ? props.duration : Infinity;\n\n let startTime: number|undefined = undefined; // in milliseconds\n let animationId: number|undefined = undefined;\n\n // the time elapsed since the start of the animation (in milliseconds)\n let elapsed: number|undefined = undefined;\n let previousTimeStamp: number|undefined = undefined;\n\n let animating = false;\n let observer: ResizeObserver|undefined = undefined;\n\n // -------------------- COMMANDS ---------------------\n\n const stop = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = false;\n\n /*if(observer !== undefined){\n observer.disconnect();\n observer = undefined;\n }*/\n\n if(animationId === undefined) return;\n window.cancelAnimationFrame(animationId);\n };\n\n const restart = () => {\n stop();\n start();\n };\n\n const pause = () => {\n animating = false;\n };\n\n const resume = () => {\n animating = true;\n };\n\n /**\n * Animation Step.\n * @param {number} timeStamp in milliseconds\n */\n const step = (timeStamp: DOMHighResTimeStamp) => {\n\n if (startTime === undefined) {\n startTime = timeStamp;\n }\n\n // the time elapsed since the start of the animation (in milliseconds)\n elapsed = timeStamp - startTime;\n\n if (animating && previousTimeStamp !== timeStamp && typeof props.callback === 'function') {\n\n // do the rendering .............\n props.callback(getResult());\n }\n\n if(elapsed <= _duration){\n previousTimeStamp = timeStamp;\n animationId = window.requestAnimationFrame(step);\n }\n else{\n stop();\n }\n };\n\n const observerHandler = (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => {\n restart();\n\n if(typeof props.resizeCallback === 'function'){\n props.resizeCallback(_entries, _observer);\n }\n };\n\n const start = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = true;\n\n if(props.restartOnResize && window.ResizeObserver && observer === undefined){\n observer = new ResizeObserver(observerHandler);\n observer.observe(document.body, { box: 'border-box' });\n }\n else{\n animationId = window.requestAnimationFrame(step);\n }\n };\n\n // --------------- GET INFO ----------------------\n\n /**\n * the time elapsed since the start of the animation (in milliseconds)\n */\n const getElapsedTime = () : number|undefined => {\n return elapsed;\n };\n\n const isAnimating = () => {\n return animating;\n };\n\n const getStartTime = () => {\n return startTime;\n };\n\n const getPercent = () => {\n if(_duration === Infinity || elapsed === undefined) return undefined;\n return elapsed * 100 / _duration;\n };\n\n const getResizeObserver = () => {\n return observer;\n };\n\n const getResult = () : IAnimationResult => {\n return {\n\n // commands --------------\n start,\n stop,\n pause,\n resume,\n restart,\n\n // information -------\n isAnimating,\n getElapsedTime,\n getStartTime,\n getPercent,\n getResizeObserver,\n };\n };\n\n return getResult();\n};\n", "import { setDecimalPlaces } from './format';\n\nexport const getCircleCircumference = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * radius, decimalPlaces);\n};\n\nexport const getEllipseCircumference = (radius1: number, radius2: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * Math.sqrt((radius1 ** 2 + radius2 ** 2) / 2), decimalPlaces);\n};\n\nexport const isAngleInCircleArc = (startAngleDeg: number, endAngleDeg: number, currentDegrees: number) : boolean => {\n\n if(startAngleDeg > endAngleDeg) {\n endAngleDeg += 360;\n }\n\n return currentDegrees >= startAngleDeg && currentDegrees <= endAngleDeg ||\n (currentDegrees + 360) >= startAngleDeg && (currentDegrees + 360) <= endAngleDeg;\n};\n\n/**\n * get the side of a square inscribed in a circle\n */\nexport const getSquareInCircleSide = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(radius * 2 / Math.sqrt(2), decimalPlaces);\n};\n", "/**\n * 1 + 2 + ... + n = n * (n + 1) / 2\n */\nexport const naturalNumbersSequenceSum = (n: number) => {\n return n * (n + 1) / 2;\n};\n\n/**\n * n = the number of terms to be added\n * a = the first term in the sequence\n * d = the constant value between terms\n */\nexport const arithmeticSequenceSum = (n: number, a: number, d: number) => {\n return (n / 2) * (2 * a + (n - 1) * d);\n};", "import { setDecimalPlaces } from './format';\n\n// -------------------- CENTRAL TENDENCY ----------------------------\n\n/**\n * Central tendency: Calculate the Average (mean = \u03BC)\n * Sum of all numbers divided by the array length.\n */\nexport const getArithmeticMean = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const sum = data.reduce((acc, val) => acc + val, 0);\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Frequency map: number ---> it's frequency\n */\nexport const getArithmeticMeanFromFrequency = (frequencyMap: Map, decimalPlaces = Infinity) => {\n\n let mean = 0;\n\n for(const [val, frequency] of frequencyMap) {\n mean += val * frequency;\n }\n\n return setDecimalPlaces(mean, decimalPlaces);\n};\n\n/**\n * Central tendency: What is the central number in the sorted array?\n * Good for lists like [3, 3, 3, 3, 3, 3, 100] - 100 here is called \"Outlier\"\n */\nexport const getMedian = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const copy = [...data].sort((num1, num2) => num1 - num2);\n const mid = Math.floor(copy.length / 2);\n\n if(copy.length % 2 === 0) {\n return setDecimalPlaces((copy[mid] + copy[mid - 1]) / 2, decimalPlaces);\n }\n else {\n return setDecimalPlaces(copy[mid], decimalPlaces);\n }\n};\n\n/**\n * Central tendency: What number is most common in the set.\n * If all numbers have the same frequency, there is no mode.\n */\nexport const getMode = (data: number[]) : number[]|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n // Count frequency of each number in the data array.\n const frequencyMap: Map = new Map();\n for (const num of data) {\n frequencyMap.set(num, (frequencyMap.get(num) || 0) + 1);\n }\n\n let maxFrequency = 0;\n let modes: number[] = [];\n\n // Find the maximum frequency\n for (const [num, frequency] of frequencyMap) {\n if (frequency > maxFrequency) {\n maxFrequency = frequency;\n modes = [num];\n }\n else if (frequency === maxFrequency) {\n modes.push(num);\n }\n }\n\n // If all numbers have the same frequency, there is no mode\n if (modes.length === data.length) {\n return undefined;\n }\n\n // Return the mode(s)\n return modes.length === 1 ? [modes[0]] : modes;\n};\n\n/*\nTODO:\n- geometric mean\n- harmonic mean\n */\n\n// -------------------- DISPERSION ----------------------------\n\n/**\n * Dispersion: the average square distance from the mean.\n * Sum of (x - mean)^2 / N\n */\nexport const getVariance1 = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + ((val - mean) ** 2), 0);\n\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Another formula of dispersion - the average square distance from the mean.\n * (Sum of x^2) / N - (mean ^ 2)\n */\nexport const getVariance = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + (val ** 2), 0);\n\n return setDecimalPlaces((sum / data.length) - (mean ** 2), decimalPlaces);\n};\n\n/**\n * \u03C3\n */\nexport const getStandardDeviation = (data: number[], decimalPlaces = Infinity) => {\n const variance = getVariance(data) ?? 0;\n return setDecimalPlaces(Math.sqrt(variance), decimalPlaces);\n};", "import { setDecimalPlaces } from './format';\nimport { getArithmeticMean, getStandardDeviation } from './statistics';\nimport { IMlNormalizeResult, IMlStandardizeResult } from '../types';\n\n// --------------------- NORMALIZE --------------------------------\n\n/**\n * Changes value to be in the range [0, 1].\n */\nexport const mlNormalizeValue = (value: number, min: number, max: number, decimalPlaces = Infinity) : number => {\n const diff = max - min;\n if(diff === 0) return 0;\n return setDecimalPlaces((value - min) / diff, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [0, 1].\n */\nexport const mlNormalizeArray = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n const copy = [...data];\n\n for(let i=0; i {\n const min = Math.min(...data);\n const max = Math.max(...data);\n const _data = mlNormalizeArray(data, min, max, decimalPlaces);\n\n return {\n min: setDecimalPlaces(min, decimalPlaces),\n max: setDecimalPlaces(max, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlNormalizeUnseenData = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n return mlNormalizeArray(data, min, max, decimalPlaces);\n};\n\n// --------------------- STANDARDIZE --------------------------------\n\n/**\n * Changes value to be in the range [-1, 1].\n */\nexport const mlStandardizeValue = (value: number, mean: number, stdDev: number, decimalPlaces = Infinity) : number => {\n if(stdDev === 0) return 0;\n return setDecimalPlaces((value - mean) / stdDev, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [-1, 1].\n */\nexport const mlStandardizeArray = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity) : number[] => {\n return [...data].map(value => mlStandardizeValue(value, mean, stdDev, decimalPlaces));\n};\n\nexport const mlStandardizeTestData = (data: number[], decimalPlaces = Infinity): IMlStandardizeResult => {\n const mean = getArithmeticMean(data) ?? 0;\n const stdDev = getStandardDeviation(data);\n const _data = mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n\n return {\n mean: setDecimalPlaces(mean, decimalPlaces),\n stdDev: setDecimalPlaces(stdDev, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlStandardizeUnseenData = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity): number[] => {\n return mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n};", "/**\n * Sum of 1 to n numbers:\n * (n * (n + 1)) / 2\n */\nexport const naturalNumbersSum1ToN = (n: number): number => {\n return (n / 2) * (n + 1);\n};\n\n/**\n * Sum of m to n numbers.\n */\nexport const naturalNumbersSumMToN = (m: number, n: number): number => {\n return (n - m + 1) * (m + n) / 2;\n};"], + "mappings": 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t)r.set(o,(r.get(o)||0)+1);let e=0,n=[];for(let[o,i]of r)i>e?(e=i,n=[o]):i===e&&n.push(o);if(n.length!==t.length)return n.length===1?[n[0]]:n},Qo=(t,r=1/0)=>{if(!t||t.length<=0)return;let e=j(t);if(e===void 0)return;let n=t.reduce((o,i)=>o+V(i-e,2),0);return c(n/t.length,r)},Tr=(t,r=1/0)=>{if(!t||t.length<=0)return;let e=j(t);if(e===void 0)return;let n=t.reduce((o,i)=>o+V(i,2),0);return c(n/t.length-V(e,2),r)},kt=(t,r=1/0)=>{var n;let e=(n=Tr(t))!=null?n:0;return c(Math.sqrt(e),r)};var _t={};h(_t,{mlNormalizeArray:()=>Qt,mlNormalizeTestData:()=>Zo,mlNormalizeUnseenData:()=>_o,mlNormalizeValue:()=>Hr,mlStandardizeArray:()=>Zt,mlStandardizeTestData:()=>Wo,mlStandardizeUnseenData:()=>Uo,mlStandardizeValue:()=>Br});var Hr=(t,r,e,n=1/0)=>{let o=e-r;return o===0?0:c((t-r)/o,n)},Qt=(t,r,e,n=1/0)=>{let o=[...t];for(let i=0;i{let 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"../src/main/linear-algebra/matrix.ts", "../src/main/linear-algebra/matrix-transformations.ts", "../src/main/random.ts", "../src/main/convert.ts", "../src/main/bezier-curves/bezier-curve.ts", "../src/main/derivative.ts", "../src/main/equations/linear-equations.ts", "../src/main/equations/quadratic-equations.ts", "../src/main/path-movement.ts", "../src/main/color.ts", "../src/main/physics.ts", "../src/main/id.ts", "../src/main/collision-detection.ts", "../src/main/animation.ts", "../src/main/circle-ellipse.ts", "../src/main/sequence.ts", "../src/main/statistics.ts", "../src/main/ml.ts", "../src/index.ts"], - "sourcesContent": ["import { Vector, Vector2, Vector3, Vector4 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { getV2Angle, setV2Angle } from '../angle';\n\n// ------------ SUM ------------------------\n\nexport const vSum = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSum(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sum = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSum(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ SUB ------------------------\n\nexport const vSub = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSub(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sub = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSub(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ MUL SCALAR ------------------------\n\nexport const vMulScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n const vector: Vector = [];\n\n for(let i=0; i {\n return vMulScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3MulScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vMulScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ DIVIDE ------------------------\n\nexport const vDivideScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vDivideScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3DivideScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vDivideScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ LENGTH ------------------------\n\nexport const vLength = (vector: Vector, decimalPlaces = Infinity) => {\n let sum = 0;\n\n for(let i=0; i {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v3Length = (vector: Vector3, decimalPlaces = Infinity) => {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v2SetLength = (v2: Vector2, newLength: number, decimalPlaces = Infinity): Vector2 => {\n const angle = getV2Angle(v2);\n return [\n setDecimalPlaces(Math.cos(angle) * newLength, decimalPlaces),\n setDecimalPlaces(Math.sin(angle) * newLength, decimalPlaces),\n ];\n};\n\n// ----------- DISTANCE ------------------------\n\nexport const vDistance = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v2Distance = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v3Distance = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\n// ------------ NORMALIZE ------------------------\n\n/**\n * Normalization creates a unit vector, which is a vector of length 1.\n */\nexport const vNormalize = (v: Vector, decimalPlaces = Infinity) : Vector => {\n const length = vLength(v);\n const unitVector: Vector = [];\n\n for(let i=0; i {\n return vNormalize(v2, decimalPlaces) as Vector2;\n};\n\nexport const v3Normalize = (v3: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vNormalize(v3, decimalPlaces) as Vector3;\n};\n\n// ------------ DOT PRODUCT ------------------------\n\nexport const vDotProduct = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n let sum = 0;\n\n for(let i=0; i {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\nexport const v3DotProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\n// ------------ CROSS PRODUCT ------------------------\n\n/**\n * Cross product is possible on 3D vectors only.\n * The cross product a \u00D7 b is defined as a vector c that is perpendicular (orthogonal) to both a and b.\n */\nexport const v3CrossProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity): Vector3 => {\n return [\n setDecimalPlaces(vector1[1] * vector2[2] - vector1[2] * vector2[1], decimalPlaces),\n setDecimalPlaces(vector1[2] * vector2[0] - vector1[0] * vector2[2], decimalPlaces),\n setDecimalPlaces(vector1[0] * vector2[1] - vector1[1] * vector2[0], decimalPlaces),\n ];\n};\n\n// --------------- INIT VECTOR HELPER -----------------\n\nexport const v2 = (defaultValue = 0): Vector2 => {\n return [defaultValue, defaultValue];\n};\n\nexport const v3 = (defaultValue = 0): Vector3 => {\n return [defaultValue, defaultValue, defaultValue];\n};\n\nexport const v4 = (defaultValue = 0): Vector4 => {\n return [defaultValue, defaultValue, defaultValue, defaultValue];\n};\n\nexport const vN = (N: number, defaultValue = 0): Vector => {\n\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n const vector: Vector = [];\n for(let i=0; i {\n let vector: Vector2 = [0, 0];\n vector = v2SetLength(vector, distance);\n return setV2Angle(vector, angleRad);\n};\n\n// --------------- EQUALITY -------------------------\n\nexport const vEqual = (vector1: Vector, vector2: Vector): boolean => {\n if(vector1.length !== vector2.length) return false;\n\n for(let i=0; i {\n const sub = v2Sub(vector2, vector1);\n return [\n -setDecimalPlaces(sub[1], decimalPlaces),\n setDecimalPlaces(sub[0], decimalPlaces)\n ];\n};", "export const setDecimalPlaces = (num: number, decimalPlaces: number | undefined = Infinity) => {\n if(decimalPlaces === Infinity) return num;\n\n if(decimalPlaces < 0){\n decimalPlaces = 0;\n }\n\n const coefficient = 10 ** decimalPlaces;\n return Math.round(num * coefficient) / coefficient;\n};", "import { Vector, Vector2, Vector3 } from '../types';\nimport { setDecimalPlaces } from './format';\nimport { v2Length, vNormalize, vDotProduct, vSub } from './linear-algebra/vector';\nimport { mod } from './other';\n\nexport const getV2Angle = (v2: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1], v2[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleInEllipse = (v2: Vector2, radii: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1]/radii[1], v2[0]/radii[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const setV2Angle = (v2: Vector2, newAngleRad: number, decimalPlaces = Infinity): Vector2 => {\n const length = v2Length(v2);\n return [\n setDecimalPlaces(Math.cos(newAngleRad) * length, decimalPlaces),\n setDecimalPlaces(Math.sin(newAngleRad) * length, decimalPlaces),\n ];\n};\n\nexport const radiansToDegrees = (radians: number, decimalPlaces = Infinity) => {\n const res = radians * (180 / Math.PI);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\nexport const degreesToRadians = (degrees: number, decimalPlaces = Infinity) => {\n const res = degrees * (Math.PI / 180);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\n/**\n * Returns the range [0, Math.PI]\n * A = Math.acos( dot(v1, v2)/(v1.length()*v2.length()) );\n */\nexport const getVNAngleBetween = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n const unitVector1 = vNormalize(vector1);\n const unitVector2 = vNormalize(vector2);\n const dotProduct = vDotProduct(unitVector1, unitVector2);\n const angle = Math.acos(dotProduct);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleBetween = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) : number => {\n // return getVNAngleBetween(vector1, vector2, decimalPlaces);\n const diff = vSub(vector1, vector2);\n const angle = Math.atan2(diff[1], diff[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV3AngleBetween = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return getVNAngleBetween(vector1, vector2, decimalPlaces);\n};\n\nexport const isAngleBetween = (angleDegrees: number, startAngleDegrees: number, endAngleDegrees: number) : boolean => {\n const distance = getAnglesSub(startAngleDegrees, endAngleDegrees);\n const distance1 = getAnglesSub(startAngleDegrees, angleDegrees);\n const distance2 = getAnglesSub(endAngleDegrees, angleDegrees);\n const totalDistance = distance1 + distance2;\n\n // Use a small threshold for floating point errors\n return Math.abs(totalDistance - distance) <= 0.001;\n}\n\nexport const isClockwise = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n return angle2Deg >= angle1Deg;\n};\n\n/**\n * Shortest distance (angular) between two angles.\n */\nexport const getAnglesSub = (angleDegrees1: number, angleDegrees2: number, decimalPlaces = Infinity) : number => {\n const angleDistance = Math.abs(mod(angleDegrees1, 360) - mod(angleDegrees2, 360));\n return setDecimalPlaces(angleDistance <= 180 ? angleDistance : 360 - angleDistance, decimalPlaces);\n};\n\nexport const getAnglesDistance = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0, decimalPlaces = Infinity) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n if(isClockwise(angle1Deg, angle2Deg, startAngleDeg)) {\n return setDecimalPlaces((angle2Deg - angle1Deg + 360) % 360, decimalPlaces);\n }\n else{\n return setDecimalPlaces((angle1Deg - angle2Deg + 360) % 360, decimalPlaces);\n }\n};\n\nexport const percentToAngle = (percent: number, startAngleDeg: number, endAngleDeg: number, circleStartAngle = 0) => {\n if(percent < 0) {\n percent = 0;\n }\n\n if(percent > 100) {\n percent = 100;\n }\n\n const distance = getAnglesDistance(startAngleDeg, endAngleDeg, circleStartAngle);\n\n const clockwise = isClockwise(startAngleDeg, endAngleDeg, circleStartAngle);\n if(clockwise) {\n return mod(circleStartAngle + (percent * distance / 100), 360);\n }\n else {\n return mod(circleStartAngle - (percent * distance / 100), 360);\n }\n};", "import { Vector2 } from '../types';\nimport { setDecimalPlaces } from './format';\n\nexport const mod = (n: number, m: number) => {\n return ((n % m) + m) % m;\n};\n\n/**\n * Convert range [a, b] to [c, d].\n * f(x) = (d - c) * (x - a) / (b - a) + c\n */\nexport const convertRange = (x: number, a: number, b: number, c: number, d: number) => {\n return (d - c) * (x - a) / (b - a) + c;\n};\n\n/**\n * Check if 2 ranges [a,b] and [c,d] overlap.\n */\nexport const doRangesOverlap = (a: number, b: number, c: number, d: number) => {\n return Math.max(a, c) <= Math.min(b, d) ;\n};\n\n// eslint-disable-next-line\nexport const isNumber = (value: any) => {\n return !isNaN(parseFloat(value)) && isFinite(value);\n};\n\n/**\n * Convert polar coordinates to cartesian coordinates.\n */\nexport const polarToCartesian = (center: Vector2, radii: Vector2, angleInRad: number, decimalPlaces = Infinity) : Vector2 => {\n const [cx, cy] = center;\n const [rx, ry] = radii;\n\n return [\n setDecimalPlaces(cx + (rx * Math.cos(angleInRad)), decimalPlaces),\n setDecimalPlaces(cy + (ry * Math.sin(angleInRad)), decimalPlaces),\n ];\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector, Vector2, Vector3 } from '../../types';\nimport { vMulScalar, vSum, vSub, vDotProduct, vN, vEqual, vDivideScalar } from './vector';\n\n// --------------- SUM ----------------------\n\nexport const mSum = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sum = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- SUB ----------------------\n\nexport const mSub = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sub = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- MUL SCALAR ----------------------\n\nexport const mMulScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vMulScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2MulScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mMulScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3MulScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mMulScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n// --------------- DIVIDE SCALAR ----------------------\n\nexport const mDivideScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vDivideScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2DivideScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mDivideScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3DivideScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mDivideScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n\n// --------------- TRANSPOSE ----------------------\n\nexport const mTranspose = (m: Matrix): Matrix => {\n\n const vectorsCount = m.length;\n if(vectorsCount <= 0) return m;\n\n const vectorLength = m[0].length;\n if(vectorLength <= 0) return m;\n\n const matrix: Matrix = [];\n for(let i=0; i {\n return mTranspose(m2);\n};\n\nexport const m3Transpose = (m3: Matrix3): Matrix => {\n return mTranspose(m3);\n};\n\n// ----------------- RESET ----------------------\n\nexport const mReset = (m: Matrix, defaultValue = 0): Matrix => {\n\n if(m.length <= 0) return [];\n\n const res: Matrix = [];\n\n for(let i=0; i {\n return mReset(m2, defaultValue) as Matrix2;\n};\n\nexport const m3Reset = (m3: Matrix3, defaultValue = 0): Matrix3 => {\n return mReset(m3, defaultValue) as Matrix3;\n};\n\n// --------------- MATRIX INIT HELPERS -----------------\n\nexport const m2x2 = (defaultValue = 0): Matrix2 => {\n return [\n [defaultValue, defaultValue],\n [defaultValue, defaultValue],\n ];\n};\n\nexport const m3x3 = (defaultValue = 0): Matrix3 => {\n return [\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const m4x4 = (defaultValue = 0): Matrix4 => {\n return [\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const mNxM = (N: number, M: number, defaultValue = 0): Matrix => {\n if(N <= 0 || M <= 0){\n throw new Error('M and N must be positive numbers.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return [\n [1, 0],\n [0, 1],\n ];\n};\n\nexport const identity3 = (): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\nexport const identity4 = (): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Identity Matrix (I).\n * M x I = I x M = M for any matrix M.\n * Identity Matrix is a special case of scale matrix.\n */\nexport const identityN = (N: number): Matrix => {\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n if(N === 0) return [];\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mDeepCopy(m2) as Matrix2;\n};\n\nexport const m3DeepCopy = (m3: Matrix3): Matrix3 => {\n return mDeepCopy(m3) as Matrix3;\n};\n\n// -------------- APPEND / PREPEND ROW OR COLUMN ---------------\n\nexport const mAppendCol = (m: Matrix, col: Vector): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n const copy = mDeepCopy(m);\n copy.push(row);\n return copy;\n};\n\nexport const m2AppendRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.push(row);\n return copy;\n};\n\nexport const m3AppendRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.push(row);\n return copy;\n};\n\nexport const mPrependRow = (m: Matrix, row: Vector) : Matrix => {\n const copy = mDeepCopy(m);\n copy.unshift(row);\n return copy;\n};\n\nexport const m2PrependRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.unshift(row);\n return copy;\n};\n\nexport const m3PrependRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.unshift(row);\n return copy;\n};\n\n// ------------ DELETE ROW OR COLUMN ----------------------------\n\nexport const mDelLastRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.pop();\n return copy;\n};\n\nexport const mDelFirstRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.shift();\n return copy;\n};\n\nexport const mDelLastColumn = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const size = m[0].length;\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n\n const matrix: Matrix = [];\n for(let i=0; i {\n\n if(matrix.length < 0) return [];\n\n if(matrix[0].length !== vector.length){\n throw new Error('The number of columns in the matrix must be equal to the length of the vector.');\n }\n\n const res: Vector = [];\n\n for(let i=0; i {\n if(matrix1.length !== matrix2.length) return false;\n\n for(let i=0; i returns matrix N (m-1 x m-1)\n * The matrix must be square.\n */\nconst mMinorHelper = (m: Matrix, row: number, col: number) => {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // prepare the matrix without provided row and column\n const matrix = mMinorHelper(m, row, col);\n\n // calculate the matrix determinant\n return mDeterminant(matrix);\n};\n\n/**\n * Calculate determinant for NxN matrix.\n * Matrix should be square.\n */\nexport const mDeterminant = (matrix: Matrix): number => {\n const size = matrix.length;\n if(size === 0) return 1;\n\n if(size !== matrix[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return matrix[0][0];\n if(size === 2) return m2Determinant(matrix as Matrix2);\n\n let d = 0;\n\n for(let i=0; i {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return m2[0][0] * m2[1][1] - m2[1][0] * m2[0][1];\n};\n\n/**\n * Calculate determinant for 3x3 matrix.\n * Matrix should be square.\n */\nexport const m3Determinant = (m3: Matrix3): number => {\n if(m3.length !== m3[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return mDeterminant(m3);\n};\n\n// ------------------ INVERSE -----------------------\n\nexport const m2Adjugate = (m2: Matrix2): Matrix2|null => {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return [\n [m2[1][1], -m2[0][1]],\n [-m2[1][0], m2[0][0]],\n ];\n};\n\nexport const m3Adjugate = (m3: Matrix3) : Matrix3|null => {\n return mAdjugate(m3) as (Matrix3|null);\n};\n\n/**\n * Adjugate is a transpose of a cofactor matrix\n */\nexport const mAdjugate = (m: Matrix): Matrix|null => {\n\n const size = m.length;\n if(size <= 0) return null;\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return m;\n\n if(size === 2) return m2Adjugate(m as Matrix2);\n\n // build a cofactor matrix ----------------\n const cofactors: Matrix = [];\n\n for(let i=0; i {\n if(m.length > 0 && m.length !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = mDeterminant(m);\n return d === 0;\n};\n\n/**\n * Square matrix A (nxn) is invertible is there is another square matrix B (nxn) so AxB = BxA = I\n * For A (2x2) matrix, the inverse is:\n * (1 / (determinant(A))) * adj(A)\n */\nexport const m2Inverse = (m2: Matrix2, decimalPlaces = Infinity): (Matrix2 | null) => {\n if(m2.length > 0 && m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = m2Determinant(m2);\n if(d === 0) return null;\n\n const adj = m2Adjugate(m2);\n if(adj === null) return null;\n\n return m2DivideScalar(adj, d, decimalPlaces);\n};\n\nexport const m3Inverse = (m3: Matrix3, decimalPlaces = Infinity): (Matrix3 | null) => {\n return mInverse(m3, decimalPlaces) as (Matrix3|null);\n};\n\nexport const mInverse = (m: Matrix, decimalPlaces = Infinity): (Matrix | null) => {\n const size = m.length;\n\n if(size > 0 && size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // find a determinant ----------------------\n const d = mDeterminant(m);\n\n // find an Adjugate - a transpose of a cofactor matrix\n const adj = mAdjugate(m);\n if(adj === null) return null;\n\n return mDivideScalar(adj, d, decimalPlaces);\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector2, Vector3, Vector4 } from '../../types';\nimport { v2Normalize, v3MulScalar, v3Normalize } from './vector';\nimport { mMulVector, mMul } from './matrix';\nimport { setDecimalPlaces } from '../format';\n\n/*\nAny 2D affine transformation can be decomposed\ninto a rotation, followed by a scaling, followed by a\nshearing, and followed by a translation.\n---------------------------------------------------------\nAffine matrix = translation x shearing x scaling x rotation\n */\n\n// ----------------- CSS -------------------------------------\n\n/**\n * Matrix 2D in non-homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2ToCSS = (m: Matrix2) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, 0, 0)`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2hToCSS = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, ${ tx }, ${ ty })`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m2hToCSS3d = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix3d(${ a }, ${ b }, 0, 0, ${ c }, ${ d }, 0, 0, 0, 0, 1, 0, ${ tx }, ${ ty }, 0, 1)`;\n};\n\n/**\n * Matrix 3D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m3hToCSS3d = (m: Matrix4) : string => {\n\n return `matrix3d(\n ${ m[0][0] }, ${ m[0][1] }, ${ m[0][2] }, ${ m[0][3] },\n ${ m[1][0] }, ${ m[1][1] }, ${ m[1][2] }, ${ m[1][3] },\n ${ m[2][0] }, ${ m[2][1] }, ${ m[2][2] }, ${ m[2][3] },\n ${ m[3][0] }, ${ m[3][1] }, ${ m[3][2] }, ${ m[3][3] }\n )`;\n};\n\n// ---------------- TRANSLATION MATRICES ----------------------\n\nexport const m2Translation = (position: Vector2, decimalPlaces = Infinity): Matrix2 => {\n\n return [\n [1, 0],\n [0, 1],\n [setDecimalPlaces(position[0], decimalPlaces), setDecimalPlaces(position[1], decimalPlaces)],\n ];\n};\n\nexport const m3Translation = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n [\n setDecimalPlaces(position[0], decimalPlaces),\n setDecimalPlaces(position[1], decimalPlaces),\n setDecimalPlaces(position[2], decimalPlaces)\n ],\n ];\n};\n\n/**\n * 2D Translation matrix in homogeneous coordinates.\n */\nexport const m2TranslationH = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1],\n ];\n};\n\n/**\n * 3D Translation matrix in homogeneous coordinates.\n */\nexport const m3TranslationH = (position: Vector4, decimalPlaces = Infinity): Matrix4 => {\n\n return [\n [1, 0, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, 0, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1, setDecimalPlaces(position[2], decimalPlaces)],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- ROTATION MATRICES -------------------------\n\n/**\n * Rotation of an angle about the origin.\n */\nexport const m2Rotation = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix2 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin],\n [sin, cos],\n ] :\n [\n [cos, sin],\n [-sin, cos],\n ];\n};\n\n/**\n * Rotation of an angle about the origin in homogeneous coordinates (clockwise).\n */\nexport const m2RotationH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ]:\n [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation of an angle \"angleRad\" around the given point (transformOrigin) in homogeneous coordinates (clockwise).\n * result_vector = TranslationMatrix(x, y) * RotationMatrix() * TranslationMatrix(-x, -y) * position_vector\n */\nexport const m2RotationAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const rotation = m2RotationH(angleRad, isClockwise, decimalPlaces);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, rotation);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2RotateAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n position: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2RotationAroundPointH(angleRad, transformOrigin, isClockwise, decimalPlaces);\n return mMulVector(mat3h, position) as Vector3;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2Rotate = (angleRad: number, vector: Vector2, isClockwise = true, decimalPlaces = Infinity): Vector2 => {\n const unitVector = v2Normalize(vector);\n return mMulVector(m2Rotation(angleRad, isClockwise, decimalPlaces), unitVector) as Vector2;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2RotateH = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m2RotationH(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the X axis (clockwise).\n */\nexport const m3RotationX = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0],\n [0, cos, -sin],\n [0, sin, cos],\n ] :\n [\n [1, 0, 0],\n [0, cos, sin],\n [0, -sin, cos],\n ];\n};\n\n/**\n * Rotation around the X axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationXH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0, 0],\n [0, cos, -sin, 0],\n [0, sin, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [1, 0, 0, 0],\n [0, cos, sin, 0],\n [0, -sin, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateX = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationX(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Y axis (clockwise).\n */\nexport const m3RotationY = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin],\n [0, 1, 0],\n [-sin, 0, cos],\n ] :\n [\n [cos, 0, -sin],\n [0, 1, 0],\n [sin, 0, cos],\n ];\n};\n\n/**\n * Rotation around the Y axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationYH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin, 0],\n [0, 1, 0, 0],\n [-sin, 0, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [cos, 0, -sin, 0],\n [0, 1, 0, 0],\n [sin, 0, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateY = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationY(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Z axis (clockwise).\n */\nexport const m3RotationZ = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ] : [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation around the Z axis (clockwise)- in homogeneous coordinates\n */\nexport const m3RotationZH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0, 0],\n [sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ] : [\n [cos, sin, 0, 0],\n [-sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateZ = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationZ(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n// ---------------- SCALE MATRICES -------------\n\n/**\n * Get matrix for arbitrary scaling pivot point.\n * result_vector = TranslationMatrix(x, y) * ScaleMatrix() * TranslationMatrix(-x, -y) * scale_vector\n */\nexport const m2ScaleAtPointHMatrix = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const scale = m2ScaleH(scaleVector);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, scale);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2ScaleAtPointH = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n point: Vector3,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2ScaleAtPointHMatrix(scaleVector, transformOrigin, decimalPlaces);\n return mMulVector(mat3h, point) as Vector3;\n};\n\nexport const m2Scale = (scaleVector: Vector2): Matrix2 => {\n return [\n [scaleVector[0], 0],\n [0, scaleVector[1]],\n ];\n};\n\nexport const v2Scale = (scaleVector: Vector2, vector: Vector2): Vector2 => {\n return mMulVector(m2Scale(scaleVector), vector) as Vector2;\n};\n\n/**\n * homogeneous coordinates\n */\nexport const m2ScaleH = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, 1],\n ];\n};\n\nexport const m3Scale = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, scaleVector[2]],\n ];\n};\n\nexport const m3ScaleH = (scaleVector: Vector4): Matrix4 => {\n return [\n [scaleVector[0], 0, 0, 0],\n [0, scaleVector[1], 0, 0],\n [0, 0, scaleVector[2], 0],\n [0, 0, 0, 1]\n ];\n};\n\nexport const v3Scale = (scaleVector: Vector3, vector: Vector3): Vector3 => {\n return mMulVector(m3Scale(scaleVector), vector) as Vector3;\n};\n\n/**\n * Stretch, parallel to the x-axis.\n */\nexport const m2ScaleX = (scale: number): Matrix2 => {\n return [\n [scale, 0],\n [0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the x-axis - homogeneous coordinates\n */\nexport const m2ScaleXH = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleX = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleXH = (scale: number): Matrix4 => {\n return [\n [scale, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleY = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleYH = (scale: number): Matrix => {\n return [\n [1, 0, 0, 0],\n [0, scale, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZ = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, scale],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZH = (scale: number): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, scale, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis.\n */\nexport const m2ScaleY = (scale: number): Matrix2 => {\n return [\n [1, 0],\n [0, scale],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis - homogeneous coordinates\n */\nexport const m2ScaleYH = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n// ---------------- REFLECTION MATRICES -------------------------\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOrigin = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOriginH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection about the origin in non-homogeneous coordinates\n */\nexport const m3ReflectionOrigin = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection about the origin in homogeneous coordinates\n */\nexport const m3ReflectionOriginH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection about y=-x\n */\nexport const m2ReflectionYmX = (): Matrix2 => {\n\n return [\n [0, -1],\n [-1, 0],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionX = (): Matrix2 => {\n\n return [\n [1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionXH = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection in the y-axis.\n */\nexport const m2ReflectionY = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, 1],\n ];\n};\n\nexport const m2ReflectionYH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionYZ = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in homogeneous coordinates\n */\nexport const m3ReflectionYZH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXZ = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in homogeneous coordinates\n */\nexport const m3ReflectionXZH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXY = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in homogeneous coordinates\n */\nexport const m3ReflectionXYH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- SHEARING MATRICES -------------------------\n\n\n/**\n * Shearing in y-axis, with x-axis fixed with (0,1) moving to (factor, 1)\n */\nexport const m2ShearingY = (factor: number): Matrix2 => {\n\n return [\n [1, factor],\n [0, 1],\n ];\n};\n\n/**\n * Shearing in x-axis, with y-axis fixed with (1,0) moving to (1, factor)\n */\nexport const m2ShearingX = (factor: number): Matrix2 => {\n\n return [\n [1, 0],\n [factor, 1],\n ];\n};", "import { setDecimalPlaces } from './format';\n\n/**\n * Returns a random number in the [min,max] range.\n */\nexport const getRandom = (min: number, max: number, decimalPlaces = Infinity): number => {\n return setDecimalPlaces(Math.random() * (max - min) + min, decimalPlaces);\n};\n\n/**\n * Returns a random integer number in the [min,max] range.\n */\nexport const getRandomInt = (min: number, max: number): number => {\n return Math.floor(Math.random() * (max - min + 1) + min);\n};\n\nexport const getRandomBoolean = () => Math.random() < 0.5;\n\n/* eslint-disable @typescript-eslint/no-explicit-any */\nexport const getRandomItemFromArray = (array: any[]) => {\n const randomIndex = getRandomInt(0, array.length - 1);\n return array[randomIndex];\n};", "export const stringToNumber = (value: string|undefined|null|number, defaultNumber: number) => {\n if(value === undefined || value === null) return defaultNumber;\n const res = Number(value) ?? defaultNumber;\n return isNaN(res) ? defaultNumber : res;\n};", "import { IBBox, Vector, Vector2, Vector3 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport {\n dxV2CubicBezierCurve,\n dxV2QuadraticBezierCurve,\n dxV3CubicBezierCurve,\n dxV3QuadraticBezierCurve\n} from '../derivative';\nimport { v2Normalize, v3Normalize } from '../linear-algebra/vector';\nimport { linearEquation } from '../equations/linear-equations';\nimport { quadraticEquation } from '../equations/quadratic-equations';\nimport { isNumber } from '../other';\n\n/**\n * B\u00E9zier Curves\n * quadratic: y = P1 * (1-t)\u00B2 + P2 * 2 * (1-t)t + P3 * t\u00B2\n * t in range [0, 1]\n */\n\n// -------------------- GET POINT ON CURVE --------------------------\n\n/**\n * Get a point on a quadratic B\u00E9zier curve as a function of time.\n */\nexport const v2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n/**\n * Get a point on a cubic B\u00E9zier curve as a function of time.\n */\nexport const v2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n// -------------------- TANGENT --------------------------\n\n/**\n * Tangent indicates the direction of travel at specific points along the B\u00E9zier curve,\n * and is literally just the first derivative of our curve.\n */\nexport const v2QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\nexport const v2CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\n// -------------------- NORMAL --------------------------\n\n/**\n * Normal is a vector that runs at a right angle to the direction of the curve, and is typically of length 1.\n * To find it, we take the normalised tangent vector, and then rotate it by a 90 degrees.\n */\nexport const v2QuadraticBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2QuadraticBezierCurveTangent(t, startControlPoint, centerControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\nexport const v2CubicBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2CubicBezierCurveTangent(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\n// -------------------- EXTREMA --------------------------\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2QuadraticBezierCurveExtrema = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector => {\n\n /*\n (-2 * (1 - t)) * startControlPoint[0] + (2 - 4 * t) * centerControlPoint[0] + (2 * t) * endControlPoint[0]\n 2 * t * startControlPoint[0] - 4 * t * centerControlPoint[0] + 2 * t * endControlPoint[0] - 2 * startControlPoint[0] + 2 * centerControlPoint[0]\n t * (2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0]) + (- 2 * startControlPoint[0] + 2 * centerControlPoint[0])\n */\n\n const a1 = 2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0];\n const b1 = -2 * startControlPoint[0] + 2 * centerControlPoint[0];\n const equation1: Vector3 = [a1, b1, 0];\n const res1 = linearEquation(equation1, decimalPlaces);\n\n const a2 = 2 * startControlPoint[1] - 4 * centerControlPoint[1] + 2 * endControlPoint[1];\n const b2 = -2 * startControlPoint[1] + 2 * centerControlPoint[1];\n const equation2: Vector3 = [a2, b2, 0];\n const res2 = linearEquation(equation2, decimalPlaces);\n\n const res: Vector = [];\n\n if(isNumber(res1)){\n res.push(res1);\n }\n\n if(isNumber(res2)){\n res.push(res2);\n }\n\n return res;\n};\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2CubicBezierCurveExtrema = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2|null => {\n\n const a1 = -3 * startControlPoint[0] + 9 * center1ControlPoint[0] - 9 * center2ControlPoint[0] + 3 * endControlPoint[0];\n const b1 = 6 * startControlPoint[0] - 12 * center1ControlPoint[0] + 6 * center2ControlPoint[0];\n const c1 = -3 * startControlPoint[0] + 3 * center1ControlPoint[0];\n const equation1: Vector = [a1, b1, c1, 0];\n\n const a2 = -3 * startControlPoint[1] + 9 * center1ControlPoint[1] - 9 * center2ControlPoint[1] + 3 * endControlPoint[1];\n const b2 = 6 * startControlPoint[1] - 12 * center1ControlPoint[1] + 6 * center2ControlPoint[1];\n const c2 = -3 * startControlPoint[1] + 3 * center1ControlPoint[1];\n const equation2: Vector = [a2, b2, c2, 0];\n\n // Any value between 0 and 1 is a root that matters for B\u00E9zier curves, anything below or above that is irrelevant (because B\u00E9zier curves are only defined over the interval [0,1]).\n const res1 = quadraticEquation(equation1, decimalPlaces).filter(num => num >= 0 && num <= 1);\n const res2 = quadraticEquation(equation2, decimalPlaces).filter(num => num >= 0 && num <= 1);\n\n const res = [...res1, ...res2];\n if(res.length === 2){\n return [...res1, ...res2] as Vector2;\n }\n\n return null;\n};\n\n// -------------------- BOUNDING BOX --------------------------\n\nexport const v2QuadraticBezierBBox = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2QuadraticBezierCurveExtrema(startControlPoint, centerControlPoint, endControlPoint);\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2QuadraticBezierCurve(percent, startControlPoint, centerControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x);\n maxX = Math.max(maxX, x);\n\n minY = Math.min(minY, y);\n maxY = Math.max(maxY, y);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\nexport const v2CubicBezierBBox = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2CubicBezierCurveExtrema(startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint) || [];\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2CubicBezierCurve(percent, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x ?? Infinity);\n maxX = Math.max(maxX, x ?? -Infinity);\n\n minY = Math.min(minY, y ?? Infinity);\n maxY = Math.max(maxY, y ?? -Infinity);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\n\n", "import { setDecimalPlaces } from './format';\nimport { Vector2, Vector3 } from '../types';\n\n/**\n * u(x) and v(x) are functions ---------->\n *\n * dx(u + v) = dx(u) + dx(v)\n * dx(u - v) = dx(u) - dx(v)\n * dx(u * v) = dx(u) * v + u * dx(v)\n * dx(u / v) = (dx(u) * v - u * dx(v)) / (v ^ 2), when v(x) != 0\n */\n\n// ------------------ Derivatives of Polynomial ---------------------------\n\n/**\n * y = 3x+2\n * dxPolynomial(10, [[3, 1], [2, 0]])\n */\nexport const dxPolynomial = (x: number, polynomial: number[][], decimalPlaces = Infinity) => {\n let res = 0;\n\n for(const part of polynomial){\n if(part.length !== 2) return NaN;\n\n const coeff = part[0];\n const power = part[1];\n res += coeff * power * Math.pow(x, power - 1);\n }\n\n return setDecimalPlaces(res, decimalPlaces);\n}\n\n// ---------------------- Bezier Curves ---------------------------\n\n/**\n * Derivative of Bezier Curve is another Bezier Curve.\n * t must min in range [0, 1]\n */\nexport const dxV2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n // The derivative: P1 * (2t-2) + (2*P3-4*P2) * t + 2 * P2\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\nexport const dxV2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n\n// ----------------- Derivatives of trigonometry functions ---------------------------\n\nexport const dxSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(Math.cos(x), decimalPlaces);\n};\n\nexport const dxCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-Math.sin(x), decimalPlaces);\n};\n\nexport const dxTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.cos(x) ** 2), decimalPlaces);\n};\n\n/**\n * x != Math.PI * n, where n is an integer\n */\nexport const dxCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sin(x) ** 2), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\nexport const dxArcTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (1 + x ** 2), decimalPlaces);\n};\n\nexport const dxArcCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (1 + x ** 2), decimalPlaces);\n};\n", "import { Matrix, Matrix2, Matrix3, Vector, Vector2, Vector3 } from '../../types';\nimport { m2Inverse, m3Inverse, mInverse, mMulVector, mDelLastColumn, mGetLastColumn } from '../linear-algebra/matrix';\nimport { setDecimalPlaces } from '../format';\nimport { v2Sub } from '../linear-algebra/vector';\n\n/**\n * Linear equation\n * ax + b = c\n * x = (c - b) / a; a != 0\n */\nexport const linearEquation = (equation: Vector3, decimalPlaces = Infinity) : number => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n\n const diff = c - b;\n\n if(a === 0 && diff === 0) return Infinity; // any number is a solution\n if(a === 0) return NaN; // no solution\n\n return setDecimalPlaces(diff / a, decimalPlaces);\n};\n\n/**\n * System of 2 linear equations.\n * [x, y] = inverse(Matrix of equation parameters) x (vector of equation results)\n * ---------------\n * 3x + 2y = 7\n * -6x + 6y = 6\n */\nexport const linearEquationSystem2 = (equation1: Vector3, equation2: Vector3, decimalPlaces = Infinity) : Vector2 | null => {\n const equationParams: Matrix2 = [\n [equation1[0], equation1[1]],\n [equation2[0], equation2[1]],\n ];\n\n const inversed = m2Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector2 = [\n equation1[2],\n equation2[2]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector2;\n};\n\n/**\n * System of 3 linear equations.\n * ---------------------------------------\n * 3x + 2y + 5z = 7\n * -6x + 6y + 6z = 6\n * 2x + 7y - z = 4\n */\nexport const linearEquationSystem3 = (\n equation1: Vector,\n equation2: Vector,\n equation3: Vector,\n decimalPlaces = Infinity) : Vector3 | null => {\n const equationParams: Matrix3 = [\n [equation1[0], equation1[1], equation1[2]],\n [equation2[0], equation2[1], equation2[2]],\n [equation3[0], equation3[1], equation3[2]],\n ];\n\n const inversed = m3Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector3 = [\n equation1[3],\n equation2[3],\n equation3[3]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector3;\n};\n\n/**\n * System of N linear equations.\n */\nexport const linearEquationSystemN = (equations: Matrix, decimalPlaces = Infinity) : Vector | null => {\n if(equations.length <= 0) return null;\n\n const equationParams = mDelLastColumn(equations);\n\n const inversed = mInverse(equationParams);\n if(inversed === null) return null; // no results\n\n // the last column of the equations matrix\n const equationResults = mGetLastColumn(equations);\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector;\n};\n\n/**\n * Calculate the equation of a line given two points in a 2D space.\n * y = ax + b\n * y - y1 = m(x - x1)\n * m = (y2 - y1) / (x2 - x1)\n */\nexport const getLinearEquationBy2Points = (point1: Vector2, point2: Vector2) : {\n slope: number|undefined,\n yIntercept: number|undefined,\n xIntercept: number|undefined,\n formula: string,\n} => {\n const [deltaX, deltaY] = v2Sub(point2, point1);\n const [x, y] = point1;\n\n if(deltaX === 0) {\n return {\n slope: undefined,\n xIntercept: x,\n yIntercept: undefined,\n formula: `x = ${ x }`,\n };\n }\n\n const m = deltaY / deltaX;\n const b = y - m * x;\n let formula = '';\n\n if(m === 0) {\n formula = `y = ${ b }`;\n }\n else{\n formula = `y = ${ m === 1 ? '' : m }x`;\n\n if(b !== 0) {\n formula += ` ${ b < 0 ? '-' : '+' } ${ Math.abs(b) }`;\n }\n }\n\n return {\n slope: m,\n xIntercept: undefined,\n yIntercept: b,\n formula,\n };\n};", "import { Vector } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { linearEquation } from './linear-equations';\nimport { isNumber } from '../other';\n\n/**\n * Quadratic Equation.\n * ax^2 + bx + c = d\n */\nexport const quadraticEquation = (equation: Vector, decimalPlaces = Infinity) : Vector => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n const d = equation[3];\n\n if(a === 0){\n // it's a linear equation -------------------------------------------\n const res = linearEquation([b, c, d], decimalPlaces);\n if(isNumber(res)) return [res];\n return [];\n }\n\n const diff = c - d;\n\n const discriminant = b * b - (4 * a * diff);\n\n if(discriminant < 0){\n return []; // no results\n }\n\n if(discriminant === 0){\n return [ setDecimalPlaces(-b / (2 * a), decimalPlaces) ]; // 1 result\n }\n\n // if(determinant > 0) ---> 2 results\n const t1 = 2 * a;\n const t2 = Math.sqrt(discriminant);\n\n return [\n setDecimalPlaces((-b + t2) / t1, decimalPlaces),\n setDecimalPlaces((-b - t2) / t1, decimalPlaces),\n ];\n};", "import { Vector2 } from '../types';\nimport { v2Sub } from './linear-algebra/vector';\nimport { getV2Angle } from './angle';\nimport { convertRange } from './other';\n\n/**\n * Circle Equation\n * x^2 + y^2 = radius^2\n * ----------------------\n * Circle Parametric Equation\n * x(t) = radius * cos(t)\n * y(t) = radius * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const circleMovement = (center: Vector2, angle: number, radius: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius,\n center[1] + Math.sin(angle) * radius\n ];\n};\n\n/**\n * Circle Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const circleMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radius: number\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return circleMovement(center, angle, radius);\n};\n\n/**\n * Ellipse Equation\n * (x - centerX)^2 / (radius1^2) + (y - centerY)^2 / (radius2^2) = 1\n * -----------------------------------------------------------------\n * Ellipse Parametric Equation\n * x(t) = radius1 * cos(t)\n * y(t) = radius2 * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const ellipseMovement = (center: Vector2, angle: number, radius1: number, radius2: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius1,\n center[1] + Math.sin(angle) * radius2\n ];\n};\n\n/**\n * Ellipse Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const ellipseMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radii: Vector2\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return ellipseMovement(center, angle, radii[0], radii[1]);\n};\n\n/**\n * Sine Wave Equation (Sinusoid)\n * -----------------------------\n * const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n * amplitude = the peak deviation of the function from zero\n * frequency = number of cycles\n * phase = specifies (in radians) where in its cycle the oscillation is at t = 0.\n * think of it as \"shifting\" the starting point of the function to the right (positive p) or left (negative)\n */\nexport const sineWaveMovement = (x: number, amplitude: number, frequency: number, phase: number) : Vector2 => {\n /*\n example values:\n const amplitude = 50;\n const frequency = 0.005;\n const phase = 0;\n x: [0, 1000]\n */\n const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n\n return [x, y];\n};\n\n/**\n * Lissajous curve (Lissajous figure or Bowditch curve)\n * Parametric equation #1\n * f(t) = A * sin(k * t + m)\n * f(t) = B * sin(n * t)\n * 0 <= m <= PI/2\n * k, n >= 1\n * -----------------------\n * Parametric equation #2\n * f(t) = A * cos(k * t - m)\n * f(t) = B * cos(n * t - p)\n * -----------------------------\n * Shapes:\n * k = 1, n = 1, m = 0, p = 0 ---> line\n * A = B, k = 1, n = 1, m = PI/2, p = PI/2 ----> circle\n * A != B, k = 1, n = 1, m = PI/2, p = PI/2 ----> ellipse\n * k = 2, n = 2, m = PI/2, p = PI/2 ----> section of a parabola\n */\nexport const lissajousCurve = (\n width: number,\n height: number,\n t: number,\n k: number,\n n: number,\n m: number,\n p: number\n) :Vector2 => {\n return [\n width * Math.cos(k * t - m),\n height * Math.cos(n * t - p),\n ];\n};\n", "import { getRandom } from './random';\nimport { HSLColor, LABColor, RGBColor } from '../types';\nimport { mod } from './other';\nimport { setDecimalPlaces } from './format';\n\n// ------------------------ RANDOM COLOR -------------------------------------\n\nexport const getRandomRGBColor = () : RGBColor => {\n const hslColor = getRandomHSLColor();\n return hslToRgb(hslColor);\n};\n\nexport const getRandomHexColor = () : string => {\n const hslColor = getRandomHSLColor();\n return hslToHex(hslColor);\n};\n\nexport const getRandomHSLColor = () : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given hue\n */\nexport const getRandomHSLColorWithHue = (h: number) : HSLColor => {\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given saturation\n */\nexport const getRandomHSLColorWithSaturation = (s: number) : HSLColor => {\n const h = getRandom(1, 360);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given lightness\n */\nexport const getRandomHSLColorWithLightness = (l: number) : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n return [h, s, l];\n};\n\nexport const getRandomGrayscaleHSLColor = () : HSLColor => {\n const l = getRandom(0, 100);\n return [0, 0, l];\n};\n\nexport const getRandomHSLColorWithinRanges = (\n hueStart = 1, hueEnd = 360,\n saturationStart = 0, saturationEnd = 100,\n lightStart = 0, lightEnd = 100\n) : HSLColor => {\n const h = getRandom(hueStart, hueEnd);\n const s = getRandom(saturationStart, saturationEnd);\n const l = getRandom(lightStart, lightEnd);\n return [h, s, l];\n};\n\n// ----------------------- CONVERT COLORS --------------------------------------\n\n/**\n * helper: convert hue value to degrees.\n * @param {number} h\n * @return {number} [0, 360] degrees\n */\nconst convertHueToDegrees = (h : number) : number => {\n\n // the hue value needs to be multiplied by 60 to convert it to degrees\n h *= 60;\n\n // if hue becomes negative, you need to add 360 to, because a circle has 360 degrees\n if(h < 0){\n h += 360;\n }\n\n return h;\n // convert huw to %\n // return h * 100 / 360;\n};\n\n/**\n * get hue from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] % - we use here % instead of [0, 359] degrees\n */\nconst getHue = (r : number, g : number, b : number, min : number | undefined = undefined, max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (max === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no hue, as it's gray\n if(min === max) return 0;\n\n const diff = max - min;\n\n let h = 0;\n\n // if red is max\n if(max === r){\n h = (g - b) / diff + (g < b ? 6 : 0);\n }\n\n // if green is max\n if(max === g){\n h = 2 + (b - r) / diff;\n }\n\n // if blue is max\n if(max === b){\n h = 4 + (r - g) / diff;\n }\n\n return convertHueToDegrees(h);\n};\n\n/**\n * get luminance from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] %\n */\nconst getLuminance = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // calculate the luminance value\n // @ts-ignore\n const l = (min + max) / 2; // [0, 1]\n\n // return l value in %\n return l * 100;\n};\n\n/**\n * get saturation from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @param {number|undefined=} l - luminance in [0, 100] %\n * @return {number} [0, 100] %\n */\nconst getSaturation = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined,\n l : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no saturation, as it's gray\n if(min === max) return 0;\n\n // calculate luminance if it's not provided\n l = (l === undefined) ? getLuminance(r, g, b) : l;\n\n // check the level of luminance\n const s = (l <= 50) ?\n // @ts-ignore\n ((max - min) / (max + min)) : // this formula is used when luminance <= 50%\n // @ts-ignore\n (max - min) / (2.0 - max - min); // this formula is used when luminance > 50%\n\n // return saturation in %\n return s * 100;\n};\n\nexport const rgbToHsl = (rgb: RGBColor, decimalPlaces = Infinity): HSLColor => {\n\n // convert rgb values to the range [0, 1]\n const r = rgb[0] / 255;\n const g = rgb[1] / 255;\n const b = rgb[2] / 255;\n\n // find the minimum and maximum values of r, g, and b\n const min = Math.min(r, g, b);\n const max = Math.max(r, g, b);\n\n // calculate the luminance value in %\n const l = getLuminance(r, g, b, min, max);\n\n // calculate the saturation in %\n const s = getSaturation(r, g, b, min, max, l);\n\n // calculate the hue in % (not in degrees!)\n const h = getHue(r, g, b, min, max);\n\n if(h > 360 || s > 100 || l > 100){\n return [0, 0, 100];\n }\n\n if(h < 0 || s < 0 || l < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(h, decimalPlaces),\n setDecimalPlaces(s, decimalPlaces),\n setDecimalPlaces(l, decimalPlaces),\n ];\n};\n\n/**\n * helper: HSL to RGB\n */\nconst hslToRgbHelper = (helper1 : number, helper2 : number, colorHelper : number) : number => {\n\n // all values need to be between 0 and 1\n // if you get a negative value you need to add 1 to it\n if(colorHelper < 0) colorHelper += 1;\n\n // if you get a value above 1 you need to subtract 1 from it.\n if(colorHelper > 1) colorHelper -= 1;\n\n if(colorHelper * 6 < 1) return helper2 + (helper1 - helper2) * 6 * colorHelper;\n\n if(colorHelper * 2 < 1) return helper1;\n\n if(colorHelper * 3 < 2){\n return helper2 + (helper1 - helper2) * (0.666 - colorHelper) * 6;\n }\n else{\n return helper2;\n }\n};\n\nexport const hslToRgb = (hsl: HSLColor, decimalPlaces = Infinity): RGBColor => {\n\n // convert all values to [0, 1] from %\n const h = hsl[0] / 100;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n // if there is no saturation -> it\u2019s grey\n if(s === 0){\n // convert the luminance from [0, 1] to [0, 255]\n const gray = l * 255;\n return [gray, gray, gray];\n }\n\n // check the level of luminance\n const helper1 = (l < 0.5) ?\n (l * (1.0 + s)) :\n (l + s - l * s);\n\n const helper2 = 2 * l - helper1;\n\n const rHelper = h + 0.333;\n const gHelper = h;\n const bHelper = h - 0.333;\n\n let r = hslToRgbHelper(helper1, helper2, rHelper);\n let g = hslToRgbHelper(helper1, helper2, gHelper);\n let b = hslToRgbHelper(helper1, helper2, bHelper);\n\n // convert rgb to [0, 255]\n r *= 255;\n g *= 255;\n b *= 255;\n\n if(r > 255 || g > 255 || b > 255){\n return [255, 255, 255];\n }\n\n if(r < 0 || g < 0 || b < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(r, decimalPlaces),\n setDecimalPlaces(g, decimalPlaces),\n setDecimalPlaces(b, decimalPlaces),\n ];\n};\n\n/**\n * HSL to hex\n * hslToHex(360, 100, 50) // [360, 100, 5] ==> \"#ff0000\" (red)\n */\nexport const hslToHex = (hsl: HSLColor) => {\n\n if(hsl[0] > 360 || hsl[1] > 100 || hsl[2] > 100){\n return '#ffffff';\n }\n\n if(hsl[0] < 0 || hsl[1] < 0 || hsl[2] < 0){\n return '#000000';\n }\n\n const h = hsl[0] / 360;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n let r, g, b;\n if (s === 0) {\n r = g = b = l; // achromatic\n } else {\n const hue2rgb = (p: number, q: number, t: number) => {\n if (t < 0) t += 1;\n if (t > 1) t -= 1;\n if (t < 1 / 6) return p + (q - p) * 6 * t;\n if (t < 1 / 2) return q;\n if (t < 2 / 3) return p + (q - p) * (2 / 3 - t) * 6;\n return p;\n };\n const q = l < 0.5 ? l * (1 + s) : l + s - l * s;\n const p = 2 * l - q;\n r = hue2rgb(p, q, h + 1 / 3);\n g = hue2rgb(p, q, h);\n b = hue2rgb(p, q, h - 1 / 3);\n }\n const toHex = (x: number) => {\n const hex = Math.round(x * 255).toString(16);\n return hex.length === 1 ? '0' + hex : hex;\n };\n\n return `#${toHex(r)}${toHex(g)}${toHex(b)}`;\n};\n\n/**\n * RGB to HEX\n * rgbToHex([235, 64, 52]) // #eb4034\n */\nexport const rgbToHex = (rgb: RGBColor) => {\n const [r, g, b] = rgb;\n return '#' + (1 << 24 | r << 16 | g << 8 | b).toString(16).slice(1);\n};\n\nexport const hexToRgb = (hex: string) : RGBColor | null => {\n\n const shorthandRegex = /^#?([a-f\\d])([a-f\\d])([a-f\\d])$/i;\n const _hex = hex.replace(shorthandRegex, (_m, r, g, b) => {\n return r + r + g + g + b + b;\n });\n\n const result = /^#?([a-f\\d]{2})([a-f\\d]{2})([a-f\\d]{2})$/i.exec(_hex);\n if(!result) return null;\n\n const r = parseInt(result[1], 16);\n const g = parseInt(result[2], 16);\n const b = parseInt(result[3], 16);\n\n return [r, g, b];\n};\n\nexport const rgbToLab = (rgb: RGBColor, decimalPlaces = Infinity) : LABColor => {\n\n let r = rgb[0] / 255;\n let g = rgb[1] / 255;\n let b = rgb[2] / 255;\n\n r = (r > 0.04045) ? Math.pow((r + 0.055) / 1.055, 2.4) : r / 12.92;\n g = (g > 0.04045) ? Math.pow((g + 0.055) / 1.055, 2.4) : g / 12.92;\n b = (b > 0.04045) ? Math.pow((b + 0.055) / 1.055, 2.4) : b / 12.92;\n\n let x = (r * 0.4124 + g * 0.3576 + b * 0.1805) / 0.95047;\n let y = (r * 0.2126 + g * 0.7152 + b * 0.0722) / 1.00000;\n let z = (r * 0.0193 + g * 0.1192 + b * 0.9505) / 1.08883;\n\n x = (x > 0.008856) ? Math.pow(x, 1/3) : (7.787 * x) + 16/116;\n y = (y > 0.008856) ? Math.pow(y, 1/3) : (7.787 * y) + 16/116;\n z = (z > 0.008856) ? Math.pow(z, 1/3) : (7.787 * z) + 16/116;\n\n return [\n setDecimalPlaces((116 * y) - 16, decimalPlaces),\n setDecimalPlaces(500 * (x - y), decimalPlaces),\n setDecimalPlaces(200 * (y - z), decimalPlaces),\n ];\n};\n\nexport const labToRgb = (lab: LABColor, decimalPlaces = Infinity) : RGBColor => {\n let y = (lab[0] + 16) / 116;\n let x = lab[1] / 500 + y;\n let z = y - lab[2] / 200;\n\n x = 0.95047 * ((x * x * x > 0.008856) ? x * x * x : (x - 16/116) / 7.787);\n y = 1.00000 * ((y * y * y > 0.008856) ? y * y * y : (y - 16/116) / 7.787);\n z = 1.08883 * ((z * z * z > 0.008856) ? z * z * z : (z - 16/116) / 7.787);\n\n let r = x * 3.2406 + y * -1.5372 + z * -0.4986;\n let g = x * -0.9689 + y * 1.8758 + z * 0.0415;\n let b = x * 0.0557 + y * -0.2040 + z * 1.0570;\n\n r = (r > 0.0031308) ? (1.055 * Math.pow(r, 1/2.4) - 0.055) : 12.92 * r;\n g = (g > 0.0031308) ? (1.055 * Math.pow(g, 1/2.4) - 0.055) : 12.92 * g;\n b = (b > 0.0031308) ? (1.055 * Math.pow(b, 1/2.4) - 0.055) : 12.92 * b;\n\n return [\n setDecimalPlaces(Math.max(0, Math.min(1, r)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, g)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, b)) * 255, decimalPlaces),\n ];\n};\n\n// ----------------------- GET SHIFTED COLORS --------------------------------------\n\nexport const getShiftedHue = (color: HSLColor, shift = 180) : HSLColor => {\n let hue = color[0];\n hue += shift;\n\n if (hue > 360 || hue < 0) {\n hue = mod(hue, 360);\n }\n\n return [hue, color[1], color[2]];\n};\n\nexport const getShiftedLightness = (color: HSLColor, shift = 10) : HSLColor => {\n let lightness = color[2];\n lightness += shift;\n\n if (lightness > 100 || lightness < 0) {\n lightness = mod(lightness, 100);\n }\n\n return [color[0], color[1], lightness];\n};\n\nexport const getShiftedSaturation = (color: HSLColor, shift = 10) : HSLColor => {\n let saturation = color[1];\n saturation += shift;\n\n if (saturation > 100) {\n saturation -= 100;\n }\n\n if(saturation < 0){\n saturation += 100;\n }\n\n return [color[0], saturation, color[2]];\n};\n\n// ----------------------- SIMILAR COLORS --------------------------------------\n\n/**\n * Measure the perceptual difference between two RGB colors using the CIE76 color difference formula:\n * delta = Math.sqrt((L2 - L1)^2 + (a2 - a1)^2 + (b2 - b1)^2)\n * https://en.wikipedia.org/wiki/Color_difference\n * https://stackoverflow.com/questions/13586999/color-difference-similarity-between-two-values-with-js\n * <= 1.0 Not perceptible by human eyes.\n * 1 - 2 Perceptible through close observation.\n * 2 - 10 Perceptible at a glance.\n * 11 - 49 Colors are more similar than opposite\n * 100 Colors are exact opposite\n */\nexport const getColorsDelta = (rgbA: RGBColor, rgbB: RGBColor, decimalPlaces = Infinity) => {\n const labA = rgbToLab(rgbA, decimalPlaces);\n const labB = rgbToLab(rgbB, decimalPlaces);\n\n // differences between the LAB components of the two colors\n const deltaL = labA[0] - labB[0];\n const deltaA = labA[1] - labB[1];\n const deltaB = labA[2] - labB[2];\n\n // chroma components\n const c1 = Math.sqrt(labA[1] * labA[1] + labA[2] * labA[2]);\n const c2 = Math.sqrt(labB[1] * labB[1] + labB[2] * labB[2]);\n const deltaC = c1 - c2;\n\n // difference in hue, deltaH, which takes into account both the differences\n // in the a* and b* components of LAB and the differences in chroma.\n let deltaH = deltaA * deltaA + deltaB * deltaB - deltaC * deltaC;\n deltaH = deltaH < 0 ? 0 : Math.sqrt(deltaH);\n\n const sc = 1.0 + 0.045 * c1;\n const sh = 1.0 + 0.015 * c1;\n\n // It applies weighting factors to the differences in lightness (deltaL),\n // chroma (deltaC), and hue (deltaH).\n const deltaLKlsl = deltaL / (1.0);\n const deltaCkcsc = deltaC / (sc);\n const deltaHkhsh = deltaH / (sh);\n\n // It computes the final color difference using the CIE76 formula:\n // deltaE = sqrt(deltaLKlsl^2 + deltaCkcsc^2 + deltaHkhsh^2),\n // where deltaLKlsl is the weighted lightness difference,\n // deltaCkcsc is the weighted chroma difference,\n // and deltaHkhsh is the weighted hue difference.\n const i = deltaLKlsl * deltaLKlsl + deltaCkcsc * deltaCkcsc + deltaHkhsh * deltaHkhsh;\n\n // It returns the calculated color difference,\n // optionally rounded to the specified number of decimal places.\n return i < 0 ? 0 : Math.sqrt(i);\n};\n", "import { Vector2 } from '../types';\n\n/**\n * Speed = how far something moves in a given amount of time.\n * Speed is also a vector:\n * magnitude = distance\n * direction = time\n */\nexport type Speed = Vector2;\n\n/**\n * Velocity is a measure of how fast an object is moving in a particular direction.\n * Velocity = Distance traveled / Time taken\n * It has a magnitude and direction, and can be represented as a vector.\n */\nexport type Velocity = Vector2;\n\n/**\n * Acceleration is a measure of how quickly an object's velocity changes over time.\n * Acceleration = (Final velocity - Initial velocity) / Time taken\n * a = (vf - v0)/t.\n * Distance = Initial velocity * time + (acceleration * time^2) / 2\n * It also has a magnitude and direction, and can be represented as a vector.\n * When the direction is negative ----> it's a \"slowdown\" movement\n */\nexport type Acceleration = Vector2;\n\n/**\n * Gravity is the force that attracts two objects with mass toward each other.\n * Newton's law of universal gravitation formula:\n * Gravitational force = (Gravitational constant * Mass of object 1 * Mass of object 2) / Distance between objects^2\n * It also has a magnitude and direction, and can be represented as a vector.\n * magnitude = the strength of the gravitational force\n * direction = the direction in which the force is acting (the direction of the gravitational force is always toward the center of mass of the objects involved)\n */\nexport type Gravity = Vector2;\n\n", "/**\n * guid like '932ade5e-c515-4807-ac01-73b20ab3fb66'\n */\nexport const guid = () => {\n return 'xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx'.replace(/[xy]/g, (c) => {\n const r = Math.random() * 16 | 0;\n return (c == 'x' ? r : r & 0x3 | 0x8).toString(16);\n });\n};\n\n/**\n * id like 'df4unio1opulby2uqh4'\n */\nexport const newId = () => {\n return Math.random().toString(36).substring(2) + (new Date()).getTime().toString(36);\n};\n", "import { ICircle, IPolygon, IRect, Matrix2, Vector2 } from '../types';\nimport { mod } from './other';\nimport { v2GetNormal, v2DotProduct } from './linear-algebra/vector';\n\n/**\n * Rectangles collision detection.\n * Rectangles should not be rotated.\n * The algorithm works by ensuring there is no gap between any of the 4 sides of the rectangles.\n * Any gap means a collision does not exist.\n * Returns true if collision is detected.\n */\nexport const rectCollide = (rect1: IRect, rect2: IRect) : boolean => {\n return rect1.x <= rect2.x + rect2.w &&\n rect1.x + rect1.w >= rect2.x &&\n rect1.y <= rect2.y + rect2.h &&\n rect1.h + rect1.y >= rect2.y;\n};\n\n/**\n * Circles collision detection.\n * This algorithm works by taking the center points of the two circles\n * and ensuring the distance between the center points\n * are less than the two radii added together.\n * Returns true if collision is detected.\n */\nexport const circleCollide = (circle1: ICircle, circle2: ICircle) => {\n const dx = Math.abs(circle1.cx - circle2.cx);\n const dy = Math.abs(circle1.cy - circle2.cy);\n const distance = Math.sqrt(dx * dx + dy * dy);\n return distance <= circle1.r + circle2.r;\n};\n\n//-------------------- Separating Axis Theorem (SAT) Collision detection -------------------------\n\nconst getEdges = (poly: IPolygon) : Matrix2[] => {\n const edges: Matrix2[] = [];\n\n for(let i= 0; i {\n const edges: Matrix2[] = [];\n\n // collect polygon edges, and combine then into a single array\n edges.push(...getEdges(poly1));\n edges.push(...getEdges(poly2));\n\n // for each edge, find the normal vector and project both polygons onto it\n for (const edge of edges) {\n const normal = v2GetNormal(edge[0], edge[1]);\n const p1Proj = projectPolygon(poly1, normal);\n const p2Proj = projectPolygon(poly2, normal);\n\n // Check if the projections overlap\n const isOverlap = p1Proj.max >= p2Proj.min && p2Proj.max >= p1Proj.min;\n\n // Check if the projections overlap; if not, the polygons do not collide\n if (!isOverlap) return false;\n }\n\n // If all tests pass, the polygons overlap and collide\n return true;\n};\n\n/**\n * Project every polygon point onto the normal.\n * Then find min and max.\n */\nconst projectPolygon = (polygon: IPolygon, normal: Vector2): { min: number, max: number } => {\n let min = Infinity;\n let max = -Infinity;\n\n // Project each vertex of the polygon onto the axis\n for (const vertex of polygon) {\n const projection = v2DotProduct(vertex, normal);\n min = Math.min(min, projection);\n max = Math.max(max, projection);\n }\n\n return { min, max };\n};", "export interface IAnimationProps {\n duration?: number;\n callback: (result: IAnimationResult) => void;\n restartOnResize?: boolean;\n resizeCallback?: (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => void;\n}\n\nexport interface IAnimationResult {\n start: () => void;\n stop: () => void;\n pause: () => void;\n resume: () => void;\n restart: () => void;\n isAnimating: () => boolean;\n getStartTime: () => number|undefined;\n getElapsedTime: () => number|undefined;\n getPercent: () => number|undefined;\n getResizeObserver: () => ResizeObserver|undefined;\n}\n\nexport const animate = (props: IAnimationProps) : IAnimationResult => {\n\n const _duration = props.duration !== undefined ? props.duration : Infinity;\n\n let startTime: number|undefined = undefined; // in milliseconds\n let animationId: number|undefined = undefined;\n\n // the time elapsed since the start of the animation (in milliseconds)\n let elapsed: number|undefined = undefined;\n let previousTimeStamp: number|undefined = undefined;\n\n let animating = false;\n let observer: ResizeObserver|undefined = undefined;\n\n // -------------------- COMMANDS ---------------------\n\n const stop = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = false;\n\n /*if(observer !== undefined){\n observer.disconnect();\n observer = undefined;\n }*/\n\n if(animationId === undefined) return;\n window.cancelAnimationFrame(animationId);\n };\n\n const restart = () => {\n stop();\n start();\n };\n\n const pause = () => {\n animating = false;\n };\n\n const resume = () => {\n animating = true;\n };\n\n /**\n * Animation Step.\n * @param {number} timeStamp in milliseconds\n */\n const step = (timeStamp: DOMHighResTimeStamp) => {\n\n if (startTime === undefined) {\n startTime = timeStamp;\n }\n\n // the time elapsed since the start of the animation (in milliseconds)\n elapsed = timeStamp - startTime;\n\n if (animating && previousTimeStamp !== timeStamp && typeof props.callback === 'function') {\n\n // do the rendering .............\n props.callback(getResult());\n }\n\n if(elapsed <= _duration){\n previousTimeStamp = timeStamp;\n animationId = window.requestAnimationFrame(step);\n }\n else{\n stop();\n }\n };\n\n const observerHandler = (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => {\n restart();\n\n if(typeof props.resizeCallback === 'function'){\n props.resizeCallback(_entries, _observer);\n }\n };\n\n const start = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = true;\n\n if(props.restartOnResize && window.ResizeObserver && observer === undefined){\n observer = new ResizeObserver(observerHandler);\n observer.observe(document.body, { box: 'border-box' });\n }\n else{\n animationId = window.requestAnimationFrame(step);\n }\n };\n\n // --------------- GET INFO ----------------------\n\n /**\n * the time elapsed since the start of the animation (in milliseconds)\n */\n const getElapsedTime = () : number|undefined => {\n return elapsed;\n };\n\n const isAnimating = () => {\n return animating;\n };\n\n const getStartTime = () => {\n return startTime;\n };\n\n const getPercent = () => {\n if(_duration === Infinity || elapsed === undefined) return undefined;\n return elapsed * 100 / _duration;\n };\n\n const getResizeObserver = () => {\n return observer;\n };\n\n const getResult = () : IAnimationResult => {\n return {\n\n // commands --------------\n start,\n stop,\n pause,\n resume,\n restart,\n\n // information -------\n isAnimating,\n getElapsedTime,\n getStartTime,\n getPercent,\n getResizeObserver,\n };\n };\n\n return getResult();\n};\n", "import { setDecimalPlaces } from './format';\n\nexport const getCircleCircumference = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * radius, decimalPlaces);\n};\n\nexport const getEllipseCircumference = (radius1: number, radius2: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * Math.sqrt((radius1 ** 2 + radius2 ** 2) / 2), decimalPlaces);\n};\n\nexport const isAngleInCircleArc = (startAngleDeg: number, endAngleDeg: number, currentDegrees: number) : boolean => {\n\n if(startAngleDeg > endAngleDeg) {\n endAngleDeg += 360;\n }\n\n return currentDegrees >= startAngleDeg && currentDegrees <= endAngleDeg ||\n (currentDegrees + 360) >= startAngleDeg && (currentDegrees + 360) <= endAngleDeg;\n};\n\n/**\n * get the side of a square inscribed in a circle\n */\nexport const getSquareInCircleSide = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(radius * 2 / Math.sqrt(2), decimalPlaces);\n};\n", "/**\n * 1 + 2 + ... + n = n * (n + 1) / 2\n */\nexport const naturalNumbersSequenceSum = (n: number) => {\n return n * (n + 1) / 2;\n};\n\n/**\n * n = the number of terms to be added\n * a = the first term in the sequence\n * d = the constant value between terms\n */\nexport const arithmeticSequenceSum = (n: number, a: number, d: number) => {\n return (n / 2) * (2 * a + (n - 1) * d);\n};", "import { setDecimalPlaces } from './format';\n\n// -------------------- CENTRAL TENDENCY ----------------------------\n\n/**\n * Central tendency: Calculate the Average (mean = \u03BC)\n * Sum of all numbers divided by the array length.\n */\nexport const getArithmeticMean = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const sum = data.reduce((acc, val) => acc + val, 0);\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Frequency map: number ---> it's frequency\n */\nexport const getArithmeticMeanFromFrequency = (frequencyMap: Map, decimalPlaces = Infinity) => {\n\n let mean = 0;\n\n for(const [val, frequency] of frequencyMap) {\n mean += val * frequency;\n }\n\n return setDecimalPlaces(mean, decimalPlaces);\n};\n\n/**\n * Central tendency: What is the central number in the sorted array?\n * Good for lists like [3, 3, 3, 3, 3, 3, 100] - 100 here is called \"Outlier\"\n */\nexport const getMedian = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const copy = [...data].sort((num1, num2) => num1 - num2);\n const mid = Math.floor(copy.length / 2);\n\n if(copy.length % 2 === 0) {\n return setDecimalPlaces((copy[mid] + copy[mid - 1]) / 2, decimalPlaces);\n }\n else {\n return setDecimalPlaces(copy[mid], decimalPlaces);\n }\n};\n\n/**\n * Central tendency: What number is most common in the set.\n * If all numbers have the same frequency, there is no mode.\n */\nexport const getMode = (data: number[]) : number[]|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n // Count frequency of each number in the data array.\n const frequencyMap: Map = new Map();\n for (const num of data) {\n frequencyMap.set(num, (frequencyMap.get(num) || 0) + 1);\n }\n\n let maxFrequency = 0;\n let modes: number[] = [];\n\n // Find the maximum frequency\n for (const [num, frequency] of frequencyMap) {\n if (frequency > maxFrequency) {\n maxFrequency = frequency;\n modes = [num];\n }\n else if (frequency === maxFrequency) {\n modes.push(num);\n }\n }\n\n // If all numbers have the same frequency, there is no mode\n if (modes.length === data.length) {\n return undefined;\n }\n\n // Return the mode(s)\n return modes.length === 1 ? [modes[0]] : modes;\n};\n\n/*\nTODO:\n- geometric mean\n- harmonic mean\n */\n\n// -------------------- DISPERSION ----------------------------\n\n/**\n * Dispersion: the average square distance from the mean.\n * Sum of (x - mean)^2 / N\n */\nexport const getVariance1 = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + ((val - mean) ** 2), 0);\n\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Another formula of dispersion - the average square distance from the mean.\n * (Sum of x^2) / N - (mean ^ 2)\n */\nexport const getVariance = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + (val ** 2), 0);\n\n return setDecimalPlaces((sum / data.length) - (mean ** 2), decimalPlaces);\n};\n\n/**\n * \u03C3\n */\nexport const getStandardDeviation = (data: number[], decimalPlaces = Infinity) => {\n const variance = getVariance(data) ?? 0;\n return setDecimalPlaces(Math.sqrt(variance), decimalPlaces);\n};", "import { setDecimalPlaces } from './format';\nimport { getArithmeticMean, getStandardDeviation } from './statistics';\nimport { IMlNormalizeResult, IMlStandardizeResult } from '../types';\n\n// --------------------- NORMALIZE --------------------------------\n\n/**\n * Changes value to be in the range [0, 1].\n */\nexport const mlNormalizeValue = (value: number, min: number, max: number, decimalPlaces = Infinity) : number => {\n const diff = max - min;\n if(diff === 0) return 0;\n return setDecimalPlaces((value - min) / diff, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [0, 1].\n */\nexport const mlNormalizeArray = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n const copy = [...data];\n\n for(let i=0; i {\n const min = Math.min(...data);\n const max = Math.max(...data);\n const _data = mlNormalizeArray(data, min, max, decimalPlaces);\n\n return {\n min: setDecimalPlaces(min, decimalPlaces),\n max: setDecimalPlaces(max, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlNormalizeUnseenData = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n return mlNormalizeArray(data, min, max, decimalPlaces);\n};\n\n// --------------------- STANDARDIZE --------------------------------\n\n/**\n * Changes value to be in the range [-1, 1].\n */\nexport const mlStandardizeValue = (value: number, mean: number, stdDev: number, decimalPlaces = Infinity) : number => {\n if(stdDev === 0) return 0;\n return setDecimalPlaces((value - mean) / stdDev, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [-1, 1].\n */\nexport const mlStandardizeArray = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity) : number[] => {\n return [...data].map(value => mlStandardizeValue(value, mean, stdDev, decimalPlaces));\n};\n\nexport const mlStandardizeTestData = (data: number[], decimalPlaces = Infinity): IMlStandardizeResult => {\n const mean = getArithmeticMean(data) ?? 0;\n const stdDev = getStandardDeviation(data);\n const _data = mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n\n return {\n mean: setDecimalPlaces(mean, decimalPlaces),\n stdDev: setDecimalPlaces(stdDev, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlStandardizeUnseenData = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity): number[] => {\n return mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n};", "import * as vector from './main/linear-algebra/vector';\nimport * as matrix from './main/linear-algebra/matrix';\nimport * as matrixTransformations from './main/linear-algebra/matrix-transformations';\nimport * as format from './main/format';\nimport * as angle from './main/angle';\nimport * as random from './main/random';\nimport * as other from './main/other';\nimport * as convert from './main/convert';\nimport * as bezierCurve from './main/bezier-curves/bezier-curve';\nimport * as equations from './main/equations/linear-equations';\nimport * as pathMovement from './main/path-movement';\nimport * as color from './main/color';\nimport * as physics from './main/physics';\nimport * as id from './main/id';\nimport * as derivative from './main/derivative';\nimport * as collisions from './main/collision-detection';\nimport * as animation from './main/animation';\nimport * as circleEllipse from './main/circle-ellipse';\nimport * as sequence from './main/sequence';\nimport * as statistics from './main/statistics';\nimport * as ml from './main/ml';\n\nconst api = {\n ...vector,\n ...matrix,\n ...matrixTransformations,\n ...format,\n ...angle,\n ...random,\n ...other,\n ...convert,\n ...bezierCurve,\n ...equations,\n ...pathMovement,\n ...color,\n ...physics,\n ...id,\n ...derivative,\n ...collisions,\n ...animation,\n ...circleEllipse,\n ...sequence,\n ...statistics,\n ...ml,\n};\n\ndeclare global {\n interface Window {\n mzMath: typeof api,\n }\n}\n\nwindow.mzMath = window.mzMath || api;\n\nexport * from './main/linear-algebra/vector';\nexport * from './main/linear-algebra/matrix';\nexport * from './main/linear-algebra/matrix-transformations';\nexport * from './main/format';\nexport * from './main/angle';\nexport * from './main/random';\nexport * from './main/other';\nexport * from './main/convert';\nexport * from './main/bezier-curves/bezier-curve';\nexport * from './main/equations/linear-equations';\nexport * from './main/path-movement';\nexport * from './main/color';\nexport * from './main/physics';\nexport * from './main/id';\nexport * from 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"id_exports", "__export", "guid", "newId", "c", "collision_detection_exports", "__export", "circleCollide", "convexPolygonsCollide", "rectCollide", "rectCollide", "rect1", "rect2", "circleCollide", "circle1", "circle2", "dx", "dy", "getEdges", "poly", "edges", "i", "nextIndex", "mod", "edge", "convexPolygonsCollide", "poly1", "poly2", "normal", "v2GetNormal", "p1Proj", "projectPolygon", "p2Proj", "polygon", "min", "max", "vertex", "projection", "v2DotProduct", "animation_exports", "__export", "animate", "props", "_duration", "startTime", "animationId", "elapsed", "previousTimeStamp", "animating", "observer", "stop", "restart", "start", "pause", "resume", "step", "timeStamp", "getResult", "observerHandler", "_entries", "_observer", "getElapsedTime", "isAnimating", "getStartTime", "getPercent", "getResizeObserver", "circle_ellipse_exports", "__export", "getCircleCircumference", "getEllipseCircumference", "getSquareInCircleSide", "isAngleInCircleArc", "getCircleCircumference", "radius", "decimalPlaces", "setDecimalPlaces", "getEllipseCircumference", "radius1", "radius2", "__pow", "isAngleInCircleArc", "startAngleDeg", "endAngleDeg", "currentDegrees", "getSquareInCircleSide", "sequence_exports", "__export", "arithmeticSequenceSum", "naturalNumbersSequenceSum", "n", "a", "d", "statistics_exports", "__export", "getArithmeticMean", "getArithmeticMeanFromFrequency", "getMedian", "getMode", "getStandardDeviation", "getVariance", "getVariance1", "getArithmeticMean", "data", "decimalPlaces", "sum", "acc", "val", "setDecimalPlaces", "getArithmeticMeanFromFrequency", "frequencyMap", "mean", "frequency", "getMedian", "copy", "num1", "num2", "mid", "getMode", "num", "maxFrequency", "modes", "getVariance1", "__pow", "getVariance", "getStandardDeviation", "_a", "variance", "ml_exports", "__export", "mlNormalizeArray", "mlNormalizeTestData", "mlNormalizeUnseenData", "mlNormalizeValue", "mlStandardizeArray", "mlStandardizeTestData", "mlStandardizeUnseenData", "mlStandardizeValue", "mlNormalizeValue", "value", "min", "max", "decimalPlaces", "diff", "setDecimalPlaces", "mlNormalizeArray", "data", "copy", "mlNormalizeTestData", "_data", "mlNormalizeUnseenData", "mlStandardizeValue", "mean", "stdDev", "mlStandardizeArray", "mlStandardizeTestData", "_a", "getArithmeticMean", "getStandardDeviation", "mlStandardizeUnseenData", "api", "__spreadValues", "vector_exports", "matrix_exports", "matrix_transformations_exports", "format_exports", "angle_exports", "random_exports", "other_exports", "convert_exports", "bezier_curve_exports", "linear_equations_exports", "path_movement_exports", "color_exports", "physics_exports", "id_exports", "derivative_exports", "collision_detection_exports", "animation_exports", "circle_ellipse_exports", "sequence_exports", "statistics_exports", "ml_exports"] + "sources": ["../src/main/linear-algebra/vector.ts", "../src/main/format.ts", "../src/main/angle.ts", "../src/main/other.ts", "../src/main/linear-algebra/matrix.ts", "../src/main/linear-algebra/matrix-transformations.ts", "../src/main/random.ts", "../src/main/convert.ts", "../src/main/bezier-curves/bezier-curve.ts", "../src/main/derivative.ts", "../src/main/equations/linear-equations.ts", "../src/main/equations/quadratic-equations.ts", "../src/main/path-movement.ts", "../src/main/color.ts", "../src/main/physics.ts", "../src/main/id.ts", "../src/main/collision-detection.ts", "../src/main/animation.ts", "../src/main/circle-ellipse.ts", "../src/main/sequence.ts", "../src/main/statistics.ts", "../src/main/ml.ts", "../src/main/series.ts", "../src/index.ts"], + "sourcesContent": ["import { Vector, Vector2, Vector3, Vector4 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { getV2Angle, setV2Angle } from '../angle';\n\n// ------------ SUM ------------------------\n\nexport const vSum = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSum(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sum = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSum(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ SUB ------------------------\n\nexport const vSub = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSub(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sub = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSub(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ MUL SCALAR ------------------------\n\nexport const vMulScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n const vector: Vector = [];\n\n for(let i=0; i {\n return vMulScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3MulScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vMulScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ DIVIDE ------------------------\n\nexport const vDivideScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vDivideScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3DivideScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vDivideScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ LENGTH ------------------------\n\nexport const vLength = (vector: Vector, decimalPlaces = Infinity) => {\n let sum = 0;\n\n for(let i=0; i {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v3Length = (vector: Vector3, decimalPlaces = Infinity) => {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v2SetLength = (v2: Vector2, newLength: number, decimalPlaces = Infinity): Vector2 => {\n const angle = getV2Angle(v2);\n return [\n setDecimalPlaces(Math.cos(angle) * newLength, decimalPlaces),\n setDecimalPlaces(Math.sin(angle) * newLength, decimalPlaces),\n ];\n};\n\n// ----------- DISTANCE ------------------------\n\nexport const vDistance = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v2Distance = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v3Distance = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\n// ------------ NORMALIZE ------------------------\n\n/**\n * Normalization creates a unit vector, which is a vector of length 1.\n */\nexport const vNormalize = (v: Vector, decimalPlaces = Infinity) : Vector => {\n const length = vLength(v);\n const unitVector: Vector = [];\n\n for(let i=0; i {\n return vNormalize(v2, decimalPlaces) as Vector2;\n};\n\nexport const v3Normalize = (v3: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vNormalize(v3, decimalPlaces) as Vector3;\n};\n\n// ------------ DOT PRODUCT ------------------------\n\nexport const vDotProduct = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n let sum = 0;\n\n for(let i=0; i {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\nexport const v3DotProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\n// ------------ CROSS PRODUCT ------------------------\n\n/**\n * Cross product is possible on 3D vectors only.\n * The cross product a \u00D7 b is defined as a vector c that is perpendicular (orthogonal) to both a and b.\n */\nexport const v3CrossProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity): Vector3 => {\n return [\n setDecimalPlaces(vector1[1] * vector2[2] - vector1[2] * vector2[1], decimalPlaces),\n setDecimalPlaces(vector1[2] * vector2[0] - vector1[0] * vector2[2], decimalPlaces),\n setDecimalPlaces(vector1[0] * vector2[1] - vector1[1] * vector2[0], decimalPlaces),\n ];\n};\n\n// --------------- INIT VECTOR HELPER -----------------\n\nexport const v2 = (defaultValue = 0): Vector2 => {\n return [defaultValue, defaultValue];\n};\n\nexport const v3 = (defaultValue = 0): Vector3 => {\n return [defaultValue, defaultValue, defaultValue];\n};\n\nexport const v4 = (defaultValue = 0): Vector4 => {\n return [defaultValue, defaultValue, defaultValue, defaultValue];\n};\n\nexport const vN = (N: number, defaultValue = 0): Vector => {\n\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n const vector: Vector = [];\n for(let i=0; i {\n let vector: Vector2 = [0, 0];\n vector = v2SetLength(vector, distance);\n return setV2Angle(vector, angleRad);\n};\n\n// --------------- EQUALITY -------------------------\n\nexport const vEqual = (vector1: Vector, vector2: Vector): boolean => {\n if(vector1.length !== vector2.length) return false;\n\n for(let i=0; i {\n const sub = v2Sub(vector2, vector1);\n return [\n -setDecimalPlaces(sub[1], decimalPlaces),\n setDecimalPlaces(sub[0], decimalPlaces)\n ];\n};", "export const setDecimalPlaces = (num: number, decimalPlaces: number | undefined = Infinity) => {\n if(decimalPlaces === Infinity) return num;\n\n if(decimalPlaces < 0){\n decimalPlaces = 0;\n }\n\n const coefficient = 10 ** decimalPlaces;\n return Math.round(num * coefficient) / coefficient;\n};", "import { Vector, Vector2, Vector3 } from '../types';\nimport { setDecimalPlaces } from './format';\nimport { v2Length, vNormalize, vDotProduct, vSub } from './linear-algebra/vector';\nimport { mod } from './other';\n\nexport const getV2Angle = (v2: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1], v2[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleInEllipse = (v2: Vector2, radii: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1]/radii[1], v2[0]/radii[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const setV2Angle = (v2: Vector2, newAngleRad: number, decimalPlaces = Infinity): Vector2 => {\n const length = v2Length(v2);\n return [\n setDecimalPlaces(Math.cos(newAngleRad) * length, decimalPlaces),\n setDecimalPlaces(Math.sin(newAngleRad) * length, decimalPlaces),\n ];\n};\n\nexport const radiansToDegrees = (radians: number, decimalPlaces = Infinity) => {\n const res = radians * (180 / Math.PI);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\nexport const degreesToRadians = (degrees: number, decimalPlaces = Infinity) => {\n const res = degrees * (Math.PI / 180);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\n/**\n * Returns the range [0, Math.PI]\n * A = Math.acos( dot(v1, v2)/(v1.length()*v2.length()) );\n */\nexport const getVNAngleBetween = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n const unitVector1 = vNormalize(vector1);\n const unitVector2 = vNormalize(vector2);\n const dotProduct = vDotProduct(unitVector1, unitVector2);\n const angle = Math.acos(dotProduct);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleBetween = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) : number => {\n // return getVNAngleBetween(vector1, vector2, decimalPlaces);\n const diff = vSub(vector1, vector2);\n const angle = Math.atan2(diff[1], diff[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV3AngleBetween = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return getVNAngleBetween(vector1, vector2, decimalPlaces);\n};\n\nexport const isAngleBetween = (angleDegrees: number, startAngleDegrees: number, endAngleDegrees: number) : boolean => {\n const distance = getAnglesSub(startAngleDegrees, endAngleDegrees);\n const distance1 = getAnglesSub(startAngleDegrees, angleDegrees);\n const distance2 = getAnglesSub(endAngleDegrees, angleDegrees);\n const totalDistance = distance1 + distance2;\n\n // Use a small threshold for floating point errors\n return Math.abs(totalDistance - distance) <= 0.001;\n}\n\nexport const isClockwise = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n return angle2Deg >= angle1Deg;\n};\n\n/**\n * Shortest distance (angular) between two angles.\n */\nexport const getAnglesSub = (angleDegrees1: number, angleDegrees2: number, decimalPlaces = Infinity) : number => {\n const angleDistance = Math.abs(mod(angleDegrees1, 360) - mod(angleDegrees2, 360));\n return setDecimalPlaces(angleDistance <= 180 ? angleDistance : 360 - angleDistance, decimalPlaces);\n};\n\nexport const getAnglesDistance = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0, decimalPlaces = Infinity) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n if(isClockwise(angle1Deg, angle2Deg, startAngleDeg)) {\n return setDecimalPlaces((angle2Deg - angle1Deg + 360) % 360, decimalPlaces);\n }\n else{\n return setDecimalPlaces((angle1Deg - angle2Deg + 360) % 360, decimalPlaces);\n }\n};\n\nexport const percentToAngle = (percent: number, startAngleDeg: number, endAngleDeg: number, circleStartAngle = 0) => {\n if(percent < 0) {\n percent = 0;\n }\n\n if(percent > 100) {\n percent = 100;\n }\n\n const distance = getAnglesDistance(startAngleDeg, endAngleDeg, circleStartAngle);\n\n const clockwise = isClockwise(startAngleDeg, endAngleDeg, circleStartAngle);\n if(clockwise) {\n return mod(circleStartAngle + (percent * distance / 100), 360);\n }\n else {\n return mod(circleStartAngle - (percent * distance / 100), 360);\n }\n};", "import { Vector2 } from '../types';\nimport { setDecimalPlaces } from './format';\n\nexport const mod = (n: number, m: number) => {\n return ((n % m) + m) % m;\n};\n\n/**\n * Convert range [a, b] to [c, d].\n * f(x) = (d - c) * (x - a) / (b - a) + c\n */\nexport const convertRange = (x: number, a: number, b: number, c: number, d: number) => {\n return (d - c) * (x - a) / (b - a) + c;\n};\n\n/**\n * Check if 2 ranges [a,b] and [c,d] overlap.\n */\nexport const doRangesOverlap = (a: number, b: number, c: number, d: number) => {\n return Math.max(a, c) <= Math.min(b, d) ;\n};\n\n// eslint-disable-next-line\nexport const isNumber = (value: any) => {\n return !isNaN(parseFloat(value)) && isFinite(value);\n};\n\n/**\n * Convert polar coordinates to cartesian coordinates.\n */\nexport const polarToCartesian = (center: Vector2, radii: Vector2, angleInRad: number, decimalPlaces = Infinity) : Vector2 => {\n const [cx, cy] = center;\n const [rx, ry] = radii;\n\n return [\n setDecimalPlaces(cx + (rx * Math.cos(angleInRad)), decimalPlaces),\n setDecimalPlaces(cy + (ry * Math.sin(angleInRad)), decimalPlaces),\n ];\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector, Vector2, Vector3 } from '../../types';\nimport { vMulScalar, vSum, vSub, vDotProduct, vN, vEqual, vDivideScalar } from './vector';\n\n// --------------- SUM ----------------------\n\nexport const mSum = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sum = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- SUB ----------------------\n\nexport const mSub = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sub = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- MUL SCALAR ----------------------\n\nexport const mMulScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vMulScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2MulScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mMulScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3MulScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mMulScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n// --------------- DIVIDE SCALAR ----------------------\n\nexport const mDivideScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vDivideScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2DivideScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mDivideScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3DivideScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mDivideScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n\n// --------------- TRANSPOSE ----------------------\n\nexport const mTranspose = (m: Matrix): Matrix => {\n\n const vectorsCount = m.length;\n if(vectorsCount <= 0) return m;\n\n const vectorLength = m[0].length;\n if(vectorLength <= 0) return m;\n\n const matrix: Matrix = [];\n for(let i=0; i {\n return mTranspose(m2);\n};\n\nexport const m3Transpose = (m3: Matrix3): Matrix => {\n return mTranspose(m3);\n};\n\n// ----------------- RESET ----------------------\n\nexport const mReset = (m: Matrix, defaultValue = 0): Matrix => {\n\n if(m.length <= 0) return [];\n\n const res: Matrix = [];\n\n for(let i=0; i {\n return mReset(m2, defaultValue) as Matrix2;\n};\n\nexport const m3Reset = (m3: Matrix3, defaultValue = 0): Matrix3 => {\n return mReset(m3, defaultValue) as Matrix3;\n};\n\n// --------------- MATRIX INIT HELPERS -----------------\n\nexport const m2x2 = (defaultValue = 0): Matrix2 => {\n return [\n [defaultValue, defaultValue],\n [defaultValue, defaultValue],\n ];\n};\n\nexport const m3x3 = (defaultValue = 0): Matrix3 => {\n return [\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const m4x4 = (defaultValue = 0): Matrix4 => {\n return [\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const mNxM = (N: number, M: number, defaultValue = 0): Matrix => {\n if(N <= 0 || M <= 0){\n throw new Error('M and N must be positive numbers.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return [\n [1, 0],\n [0, 1],\n ];\n};\n\nexport const identity3 = (): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\nexport const identity4 = (): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Identity Matrix (I).\n * M x I = I x M = M for any matrix M.\n * Identity Matrix is a special case of scale matrix.\n */\nexport const identityN = (N: number): Matrix => {\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n if(N === 0) return [];\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mDeepCopy(m2) as Matrix2;\n};\n\nexport const m3DeepCopy = (m3: Matrix3): Matrix3 => {\n return mDeepCopy(m3) as Matrix3;\n};\n\n// -------------- APPEND / PREPEND ROW OR COLUMN ---------------\n\nexport const mAppendCol = (m: Matrix, col: Vector): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n const copy = mDeepCopy(m);\n copy.push(row);\n return copy;\n};\n\nexport const m2AppendRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.push(row);\n return copy;\n};\n\nexport const m3AppendRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.push(row);\n return copy;\n};\n\nexport const mPrependRow = (m: Matrix, row: Vector) : Matrix => {\n const copy = mDeepCopy(m);\n copy.unshift(row);\n return copy;\n};\n\nexport const m2PrependRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.unshift(row);\n return copy;\n};\n\nexport const m3PrependRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.unshift(row);\n return copy;\n};\n\n// ------------ DELETE ROW OR COLUMN ----------------------------\n\nexport const mDelLastRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.pop();\n return copy;\n};\n\nexport const mDelFirstRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.shift();\n return copy;\n};\n\nexport const mDelLastColumn = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const size = m[0].length;\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n\n const matrix: Matrix = [];\n for(let i=0; i {\n\n if(matrix.length < 0) return [];\n\n if(matrix[0].length !== vector.length){\n throw new Error('The number of columns in the matrix must be equal to the length of the vector.');\n }\n\n const res: Vector = [];\n\n for(let i=0; i {\n if(matrix1.length !== matrix2.length) return false;\n\n for(let i=0; i returns matrix N (m-1 x m-1)\n * The matrix must be square.\n */\nconst mMinorHelper = (m: Matrix, row: number, col: number) => {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // prepare the matrix without provided row and column\n const matrix = mMinorHelper(m, row, col);\n\n // calculate the matrix determinant\n return mDeterminant(matrix);\n};\n\n/**\n * Calculate determinant for NxN matrix.\n * Matrix should be square.\n */\nexport const mDeterminant = (matrix: Matrix): number => {\n const size = matrix.length;\n if(size === 0) return 1;\n\n if(size !== matrix[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return matrix[0][0];\n if(size === 2) return m2Determinant(matrix as Matrix2);\n\n let d = 0;\n\n for(let i=0; i {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return m2[0][0] * m2[1][1] - m2[1][0] * m2[0][1];\n};\n\n/**\n * Calculate determinant for 3x3 matrix.\n * Matrix should be square.\n */\nexport const m3Determinant = (m3: Matrix3): number => {\n if(m3.length !== m3[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return mDeterminant(m3);\n};\n\n// ------------------ INVERSE -----------------------\n\nexport const m2Adjugate = (m2: Matrix2): Matrix2|null => {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return [\n [m2[1][1], -m2[0][1]],\n [-m2[1][0], m2[0][0]],\n ];\n};\n\nexport const m3Adjugate = (m3: Matrix3) : Matrix3|null => {\n return mAdjugate(m3) as (Matrix3|null);\n};\n\n/**\n * Adjugate is a transpose of a cofactor matrix\n */\nexport const mAdjugate = (m: Matrix): Matrix|null => {\n\n const size = m.length;\n if(size <= 0) return null;\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return m;\n\n if(size === 2) return m2Adjugate(m as Matrix2);\n\n // build a cofactor matrix ----------------\n const cofactors: Matrix = [];\n\n for(let i=0; i {\n if(m.length > 0 && m.length !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = mDeterminant(m);\n return d === 0;\n};\n\n/**\n * Square matrix A (nxn) is invertible is there is another square matrix B (nxn) so AxB = BxA = I\n * For A (2x2) matrix, the inverse is:\n * (1 / (determinant(A))) * adj(A)\n */\nexport const m2Inverse = (m2: Matrix2, decimalPlaces = Infinity): (Matrix2 | null) => {\n if(m2.length > 0 && m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = m2Determinant(m2);\n if(d === 0) return null;\n\n const adj = m2Adjugate(m2);\n if(adj === null) return null;\n\n return m2DivideScalar(adj, d, decimalPlaces);\n};\n\nexport const m3Inverse = (m3: Matrix3, decimalPlaces = Infinity): (Matrix3 | null) => {\n return mInverse(m3, decimalPlaces) as (Matrix3|null);\n};\n\nexport const mInverse = (m: Matrix, decimalPlaces = Infinity): (Matrix | null) => {\n const size = m.length;\n\n if(size > 0 && size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // find a determinant ----------------------\n const d = mDeterminant(m);\n\n // find an Adjugate - a transpose of a cofactor matrix\n const adj = mAdjugate(m);\n if(adj === null) return null;\n\n return mDivideScalar(adj, d, decimalPlaces);\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector2, Vector3, Vector4 } from '../../types';\nimport { v2Normalize, v3MulScalar, v3Normalize } from './vector';\nimport { mMulVector, mMul } from './matrix';\nimport { setDecimalPlaces } from '../format';\n\n/*\nAny 2D affine transformation can be decomposed\ninto a rotation, followed by a scaling, followed by a\nshearing, and followed by a translation.\n---------------------------------------------------------\nAffine matrix = translation x shearing x scaling x rotation\n */\n\n// ----------------- CSS -------------------------------------\n\n/**\n * Matrix 2D in non-homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2ToCSS = (m: Matrix2) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, 0, 0)`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2hToCSS = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, ${ tx }, ${ ty })`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m2hToCSS3d = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix3d(${ a }, ${ b }, 0, 0, ${ c }, ${ d }, 0, 0, 0, 0, 1, 0, ${ tx }, ${ ty }, 0, 1)`;\n};\n\n/**\n * Matrix 3D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m3hToCSS3d = (m: Matrix4) : string => {\n\n return `matrix3d(\n ${ m[0][0] }, ${ m[0][1] }, ${ m[0][2] }, ${ m[0][3] },\n ${ m[1][0] }, ${ m[1][1] }, ${ m[1][2] }, ${ m[1][3] },\n ${ m[2][0] }, ${ m[2][1] }, ${ m[2][2] }, ${ m[2][3] },\n ${ m[3][0] }, ${ m[3][1] }, ${ m[3][2] }, ${ m[3][3] }\n )`;\n};\n\n// ---------------- TRANSLATION MATRICES ----------------------\n\nexport const m2Translation = (position: Vector2, decimalPlaces = Infinity): Matrix2 => {\n\n return [\n [1, 0],\n [0, 1],\n [setDecimalPlaces(position[0], decimalPlaces), setDecimalPlaces(position[1], decimalPlaces)],\n ];\n};\n\nexport const m3Translation = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n [\n setDecimalPlaces(position[0], decimalPlaces),\n setDecimalPlaces(position[1], decimalPlaces),\n setDecimalPlaces(position[2], decimalPlaces)\n ],\n ];\n};\n\n/**\n * 2D Translation matrix in homogeneous coordinates.\n */\nexport const m2TranslationH = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1],\n ];\n};\n\n/**\n * 3D Translation matrix in homogeneous coordinates.\n */\nexport const m3TranslationH = (position: Vector4, decimalPlaces = Infinity): Matrix4 => {\n\n return [\n [1, 0, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, 0, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1, setDecimalPlaces(position[2], decimalPlaces)],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- ROTATION MATRICES -------------------------\n\n/**\n * Rotation of an angle about the origin.\n */\nexport const m2Rotation = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix2 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin],\n [sin, cos],\n ] :\n [\n [cos, sin],\n [-sin, cos],\n ];\n};\n\n/**\n * Rotation of an angle about the origin in homogeneous coordinates (clockwise).\n */\nexport const m2RotationH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ]:\n [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation of an angle \"angleRad\" around the given point (transformOrigin) in homogeneous coordinates (clockwise).\n * result_vector = TranslationMatrix(x, y) * RotationMatrix() * TranslationMatrix(-x, -y) * position_vector\n */\nexport const m2RotationAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const rotation = m2RotationH(angleRad, isClockwise, decimalPlaces);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, rotation);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2RotateAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n position: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2RotationAroundPointH(angleRad, transformOrigin, isClockwise, decimalPlaces);\n return mMulVector(mat3h, position) as Vector3;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2Rotate = (angleRad: number, vector: Vector2, isClockwise = true, decimalPlaces = Infinity): Vector2 => {\n const unitVector = v2Normalize(vector);\n return mMulVector(m2Rotation(angleRad, isClockwise, decimalPlaces), unitVector) as Vector2;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2RotateH = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m2RotationH(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the X axis (clockwise).\n */\nexport const m3RotationX = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0],\n [0, cos, -sin],\n [0, sin, cos],\n ] :\n [\n [1, 0, 0],\n [0, cos, sin],\n [0, -sin, cos],\n ];\n};\n\n/**\n * Rotation around the X axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationXH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0, 0],\n [0, cos, -sin, 0],\n [0, sin, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [1, 0, 0, 0],\n [0, cos, sin, 0],\n [0, -sin, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateX = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationX(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Y axis (clockwise).\n */\nexport const m3RotationY = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin],\n [0, 1, 0],\n [-sin, 0, cos],\n ] :\n [\n [cos, 0, -sin],\n [0, 1, 0],\n [sin, 0, cos],\n ];\n};\n\n/**\n * Rotation around the Y axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationYH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin, 0],\n [0, 1, 0, 0],\n [-sin, 0, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [cos, 0, -sin, 0],\n [0, 1, 0, 0],\n [sin, 0, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateY = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationY(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Z axis (clockwise).\n */\nexport const m3RotationZ = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ] : [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation around the Z axis (clockwise)- in homogeneous coordinates\n */\nexport const m3RotationZH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0, 0],\n [sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ] : [\n [cos, sin, 0, 0],\n [-sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateZ = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationZ(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n// ---------------- SCALE MATRICES -------------\n\n/**\n * Get matrix for arbitrary scaling pivot point.\n * result_vector = TranslationMatrix(x, y) * ScaleMatrix() * TranslationMatrix(-x, -y) * scale_vector\n */\nexport const m2ScaleAtPointHMatrix = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const scale = m2ScaleH(scaleVector);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, scale);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2ScaleAtPointH = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n point: Vector3,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2ScaleAtPointHMatrix(scaleVector, transformOrigin, decimalPlaces);\n return mMulVector(mat3h, point) as Vector3;\n};\n\nexport const m2Scale = (scaleVector: Vector2): Matrix2 => {\n return [\n [scaleVector[0], 0],\n [0, scaleVector[1]],\n ];\n};\n\nexport const v2Scale = (scaleVector: Vector2, vector: Vector2): Vector2 => {\n return mMulVector(m2Scale(scaleVector), vector) as Vector2;\n};\n\n/**\n * homogeneous coordinates\n */\nexport const m2ScaleH = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, 1],\n ];\n};\n\nexport const m3Scale = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, scaleVector[2]],\n ];\n};\n\nexport const m3ScaleH = (scaleVector: Vector4): Matrix4 => {\n return [\n [scaleVector[0], 0, 0, 0],\n [0, scaleVector[1], 0, 0],\n [0, 0, scaleVector[2], 0],\n [0, 0, 0, 1]\n ];\n};\n\nexport const v3Scale = (scaleVector: Vector3, vector: Vector3): Vector3 => {\n return mMulVector(m3Scale(scaleVector), vector) as Vector3;\n};\n\n/**\n * Stretch, parallel to the x-axis.\n */\nexport const m2ScaleX = (scale: number): Matrix2 => {\n return [\n [scale, 0],\n [0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the x-axis - homogeneous coordinates\n */\nexport const m2ScaleXH = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleX = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleXH = (scale: number): Matrix4 => {\n return [\n [scale, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleY = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleYH = (scale: number): Matrix => {\n return [\n [1, 0, 0, 0],\n [0, scale, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZ = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, scale],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZH = (scale: number): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, scale, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis.\n */\nexport const m2ScaleY = (scale: number): Matrix2 => {\n return [\n [1, 0],\n [0, scale],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis - homogeneous coordinates\n */\nexport const m2ScaleYH = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n// ---------------- REFLECTION MATRICES -------------------------\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOrigin = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOriginH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection about the origin in non-homogeneous coordinates\n */\nexport const m3ReflectionOrigin = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection about the origin in homogeneous coordinates\n */\nexport const m3ReflectionOriginH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection about y=-x\n */\nexport const m2ReflectionYmX = (): Matrix2 => {\n\n return [\n [0, -1],\n [-1, 0],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionX = (): Matrix2 => {\n\n return [\n [1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionXH = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection in the y-axis.\n */\nexport const m2ReflectionY = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, 1],\n ];\n};\n\nexport const m2ReflectionYH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionYZ = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in homogeneous coordinates\n */\nexport const m3ReflectionYZH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXZ = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in homogeneous coordinates\n */\nexport const m3ReflectionXZH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXY = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in homogeneous coordinates\n */\nexport const m3ReflectionXYH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- SHEARING MATRICES -------------------------\n\n\n/**\n * Shearing in y-axis, with x-axis fixed with (0,1) moving to (factor, 1)\n */\nexport const m2ShearingY = (factor: number): Matrix2 => {\n\n return [\n [1, factor],\n [0, 1],\n ];\n};\n\n/**\n * Shearing in x-axis, with y-axis fixed with (1,0) moving to (1, factor)\n */\nexport const m2ShearingX = (factor: number): Matrix2 => {\n\n return [\n [1, 0],\n [factor, 1],\n ];\n};", "import { setDecimalPlaces } from './format';\n\n/**\n * Returns a random number in the [min,max] range.\n */\nexport const getRandom = (min: number, max: number, decimalPlaces = Infinity): number => {\n return setDecimalPlaces(Math.random() * (max - min) + min, decimalPlaces);\n};\n\n/**\n * Returns a random integer number in the [min,max] range.\n */\nexport const getRandomInt = (min: number, max: number): number => {\n return Math.floor(Math.random() * (max - min + 1) + min);\n};\n\nexport const getRandomBoolean = () => Math.random() < 0.5;\n\n/* eslint-disable @typescript-eslint/no-explicit-any */\nexport const getRandomItemFromArray = (array: any[]) => {\n const randomIndex = getRandomInt(0, array.length - 1);\n return array[randomIndex];\n};", "export const stringToNumber = (value: string|undefined|null|number, defaultNumber: number) => {\n if(value === undefined || value === null) return defaultNumber;\n const res = Number(value) ?? defaultNumber;\n return isNaN(res) ? defaultNumber : res;\n};", "import { IBBox, Vector, Vector2, Vector3 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport {\n dxV2CubicBezierCurve,\n dxV2QuadraticBezierCurve,\n dxV3CubicBezierCurve,\n dxV3QuadraticBezierCurve\n} from '../derivative';\nimport { v2Normalize, v3Normalize } from '../linear-algebra/vector';\nimport { linearEquation } from '../equations/linear-equations';\nimport { quadraticEquation } from '../equations/quadratic-equations';\nimport { isNumber } from '../other';\n\n/**\n * B\u00E9zier Curves\n * quadratic: y = P1 * (1-t)\u00B2 + P2 * 2 * (1-t)t + P3 * t\u00B2\n * t in range [0, 1]\n */\n\n// -------------------- GET POINT ON CURVE --------------------------\n\n/**\n * Get a point on a quadratic B\u00E9zier curve as a function of time.\n */\nexport const v2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n/**\n * Get a point on a cubic B\u00E9zier curve as a function of time.\n */\nexport const v2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n// -------------------- TANGENT --------------------------\n\n/**\n * Tangent indicates the direction of travel at specific points along the B\u00E9zier curve,\n * and is literally just the first derivative of our curve.\n */\nexport const v2QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\nexport const v2CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\n// -------------------- NORMAL --------------------------\n\n/**\n * Normal is a vector that runs at a right angle to the direction of the curve, and is typically of length 1.\n * To find it, we take the normalised tangent vector, and then rotate it by a 90 degrees.\n */\nexport const v2QuadraticBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2QuadraticBezierCurveTangent(t, startControlPoint, centerControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\nexport const v2CubicBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2CubicBezierCurveTangent(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\n// -------------------- EXTREMA --------------------------\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2QuadraticBezierCurveExtrema = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector => {\n\n /*\n (-2 * (1 - t)) * startControlPoint[0] + (2 - 4 * t) * centerControlPoint[0] + (2 * t) * endControlPoint[0]\n 2 * t * startControlPoint[0] - 4 * t * centerControlPoint[0] + 2 * t * endControlPoint[0] - 2 * startControlPoint[0] + 2 * centerControlPoint[0]\n t * (2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0]) + (- 2 * startControlPoint[0] + 2 * centerControlPoint[0])\n */\n\n const a1 = 2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0];\n const b1 = -2 * startControlPoint[0] + 2 * centerControlPoint[0];\n const equation1: Vector3 = [a1, b1, 0];\n const res1 = linearEquation(equation1, decimalPlaces);\n\n const a2 = 2 * startControlPoint[1] - 4 * centerControlPoint[1] + 2 * endControlPoint[1];\n const b2 = -2 * startControlPoint[1] + 2 * centerControlPoint[1];\n const equation2: Vector3 = [a2, b2, 0];\n const res2 = linearEquation(equation2, decimalPlaces);\n\n const res: Vector = [];\n\n if(isNumber(res1)){\n res.push(res1);\n }\n\n if(isNumber(res2)){\n res.push(res2);\n }\n\n return res;\n};\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2CubicBezierCurveExtrema = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2|null => {\n\n const a1 = -3 * startControlPoint[0] + 9 * center1ControlPoint[0] - 9 * center2ControlPoint[0] + 3 * endControlPoint[0];\n const b1 = 6 * startControlPoint[0] - 12 * center1ControlPoint[0] + 6 * center2ControlPoint[0];\n const c1 = -3 * startControlPoint[0] + 3 * center1ControlPoint[0];\n const equation1: Vector = [a1, b1, c1, 0];\n\n const a2 = -3 * startControlPoint[1] + 9 * center1ControlPoint[1] - 9 * center2ControlPoint[1] + 3 * endControlPoint[1];\n const b2 = 6 * startControlPoint[1] - 12 * center1ControlPoint[1] + 6 * center2ControlPoint[1];\n const c2 = -3 * startControlPoint[1] + 3 * center1ControlPoint[1];\n const equation2: Vector = [a2, b2, c2, 0];\n\n // Any value between 0 and 1 is a root that matters for B\u00E9zier curves, anything below or above that is irrelevant (because B\u00E9zier curves are only defined over the interval [0,1]).\n const res1 = quadraticEquation(equation1, decimalPlaces).filter(num => num >= 0 && num <= 1);\n const res2 = quadraticEquation(equation2, decimalPlaces).filter(num => num >= 0 && num <= 1);\n\n const res = [...res1, ...res2];\n if(res.length === 2){\n return [...res1, ...res2] as Vector2;\n }\n\n return null;\n};\n\n// -------------------- BOUNDING BOX --------------------------\n\nexport const v2QuadraticBezierBBox = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2QuadraticBezierCurveExtrema(startControlPoint, centerControlPoint, endControlPoint);\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2QuadraticBezierCurve(percent, startControlPoint, centerControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x);\n maxX = Math.max(maxX, x);\n\n minY = Math.min(minY, y);\n maxY = Math.max(maxY, y);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\nexport const v2CubicBezierBBox = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2CubicBezierCurveExtrema(startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint) || [];\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2CubicBezierCurve(percent, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x ?? Infinity);\n maxX = Math.max(maxX, x ?? -Infinity);\n\n minY = Math.min(minY, y ?? Infinity);\n maxY = Math.max(maxY, y ?? -Infinity);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\n\n", "import { setDecimalPlaces } from './format';\nimport { Vector2, Vector3 } from '../types';\n\n/**\n * u(x) and v(x) are functions ---------->\n *\n * dx(u + v) = dx(u) + dx(v)\n * dx(u - v) = dx(u) - dx(v)\n * dx(u * v) = dx(u) * v + u * dx(v)\n * dx(u / v) = (dx(u) * v - u * dx(v)) / (v ^ 2), when v(x) != 0\n */\n\n// ------------------ Derivatives of Polynomial ---------------------------\n\n/**\n * y = 3x+2\n * dxPolynomial(10, [[3, 1], [2, 0]])\n */\nexport const dxPolynomial = (x: number, polynomial: number[][], decimalPlaces = Infinity) => {\n let res = 0;\n\n for(const part of polynomial){\n if(part.length !== 2) return NaN;\n\n const coeff = part[0];\n const power = part[1];\n res += coeff * power * Math.pow(x, power - 1);\n }\n\n return setDecimalPlaces(res, decimalPlaces);\n}\n\n// ---------------------- Bezier Curves ---------------------------\n\n/**\n * Derivative of Bezier Curve is another Bezier Curve.\n * t must min in range [0, 1]\n */\nexport const dxV2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n // The derivative: P1 * (2t-2) + (2*P3-4*P2) * t + 2 * P2\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\nexport const dxV2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n\n// ----------------- Derivatives of trigonometry functions ---------------------------\n\nexport const dxSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(Math.cos(x), decimalPlaces);\n};\n\nexport const dxCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-Math.sin(x), decimalPlaces);\n};\n\nexport const dxTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.cos(x) ** 2), decimalPlaces);\n};\n\n/**\n * x != Math.PI * n, where n is an integer\n */\nexport const dxCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sin(x) ** 2), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\nexport const dxArcTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (1 + x ** 2), decimalPlaces);\n};\n\nexport const dxArcCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (1 + x ** 2), decimalPlaces);\n};\n", "import { Matrix, Matrix2, Matrix3, Vector, Vector2, Vector3 } from '../../types';\nimport { m2Inverse, m3Inverse, mInverse, mMulVector, mDelLastColumn, mGetLastColumn } from '../linear-algebra/matrix';\nimport { setDecimalPlaces } from '../format';\nimport { v2Sub } from '../linear-algebra/vector';\n\n/**\n * Linear equation\n * ax + b = c\n * x = (c - b) / a; a != 0\n */\nexport const linearEquation = (equation: Vector3, decimalPlaces = Infinity) : number => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n\n const diff = c - b;\n\n if(a === 0 && diff === 0) return Infinity; // any number is a solution\n if(a === 0) return NaN; // no solution\n\n return setDecimalPlaces(diff / a, decimalPlaces);\n};\n\n/**\n * System of 2 linear equations.\n * [x, y] = inverse(Matrix of equation parameters) x (vector of equation results)\n * ---------------\n * 3x + 2y = 7\n * -6x + 6y = 6\n */\nexport const linearEquationSystem2 = (equation1: Vector3, equation2: Vector3, decimalPlaces = Infinity) : Vector2 | null => {\n const equationParams: Matrix2 = [\n [equation1[0], equation1[1]],\n [equation2[0], equation2[1]],\n ];\n\n const inversed = m2Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector2 = [\n equation1[2],\n equation2[2]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector2;\n};\n\n/**\n * System of 3 linear equations.\n * ---------------------------------------\n * 3x + 2y + 5z = 7\n * -6x + 6y + 6z = 6\n * 2x + 7y - z = 4\n */\nexport const linearEquationSystem3 = (\n equation1: Vector,\n equation2: Vector,\n equation3: Vector,\n decimalPlaces = Infinity) : Vector3 | null => {\n const equationParams: Matrix3 = [\n [equation1[0], equation1[1], equation1[2]],\n [equation2[0], equation2[1], equation2[2]],\n [equation3[0], equation3[1], equation3[2]],\n ];\n\n const inversed = m3Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector3 = [\n equation1[3],\n equation2[3],\n equation3[3]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector3;\n};\n\n/**\n * System of N linear equations.\n */\nexport const linearEquationSystemN = (equations: Matrix, decimalPlaces = Infinity) : Vector | null => {\n if(equations.length <= 0) return null;\n\n const equationParams = mDelLastColumn(equations);\n\n const inversed = mInverse(equationParams);\n if(inversed === null) return null; // no results\n\n // the last column of the equations matrix\n const equationResults = mGetLastColumn(equations);\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector;\n};\n\n/**\n * Calculate the equation of a line given two points in a 2D space.\n * y = ax + b\n * y - y1 = m(x - x1)\n * m = (y2 - y1) / (x2 - x1)\n */\nexport const getLinearEquationBy2Points = (point1: Vector2, point2: Vector2) : {\n slope: number|undefined,\n yIntercept: number|undefined,\n xIntercept: number|undefined,\n formula: string,\n} => {\n const [deltaX, deltaY] = v2Sub(point2, point1);\n const [x, y] = point1;\n\n if(deltaX === 0) {\n return {\n slope: undefined,\n xIntercept: x,\n yIntercept: undefined,\n formula: `x = ${ x }`,\n };\n }\n\n const m = deltaY / deltaX;\n const b = y - m * x;\n let formula = '';\n\n if(m === 0) {\n formula = `y = ${ b }`;\n }\n else{\n formula = `y = ${ m === 1 ? '' : m }x`;\n\n if(b !== 0) {\n formula += ` ${ b < 0 ? '-' : '+' } ${ Math.abs(b) }`;\n }\n }\n\n return {\n slope: m,\n xIntercept: undefined,\n yIntercept: b,\n formula,\n };\n};", "import { Vector } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { linearEquation } from './linear-equations';\nimport { isNumber } from '../other';\n\n/**\n * Quadratic Equation.\n * ax^2 + bx + c = d\n */\nexport const quadraticEquation = (equation: Vector, decimalPlaces = Infinity) : Vector => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n const d = equation[3];\n\n if(a === 0){\n // it's a linear equation -------------------------------------------\n const res = linearEquation([b, c, d], decimalPlaces);\n if(isNumber(res)) return [res];\n return [];\n }\n\n const diff = c - d;\n\n const discriminant = b * b - (4 * a * diff);\n\n if(discriminant < 0){\n return []; // no results\n }\n\n if(discriminant === 0){\n return [ setDecimalPlaces(-b / (2 * a), decimalPlaces) ]; // 1 result\n }\n\n // if(determinant > 0) ---> 2 results\n const t1 = 2 * a;\n const t2 = Math.sqrt(discriminant);\n\n return [\n setDecimalPlaces((-b + t2) / t1, decimalPlaces),\n setDecimalPlaces((-b - t2) / t1, decimalPlaces),\n ];\n};", "import { Vector2 } from '../types';\nimport { v2Sub } from './linear-algebra/vector';\nimport { getV2Angle } from './angle';\nimport { convertRange } from './other';\n\n/**\n * Circle Equation\n * x^2 + y^2 = radius^2\n * ----------------------\n * Circle Parametric Equation\n * x(t) = radius * cos(t)\n * y(t) = radius * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const circleMovement = (center: Vector2, angle: number, radius: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius,\n center[1] + Math.sin(angle) * radius\n ];\n};\n\n/**\n * Circle Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const circleMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radius: number\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return circleMovement(center, angle, radius);\n};\n\n/**\n * Ellipse Equation\n * (x - centerX)^2 / (radius1^2) + (y - centerY)^2 / (radius2^2) = 1\n * -----------------------------------------------------------------\n * Ellipse Parametric Equation\n * x(t) = radius1 * cos(t)\n * y(t) = radius2 * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const ellipseMovement = (center: Vector2, angle: number, radius1: number, radius2: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius1,\n center[1] + Math.sin(angle) * radius2\n ];\n};\n\n/**\n * Ellipse Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const ellipseMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radii: Vector2\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return ellipseMovement(center, angle, radii[0], radii[1]);\n};\n\n/**\n * Sine Wave Equation (Sinusoid)\n * -----------------------------\n * const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n * amplitude = the peak deviation of the function from zero\n * frequency = number of cycles\n * phase = specifies (in radians) where in its cycle the oscillation is at t = 0.\n * think of it as \"shifting\" the starting point of the function to the right (positive p) or left (negative)\n */\nexport const sineWaveMovement = (x: number, amplitude: number, frequency: number, phase: number) : Vector2 => {\n /*\n example values:\n const amplitude = 50;\n const frequency = 0.005;\n const phase = 0;\n x: [0, 1000]\n */\n const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n\n return [x, y];\n};\n\n/**\n * Lissajous curve (Lissajous figure or Bowditch curve)\n * Parametric equation #1\n * f(t) = A * sin(k * t + m)\n * f(t) = B * sin(n * t)\n * 0 <= m <= PI/2\n * k, n >= 1\n * -----------------------\n * Parametric equation #2\n * f(t) = A * cos(k * t - m)\n * f(t) = B * cos(n * t - p)\n * -----------------------------\n * Shapes:\n * k = 1, n = 1, m = 0, p = 0 ---> line\n * A = B, k = 1, n = 1, m = PI/2, p = PI/2 ----> circle\n * A != B, k = 1, n = 1, m = PI/2, p = PI/2 ----> ellipse\n * k = 2, n = 2, m = PI/2, p = PI/2 ----> section of a parabola\n */\nexport const lissajousCurve = (\n width: number,\n height: number,\n t: number,\n k: number,\n n: number,\n m: number,\n p: number\n) :Vector2 => {\n return [\n width * Math.cos(k * t - m),\n height * Math.cos(n * t - p),\n ];\n};\n", "import { getRandom } from './random';\nimport { HSLColor, LABColor, RGBColor } from '../types';\nimport { mod } from './other';\nimport { setDecimalPlaces } from './format';\n\n// ------------------------ RANDOM COLOR -------------------------------------\n\nexport const getRandomRGBColor = () : RGBColor => {\n const hslColor = getRandomHSLColor();\n return hslToRgb(hslColor);\n};\n\nexport const getRandomHexColor = () : string => {\n const hslColor = getRandomHSLColor();\n return hslToHex(hslColor);\n};\n\nexport const getRandomHSLColor = () : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given hue\n */\nexport const getRandomHSLColorWithHue = (h: number) : HSLColor => {\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given saturation\n */\nexport const getRandomHSLColorWithSaturation = (s: number) : HSLColor => {\n const h = getRandom(1, 360);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given lightness\n */\nexport const getRandomHSLColorWithLightness = (l: number) : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n return [h, s, l];\n};\n\nexport const getRandomGrayscaleHSLColor = () : HSLColor => {\n const l = getRandom(0, 100);\n return [0, 0, l];\n};\n\nexport const getRandomHSLColorWithinRanges = (\n hueStart = 1, hueEnd = 360,\n saturationStart = 0, saturationEnd = 100,\n lightStart = 0, lightEnd = 100\n) : HSLColor => {\n const h = getRandom(hueStart, hueEnd);\n const s = getRandom(saturationStart, saturationEnd);\n const l = getRandom(lightStart, lightEnd);\n return [h, s, l];\n};\n\n// ----------------------- CONVERT COLORS --------------------------------------\n\n/**\n * helper: convert hue value to degrees.\n * @param {number} h\n * @return {number} [0, 360] degrees\n */\nconst convertHueToDegrees = (h : number) : number => {\n\n // the hue value needs to be multiplied by 60 to convert it to degrees\n h *= 60;\n\n // if hue becomes negative, you need to add 360 to, because a circle has 360 degrees\n if(h < 0){\n h += 360;\n }\n\n return h;\n // convert huw to %\n // return h * 100 / 360;\n};\n\n/**\n * get hue from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] % - we use here % instead of [0, 359] degrees\n */\nconst getHue = (r : number, g : number, b : number, min : number | undefined = undefined, max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (max === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no hue, as it's gray\n if(min === max) return 0;\n\n const diff = max - min;\n\n let h = 0;\n\n // if red is max\n if(max === r){\n h = (g - b) / diff + (g < b ? 6 : 0);\n }\n\n // if green is max\n if(max === g){\n h = 2 + (b - r) / diff;\n }\n\n // if blue is max\n if(max === b){\n h = 4 + (r - g) / diff;\n }\n\n return convertHueToDegrees(h);\n};\n\n/**\n * get luminance from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] %\n */\nconst getLuminance = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // calculate the luminance value\n // @ts-ignore\n const l = (min + max) / 2; // [0, 1]\n\n // return l value in %\n return l * 100;\n};\n\n/**\n * get saturation from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @param {number|undefined=} l - luminance in [0, 100] %\n * @return {number} [0, 100] %\n */\nconst getSaturation = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined,\n l : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no saturation, as it's gray\n if(min === max) return 0;\n\n // calculate luminance if it's not provided\n l = (l === undefined) ? getLuminance(r, g, b) : l;\n\n // check the level of luminance\n const s = (l <= 50) ?\n // @ts-ignore\n ((max - min) / (max + min)) : // this formula is used when luminance <= 50%\n // @ts-ignore\n (max - min) / (2.0 - max - min); // this formula is used when luminance > 50%\n\n // return saturation in %\n return s * 100;\n};\n\nexport const rgbToHsl = (rgb: RGBColor, decimalPlaces = Infinity): HSLColor => {\n\n // convert rgb values to the range [0, 1]\n const r = rgb[0] / 255;\n const g = rgb[1] / 255;\n const b = rgb[2] / 255;\n\n // find the minimum and maximum values of r, g, and b\n const min = Math.min(r, g, b);\n const max = Math.max(r, g, b);\n\n // calculate the luminance value in %\n const l = getLuminance(r, g, b, min, max);\n\n // calculate the saturation in %\n const s = getSaturation(r, g, b, min, max, l);\n\n // calculate the hue in % (not in degrees!)\n const h = getHue(r, g, b, min, max);\n\n if(h > 360 || s > 100 || l > 100){\n return [0, 0, 100];\n }\n\n if(h < 0 || s < 0 || l < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(h, decimalPlaces),\n setDecimalPlaces(s, decimalPlaces),\n setDecimalPlaces(l, decimalPlaces),\n ];\n};\n\n/**\n * helper: HSL to RGB\n */\nconst hslToRgbHelper = (helper1 : number, helper2 : number, colorHelper : number) : number => {\n\n // all values need to be between 0 and 1\n // if you get a negative value you need to add 1 to it\n if(colorHelper < 0) colorHelper += 1;\n\n // if you get a value above 1 you need to subtract 1 from it.\n if(colorHelper > 1) colorHelper -= 1;\n\n if(colorHelper * 6 < 1) return helper2 + (helper1 - helper2) * 6 * colorHelper;\n\n if(colorHelper * 2 < 1) return helper1;\n\n if(colorHelper * 3 < 2){\n return helper2 + (helper1 - helper2) * (0.666 - colorHelper) * 6;\n }\n else{\n return helper2;\n }\n};\n\nexport const hslToRgb = (hsl: HSLColor, decimalPlaces = Infinity): RGBColor => {\n\n // convert all values to [0, 1] from %\n const h = hsl[0] / 100;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n // if there is no saturation -> it\u2019s grey\n if(s === 0){\n // convert the luminance from [0, 1] to [0, 255]\n const gray = l * 255;\n return [gray, gray, gray];\n }\n\n // check the level of luminance\n const helper1 = (l < 0.5) ?\n (l * (1.0 + s)) :\n (l + s - l * s);\n\n const helper2 = 2 * l - helper1;\n\n const rHelper = h + 0.333;\n const gHelper = h;\n const bHelper = h - 0.333;\n\n let r = hslToRgbHelper(helper1, helper2, rHelper);\n let g = hslToRgbHelper(helper1, helper2, gHelper);\n let b = hslToRgbHelper(helper1, helper2, bHelper);\n\n // convert rgb to [0, 255]\n r *= 255;\n g *= 255;\n b *= 255;\n\n if(r > 255 || g > 255 || b > 255){\n return [255, 255, 255];\n }\n\n if(r < 0 || g < 0 || b < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(r, decimalPlaces),\n setDecimalPlaces(g, decimalPlaces),\n setDecimalPlaces(b, decimalPlaces),\n ];\n};\n\n/**\n * HSL to hex\n * hslToHex(360, 100, 50) // [360, 100, 5] ==> \"#ff0000\" (red)\n */\nexport const hslToHex = (hsl: HSLColor) => {\n\n if(hsl[0] > 360 || hsl[1] > 100 || hsl[2] > 100){\n return '#ffffff';\n }\n\n if(hsl[0] < 0 || hsl[1] < 0 || hsl[2] < 0){\n return '#000000';\n }\n\n const h = hsl[0] / 360;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n let r, g, b;\n if (s === 0) {\n r = g = b = l; // achromatic\n } else {\n const hue2rgb = (p: number, q: number, t: number) => {\n if (t < 0) t += 1;\n if (t > 1) t -= 1;\n if (t < 1 / 6) return p + (q - p) * 6 * t;\n if (t < 1 / 2) return q;\n if (t < 2 / 3) return p + (q - p) * (2 / 3 - t) * 6;\n return p;\n };\n const q = l < 0.5 ? l * (1 + s) : l + s - l * s;\n const p = 2 * l - q;\n r = hue2rgb(p, q, h + 1 / 3);\n g = hue2rgb(p, q, h);\n b = hue2rgb(p, q, h - 1 / 3);\n }\n const toHex = (x: number) => {\n const hex = Math.round(x * 255).toString(16);\n return hex.length === 1 ? '0' + hex : hex;\n };\n\n return `#${toHex(r)}${toHex(g)}${toHex(b)}`;\n};\n\n/**\n * RGB to HEX\n * rgbToHex([235, 64, 52]) // #eb4034\n */\nexport const rgbToHex = (rgb: RGBColor) => {\n const [r, g, b] = rgb;\n return '#' + (1 << 24 | r << 16 | g << 8 | b).toString(16).slice(1);\n};\n\nexport const hexToRgb = (hex: string) : RGBColor | null => {\n\n const shorthandRegex = /^#?([a-f\\d])([a-f\\d])([a-f\\d])$/i;\n const _hex = hex.replace(shorthandRegex, (_m, r, g, b) => {\n return r + r + g + g + b + b;\n });\n\n const result = /^#?([a-f\\d]{2})([a-f\\d]{2})([a-f\\d]{2})$/i.exec(_hex);\n if(!result) return null;\n\n const r = parseInt(result[1], 16);\n const g = parseInt(result[2], 16);\n const b = parseInt(result[3], 16);\n\n return [r, g, b];\n};\n\nexport const rgbToLab = (rgb: RGBColor, decimalPlaces = Infinity) : LABColor => {\n\n let r = rgb[0] / 255;\n let g = rgb[1] / 255;\n let b = rgb[2] / 255;\n\n r = (r > 0.04045) ? Math.pow((r + 0.055) / 1.055, 2.4) : r / 12.92;\n g = (g > 0.04045) ? Math.pow((g + 0.055) / 1.055, 2.4) : g / 12.92;\n b = (b > 0.04045) ? Math.pow((b + 0.055) / 1.055, 2.4) : b / 12.92;\n\n let x = (r * 0.4124 + g * 0.3576 + b * 0.1805) / 0.95047;\n let y = (r * 0.2126 + g * 0.7152 + b * 0.0722) / 1.00000;\n let z = (r * 0.0193 + g * 0.1192 + b * 0.9505) / 1.08883;\n\n x = (x > 0.008856) ? Math.pow(x, 1/3) : (7.787 * x) + 16/116;\n y = (y > 0.008856) ? Math.pow(y, 1/3) : (7.787 * y) + 16/116;\n z = (z > 0.008856) ? Math.pow(z, 1/3) : (7.787 * z) + 16/116;\n\n return [\n setDecimalPlaces((116 * y) - 16, decimalPlaces),\n setDecimalPlaces(500 * (x - y), decimalPlaces),\n setDecimalPlaces(200 * (y - z), decimalPlaces),\n ];\n};\n\nexport const labToRgb = (lab: LABColor, decimalPlaces = Infinity) : RGBColor => {\n let y = (lab[0] + 16) / 116;\n let x = lab[1] / 500 + y;\n let z = y - lab[2] / 200;\n\n x = 0.95047 * ((x * x * x > 0.008856) ? x * x * x : (x - 16/116) / 7.787);\n y = 1.00000 * ((y * y * y > 0.008856) ? y * y * y : (y - 16/116) / 7.787);\n z = 1.08883 * ((z * z * z > 0.008856) ? z * z * z : (z - 16/116) / 7.787);\n\n let r = x * 3.2406 + y * -1.5372 + z * -0.4986;\n let g = x * -0.9689 + y * 1.8758 + z * 0.0415;\n let b = x * 0.0557 + y * -0.2040 + z * 1.0570;\n\n r = (r > 0.0031308) ? (1.055 * Math.pow(r, 1/2.4) - 0.055) : 12.92 * r;\n g = (g > 0.0031308) ? (1.055 * Math.pow(g, 1/2.4) - 0.055) : 12.92 * g;\n b = (b > 0.0031308) ? (1.055 * Math.pow(b, 1/2.4) - 0.055) : 12.92 * b;\n\n return [\n setDecimalPlaces(Math.max(0, Math.min(1, r)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, g)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, b)) * 255, decimalPlaces),\n ];\n};\n\n// ----------------------- GET SHIFTED COLORS --------------------------------------\n\nexport const getShiftedHue = (color: HSLColor, shift = 180) : HSLColor => {\n let hue = color[0];\n hue += shift;\n\n if (hue > 360 || hue < 0) {\n hue = mod(hue, 360);\n }\n\n return [hue, color[1], color[2]];\n};\n\nexport const getShiftedLightness = (color: HSLColor, shift = 10) : HSLColor => {\n let lightness = color[2];\n lightness += shift;\n\n if (lightness > 100 || lightness < 0) {\n lightness = mod(lightness, 100);\n }\n\n return [color[0], color[1], lightness];\n};\n\nexport const getShiftedSaturation = (color: HSLColor, shift = 10) : HSLColor => {\n let saturation = color[1];\n saturation += shift;\n\n if (saturation > 100) {\n saturation -= 100;\n }\n\n if(saturation < 0){\n saturation += 100;\n }\n\n return [color[0], saturation, color[2]];\n};\n\n// ----------------------- SIMILAR COLORS --------------------------------------\n\n/**\n * Measure the perceptual difference between two RGB colors using the CIE76 color difference formula:\n * delta = Math.sqrt((L2 - L1)^2 + (a2 - a1)^2 + (b2 - b1)^2)\n * https://en.wikipedia.org/wiki/Color_difference\n * https://stackoverflow.com/questions/13586999/color-difference-similarity-between-two-values-with-js\n * <= 1.0 Not perceptible by human eyes.\n * 1 - 2 Perceptible through close observation.\n * 2 - 10 Perceptible at a glance.\n * 11 - 49 Colors are more similar than opposite\n * 100 Colors are exact opposite\n */\nexport const getColorsDelta = (rgbA: RGBColor, rgbB: RGBColor, decimalPlaces = Infinity) => {\n const labA = rgbToLab(rgbA, decimalPlaces);\n const labB = rgbToLab(rgbB, decimalPlaces);\n\n // differences between the LAB components of the two colors\n const deltaL = labA[0] - labB[0];\n const deltaA = labA[1] - labB[1];\n const deltaB = labA[2] - labB[2];\n\n // chroma components\n const c1 = Math.sqrt(labA[1] * labA[1] + labA[2] * labA[2]);\n const c2 = Math.sqrt(labB[1] * labB[1] + labB[2] * labB[2]);\n const deltaC = c1 - c2;\n\n // difference in hue, deltaH, which takes into account both the differences\n // in the a* and b* components of LAB and the differences in chroma.\n let deltaH = deltaA * deltaA + deltaB * deltaB - deltaC * deltaC;\n deltaH = deltaH < 0 ? 0 : Math.sqrt(deltaH);\n\n const sc = 1.0 + 0.045 * c1;\n const sh = 1.0 + 0.015 * c1;\n\n // It applies weighting factors to the differences in lightness (deltaL),\n // chroma (deltaC), and hue (deltaH).\n const deltaLKlsl = deltaL / (1.0);\n const deltaCkcsc = deltaC / (sc);\n const deltaHkhsh = deltaH / (sh);\n\n // It computes the final color difference using the CIE76 formula:\n // deltaE = sqrt(deltaLKlsl^2 + deltaCkcsc^2 + deltaHkhsh^2),\n // where deltaLKlsl is the weighted lightness difference,\n // deltaCkcsc is the weighted chroma difference,\n // and deltaHkhsh is the weighted hue difference.\n const i = deltaLKlsl * deltaLKlsl + deltaCkcsc * deltaCkcsc + deltaHkhsh * deltaHkhsh;\n\n // It returns the calculated color difference,\n // optionally rounded to the specified number of decimal places.\n return i < 0 ? 0 : Math.sqrt(i);\n};\n", "import { Vector2 } from '../types';\n\n/**\n * Speed = how far something moves in a given amount of time.\n * Speed is also a vector:\n * magnitude = distance\n * direction = time\n */\nexport type Speed = Vector2;\n\n/**\n * Velocity is a measure of how fast an object is moving in a particular direction.\n * Velocity = Distance traveled / Time taken\n * It has a magnitude and direction, and can be represented as a vector.\n */\nexport type Velocity = Vector2;\n\n/**\n * Acceleration is a measure of how quickly an object's velocity changes over time.\n * Acceleration = (Final velocity - Initial velocity) / Time taken\n * a = (vf - v0)/t.\n * Distance = Initial velocity * time + (acceleration * time^2) / 2\n * It also has a magnitude and direction, and can be represented as a vector.\n * When the direction is negative ----> it's a \"slowdown\" movement\n */\nexport type Acceleration = Vector2;\n\n/**\n * Gravity is the force that attracts two objects with mass toward each other.\n * Newton's law of universal gravitation formula:\n * Gravitational force = (Gravitational constant * Mass of object 1 * Mass of object 2) / Distance between objects^2\n * It also has a magnitude and direction, and can be represented as a vector.\n * magnitude = the strength of the gravitational force\n * direction = the direction in which the force is acting (the direction of the gravitational force is always toward the center of mass of the objects involved)\n */\nexport type Gravity = Vector2;\n\n", "/**\n * guid like '932ade5e-c515-4807-ac01-73b20ab3fb66'\n */\nexport const guid = () => {\n return 'xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx'.replace(/[xy]/g, (c) => {\n const r = Math.random() * 16 | 0;\n return (c == 'x' ? r : r & 0x3 | 0x8).toString(16);\n });\n};\n\n/**\n * id like 'df4unio1opulby2uqh4'\n */\nexport const newId = () => {\n return Math.random().toString(36).substring(2) + (new Date()).getTime().toString(36);\n};\n", "import { ICircle, IPolygon, IRect, Matrix2, Vector2 } from '../types';\nimport { mod } from './other';\nimport { v2GetNormal, v2DotProduct } from './linear-algebra/vector';\n\n/**\n * Rectangles collision detection.\n * Rectangles should not be rotated.\n * The algorithm works by ensuring there is no gap between any of the 4 sides of the rectangles.\n * Any gap means a collision does not exist.\n * Returns true if collision is detected.\n */\nexport const rectCollide = (rect1: IRect, rect2: IRect) : boolean => {\n return rect1.x <= rect2.x + rect2.w &&\n rect1.x + rect1.w >= rect2.x &&\n rect1.y <= rect2.y + rect2.h &&\n rect1.h + rect1.y >= rect2.y;\n};\n\n/**\n * Circles collision detection.\n * This algorithm works by taking the center points of the two circles\n * and ensuring the distance between the center points\n * are less than the two radii added together.\n * Returns true if collision is detected.\n */\nexport const circleCollide = (circle1: ICircle, circle2: ICircle) => {\n const dx = Math.abs(circle1.cx - circle2.cx);\n const dy = Math.abs(circle1.cy - circle2.cy);\n const distance = Math.sqrt(dx * dx + dy * dy);\n return distance <= circle1.r + circle2.r;\n};\n\n//-------------------- Separating Axis Theorem (SAT) Collision detection -------------------------\n\nconst getEdges = (poly: IPolygon) : Matrix2[] => {\n const edges: Matrix2[] = [];\n\n for(let i= 0; i {\n const edges: Matrix2[] = [];\n\n // collect polygon edges, and combine then into a single array\n edges.push(...getEdges(poly1));\n edges.push(...getEdges(poly2));\n\n // for each edge, find the normal vector and project both polygons onto it\n for (const edge of edges) {\n const normal = v2GetNormal(edge[0], edge[1]);\n const p1Proj = projectPolygon(poly1, normal);\n const p2Proj = projectPolygon(poly2, normal);\n\n // Check if the projections overlap\n const isOverlap = p1Proj.max >= p2Proj.min && p2Proj.max >= p1Proj.min;\n\n // Check if the projections overlap; if not, the polygons do not collide\n if (!isOverlap) return false;\n }\n\n // If all tests pass, the polygons overlap and collide\n return true;\n};\n\n/**\n * Project every polygon point onto the normal.\n * Then find min and max.\n */\nconst projectPolygon = (polygon: IPolygon, normal: Vector2): { min: number, max: number } => {\n let min = Infinity;\n let max = -Infinity;\n\n // Project each vertex of the polygon onto the axis\n for (const vertex of polygon) {\n const projection = v2DotProduct(vertex, normal);\n min = Math.min(min, projection);\n max = Math.max(max, projection);\n }\n\n return { min, max };\n};", "export interface IAnimationProps {\n duration?: number;\n callback: (result: IAnimationResult) => void;\n restartOnResize?: boolean;\n resizeCallback?: (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => void;\n}\n\nexport interface IAnimationResult {\n start: () => void;\n stop: () => void;\n pause: () => void;\n resume: () => void;\n restart: () => void;\n isAnimating: () => boolean;\n getStartTime: () => number|undefined;\n getElapsedTime: () => number|undefined;\n getPercent: () => number|undefined;\n getResizeObserver: () => ResizeObserver|undefined;\n}\n\nexport const animate = (props: IAnimationProps) : IAnimationResult => {\n\n const _duration = props.duration !== undefined ? props.duration : Infinity;\n\n let startTime: number|undefined = undefined; // in milliseconds\n let animationId: number|undefined = undefined;\n\n // the time elapsed since the start of the animation (in milliseconds)\n let elapsed: number|undefined = undefined;\n let previousTimeStamp: number|undefined = undefined;\n\n let animating = false;\n let observer: ResizeObserver|undefined = undefined;\n\n // -------------------- COMMANDS ---------------------\n\n const stop = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = false;\n\n /*if(observer !== undefined){\n observer.disconnect();\n observer = undefined;\n }*/\n\n if(animationId === undefined) return;\n window.cancelAnimationFrame(animationId);\n };\n\n const restart = () => {\n stop();\n start();\n };\n\n const pause = () => {\n animating = false;\n };\n\n const resume = () => {\n animating = true;\n };\n\n /**\n * Animation Step.\n * @param {number} timeStamp in milliseconds\n */\n const step = (timeStamp: DOMHighResTimeStamp) => {\n\n if (startTime === undefined) {\n startTime = timeStamp;\n }\n\n // the time elapsed since the start of the animation (in milliseconds)\n elapsed = timeStamp - startTime;\n\n if (animating && previousTimeStamp !== timeStamp && typeof props.callback === 'function') {\n\n // do the rendering .............\n props.callback(getResult());\n }\n\n if(elapsed <= _duration){\n previousTimeStamp = timeStamp;\n animationId = window.requestAnimationFrame(step);\n }\n else{\n stop();\n }\n };\n\n const observerHandler = (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => {\n restart();\n\n if(typeof props.resizeCallback === 'function'){\n props.resizeCallback(_entries, _observer);\n }\n };\n\n const start = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = true;\n\n if(props.restartOnResize && window.ResizeObserver && observer === undefined){\n observer = new ResizeObserver(observerHandler);\n observer.observe(document.body, { box: 'border-box' });\n }\n else{\n animationId = window.requestAnimationFrame(step);\n }\n };\n\n // --------------- GET INFO ----------------------\n\n /**\n * the time elapsed since the start of the animation (in milliseconds)\n */\n const getElapsedTime = () : number|undefined => {\n return elapsed;\n };\n\n const isAnimating = () => {\n return animating;\n };\n\n const getStartTime = () => {\n return startTime;\n };\n\n const getPercent = () => {\n if(_duration === Infinity || elapsed === undefined) return undefined;\n return elapsed * 100 / _duration;\n };\n\n const getResizeObserver = () => {\n return observer;\n };\n\n const getResult = () : IAnimationResult => {\n return {\n\n // commands --------------\n start,\n stop,\n pause,\n resume,\n restart,\n\n // information -------\n isAnimating,\n getElapsedTime,\n getStartTime,\n getPercent,\n getResizeObserver,\n };\n };\n\n return getResult();\n};\n", "import { setDecimalPlaces } from './format';\n\nexport const getCircleCircumference = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * radius, decimalPlaces);\n};\n\nexport const getEllipseCircumference = (radius1: number, radius2: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * Math.sqrt((radius1 ** 2 + radius2 ** 2) / 2), decimalPlaces);\n};\n\nexport const isAngleInCircleArc = (startAngleDeg: number, endAngleDeg: number, currentDegrees: number) : boolean => {\n\n if(startAngleDeg > endAngleDeg) {\n endAngleDeg += 360;\n }\n\n return currentDegrees >= startAngleDeg && currentDegrees <= endAngleDeg ||\n (currentDegrees + 360) >= startAngleDeg && (currentDegrees + 360) <= endAngleDeg;\n};\n\n/**\n * get the side of a square inscribed in a circle\n */\nexport const getSquareInCircleSide = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(radius * 2 / Math.sqrt(2), decimalPlaces);\n};\n", "/**\n * 1 + 2 + ... + n = n * (n + 1) / 2\n */\nexport const naturalNumbersSequenceSum = (n: number) => {\n return n * (n + 1) / 2;\n};\n\n/**\n * n = the number of terms to be added\n * a = the first term in the sequence\n * d = the constant value between terms\n */\nexport const arithmeticSequenceSum = (n: number, a: number, d: number) => {\n return (n / 2) * (2 * a + (n - 1) * d);\n};", "import { setDecimalPlaces } from './format';\n\n// -------------------- CENTRAL TENDENCY ----------------------------\n\n/**\n * Central tendency: Calculate the Average (mean = \u03BC)\n * Sum of all numbers divided by the array length.\n */\nexport const getArithmeticMean = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const sum = data.reduce((acc, val) => acc + val, 0);\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Frequency map: number ---> it's frequency\n */\nexport const getArithmeticMeanFromFrequency = (frequencyMap: Map, decimalPlaces = Infinity) => {\n\n let mean = 0;\n\n for(const [val, frequency] of frequencyMap) {\n mean += val * frequency;\n }\n\n return setDecimalPlaces(mean, decimalPlaces);\n};\n\n/**\n * Central tendency: What is the central number in the sorted array?\n * Good for lists like [3, 3, 3, 3, 3, 3, 100] - 100 here is called \"Outlier\"\n */\nexport const getMedian = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const copy = [...data].sort((num1, num2) => num1 - num2);\n const mid = Math.floor(copy.length / 2);\n\n if(copy.length % 2 === 0) {\n return setDecimalPlaces((copy[mid] + copy[mid - 1]) / 2, decimalPlaces);\n }\n else {\n return setDecimalPlaces(copy[mid], decimalPlaces);\n }\n};\n\n/**\n * Central tendency: What number is most common in the set.\n * If all numbers have the same frequency, there is no mode.\n */\nexport const getMode = (data: number[]) : number[]|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n // Count frequency of each number in the data array.\n const frequencyMap: Map = new Map();\n for (const num of data) {\n frequencyMap.set(num, (frequencyMap.get(num) || 0) + 1);\n }\n\n let maxFrequency = 0;\n let modes: number[] = [];\n\n // Find the maximum frequency\n for (const [num, frequency] of frequencyMap) {\n if (frequency > maxFrequency) {\n maxFrequency = frequency;\n modes = [num];\n }\n else if (frequency === maxFrequency) {\n modes.push(num);\n }\n }\n\n // If all numbers have the same frequency, there is no mode\n if (modes.length === data.length) {\n return undefined;\n }\n\n // Return the mode(s)\n return modes.length === 1 ? [modes[0]] : modes;\n};\n\n/*\nTODO:\n- geometric mean\n- harmonic mean\n */\n\n// -------------------- DISPERSION ----------------------------\n\n/**\n * Dispersion: the average square distance from the mean.\n * Sum of (x - mean)^2 / N\n */\nexport const getVariance1 = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + ((val - mean) ** 2), 0);\n\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Another formula of dispersion - the average square distance from the mean.\n * (Sum of x^2) / N - (mean ^ 2)\n */\nexport const getVariance = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + (val ** 2), 0);\n\n return setDecimalPlaces((sum / data.length) - (mean ** 2), decimalPlaces);\n};\n\n/**\n * \u03C3\n */\nexport const getStandardDeviation = (data: number[], decimalPlaces = Infinity) => {\n const variance = getVariance(data) ?? 0;\n return setDecimalPlaces(Math.sqrt(variance), decimalPlaces);\n};", "import { setDecimalPlaces } from './format';\nimport { getArithmeticMean, getStandardDeviation } from './statistics';\nimport { IMlNormalizeResult, IMlStandardizeResult } from '../types';\n\n// --------------------- NORMALIZE --------------------------------\n\n/**\n * Changes value to be in the range [0, 1].\n */\nexport const mlNormalizeValue = (value: number, min: number, max: number, decimalPlaces = Infinity) : number => {\n const diff = max - min;\n if(diff === 0) return 0;\n return setDecimalPlaces((value - min) / diff, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [0, 1].\n */\nexport const mlNormalizeArray = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n const copy = [...data];\n\n for(let i=0; i {\n const min = Math.min(...data);\n const max = Math.max(...data);\n const _data = mlNormalizeArray(data, min, max, decimalPlaces);\n\n return {\n min: setDecimalPlaces(min, decimalPlaces),\n max: setDecimalPlaces(max, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlNormalizeUnseenData = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n return mlNormalizeArray(data, min, max, decimalPlaces);\n};\n\n// --------------------- STANDARDIZE --------------------------------\n\n/**\n * Changes value to be in the range [-1, 1].\n */\nexport const mlStandardizeValue = (value: number, mean: number, stdDev: number, decimalPlaces = Infinity) : number => {\n if(stdDev === 0) return 0;\n return setDecimalPlaces((value - mean) / stdDev, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [-1, 1].\n */\nexport const mlStandardizeArray = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity) : number[] => {\n return [...data].map(value => mlStandardizeValue(value, mean, stdDev, decimalPlaces));\n};\n\nexport const mlStandardizeTestData = (data: number[], decimalPlaces = Infinity): IMlStandardizeResult => {\n const mean = getArithmeticMean(data) ?? 0;\n const stdDev = getStandardDeviation(data);\n const _data = mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n\n return {\n mean: setDecimalPlaces(mean, decimalPlaces),\n stdDev: setDecimalPlaces(stdDev, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlStandardizeUnseenData = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity): number[] => {\n return mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n};", "/**\n * Sum of 1 to n numbers:\n * (n * (n + 1)) / 2\n */\nexport const naturalNumbersSum1ToN = (n: number): number => {\n return (n / 2) * (n + 1);\n};\n\n/**\n * Sum of m to n numbers.\n */\nexport const naturalNumbersSumMToN = (m: number, n: number): number => {\n return (n - m + 1) * (m + n) / 2;\n};", "import * as vector from './main/linear-algebra/vector';\nimport * as matrix from './main/linear-algebra/matrix';\nimport * as matrixTransformations from './main/linear-algebra/matrix-transformations';\nimport * as format from './main/format';\nimport * as angle from './main/angle';\nimport * as random from './main/random';\nimport * as other from './main/other';\nimport * as convert from './main/convert';\nimport * as bezierCurve from './main/bezier-curves/bezier-curve';\nimport * as equations from './main/equations/linear-equations';\nimport * as pathMovement from './main/path-movement';\nimport * as color from './main/color';\nimport * as physics from './main/physics';\nimport * as id from './main/id';\nimport * as derivative from './main/derivative';\nimport * as collisions from './main/collision-detection';\nimport * as animation from './main/animation';\nimport * as circleEllipse from './main/circle-ellipse';\nimport * as sequence from './main/sequence';\nimport * as statistics from './main/statistics';\nimport * as ml from './main/ml';\nimport * as series from './main/series';\n\nconst api = {\n ...vector,\n ...matrix,\n ...matrixTransformations,\n ...format,\n ...angle,\n ...random,\n ...other,\n ...convert,\n ...bezierCurve,\n ...equations,\n ...pathMovement,\n ...color,\n ...physics,\n ...id,\n ...derivative,\n ...collisions,\n ...animation,\n ...circleEllipse,\n ...sequence,\n ...statistics,\n ...ml,\n ...series,\n};\n\ndeclare global {\n interface Window {\n mzMath: typeof api,\n }\n}\n\nwindow.mzMath = window.mzMath || api;\n\nexport * from './main/linear-algebra/vector';\nexport * from './main/linear-algebra/matrix';\nexport * from './main/linear-algebra/matrix-transformations';\nexport * from './main/format';\nexport * from './main/angle';\nexport * from './main/random';\nexport * from './main/other';\nexport * from './main/convert';\nexport * from './main/bezier-curves/bezier-curve';\nexport * from './main/equations/linear-equations';\nexport * from './main/path-movement';\nexport * from './main/color';\nexport * from './main/physics';\nexport * from './main/id';\nexport * from './main/derivative';\nexport * from './main/collision-detection';\nexport * from './main/animation';\nexport * from './main/circle-ellipse';\nexport * from './main/sequence';\nexport * from './main/statistics';\nexport * from './main/ml';\nexport * from './main/series';"], + "mappings": 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"m3x3", "m4x4", "mAdjugate", "mAppendCol", "mAppendRow", "mDeepCopy", "mDelFirstColumn", "mDelFirstRow", "mDelLastColumn", "mDelLastRow", "mDeterminant", "mDivideScalar", "mEqual", "mGetColumn", "mGetFirstColumn", "mGetLastColumn", "mInverse", "mMinor", "mMul", "mMulScalar", "mMulVector", "mNxM", "mPrependCol", "mPrependRow", "mReset", "mSub", "mSum", "mTranspose", "mSum", "matrix1", "matrix2", "decimalPlaces", "matrix", "i", "vSum", "m2Sum", "m3Sum", "mSub", "vSub", "m2Sub", "m3Sub", "mMulScalar", "m", "scalar", "v", "vMulScalar", "m2MulScalar", "m2", "m3MulScalar", "m3", "mDivideScalar", "vDivideScalar", "m2DivideScalar", "m3DivideScalar", "mTranspose", "vectorsCount", "vectorLength", "j", "m2Transpose", "m3Transpose", "mReset", "defaultValue", "res", "size", "vector", "m2Reset", "m3Reset", "m2x2", "m3x3", "m4x4", "mNxM", "N", "M", "vN", "identity2", "identity3", "identity4", "identityN", "mDeepCopy", "m2DeepCopy", "m3DeepCopy", "mAppendCol", "col", "copy", "mPrependCol", "mAppendRow", "row", "m2AppendRow", "m3AppendRow", "mPrependRow", "m2PrependRow", "m3PrependRow", "mDelLastRow", "mDelFirstRow", "mDelLastColumn", "mDelFirstColumn", "mGetFirstColumn", "mGetLastColumn", "mGetColumn", "colIndex", "mMul", "transposed", "vector1", "vector2", "product", "vDotProduct", "mMulVector", "mEqual", "vEqual", "mMinorHelper", "mMinor", "mDeterminant", "m2Determinant", "d", "minor", "param", "m3Determinant", "m2Adjugate", "m3Adjugate", "mAdjugate", "cofactors", "sign", "isSingularMatrix", "m2Inverse", "adj", "m3Inverse", "mInverse", "matrix_transformations_exports", "__export", "m2ReflectionOrigin", "m2ReflectionOriginH", "m2ReflectionX", "m2ReflectionXH", "m2ReflectionY", "m2ReflectionYH", "m2ReflectionYmX", "m2RotateAroundPointH", "m2Rotation", "m2RotationAroundPointH", "m2RotationH", "m2Scale", "m2ScaleAtPointH", "m2ScaleAtPointHMatrix", "m2ScaleH", "m2ScaleX", "m2ScaleXH", "m2ScaleY", "m2ScaleYH", "m2ShearingX", "m2ShearingY", "m2ToCSS", "m2Translation", "m2TranslationH", "m2hToCSS", "m2hToCSS3d", "m3ReflectionOrigin", "m3ReflectionOriginH", "m3ReflectionXY", "m3ReflectionXYH", "m3ReflectionXZ", "m3ReflectionXZH", "m3ReflectionYZ", "m3ReflectionYZH", "m3RotationX", "m3RotationXH", "m3RotationY", "m3RotationYH", "m3RotationZ", "m3RotationZH", "m3Scale", "m3ScaleH", "m3ScaleX", "m3ScaleXH", "m3ScaleY", "m3ScaleYH", "m3ScaleZ", "m3ScaleZH", "m3Translation", "m3TranslationH", "m3hToCSS3d", "v2Rotate", "v2RotateH", "v2Scale", "v3RotateX", "v3RotateY", "v3RotateZ", "v3Scale", "m2ToCSS", "m", "a", "b", "c", "d", "m2hToCSS", "tx", "ty", "m2hToCSS3d", "m3hToCSS3d", "m2Translation", "position", "decimalPlaces", "setDecimalPlaces", "m3Translation", "m2TranslationH", "m3TranslationH", "m2Rotation", "angleRad", "isClockwise", "cos", "sin", "m2RotationH", "m2RotationAroundPointH", "transformOrigin", "translation", "rotation", "translationBack", "v3MulScalar", "temp1", "mMul", "m2RotateAroundPointH", "mat3h", "mMulVector", "v2Rotate", "vector", "unitVector", "v2Normalize", "v2RotateH", "v3Normalize", "m3RotationX", "m3RotationXH", "v3RotateX", "m3RotationY", "m3RotationYH", "v3RotateY", "m3RotationZ", "m3RotationZH", "v3RotateZ", "m2ScaleAtPointHMatrix", "scaleVector", "scale", "m2ScaleH", "m2ScaleAtPointH", "point", "m2Scale", "v2Scale", "m3Scale", "m3ScaleH", "v3Scale", "m2ScaleX", "m2ScaleXH", "m3ScaleX", "m3ScaleXH", "m3ScaleY", "m3ScaleYH", "m3ScaleZ", "m3ScaleZH", "m2ScaleY", "m2ScaleYH", "m2ReflectionOrigin", "m2ReflectionOriginH", "m3ReflectionOrigin", "m3ReflectionOriginH", "m2ReflectionYmX", "m2ReflectionX", "m2ReflectionXH", "m2ReflectionY", "m2ReflectionYH", "m3ReflectionYZ", "m3ReflectionYZH", "m3ReflectionXZ", "m3ReflectionXZH", "m3ReflectionXY", "m3ReflectionXYH", "m2ShearingY", "factor", "m2ShearingX", "random_exports", "__export", "getRandom", "getRandomBoolean", "getRandomInt", "getRandomItemFromArray", "getRandom", "min", "max", "decimalPlaces", "setDecimalPlaces", "getRandomInt", "getRandomBoolean", "getRandomItemFromArray", "array", "randomIndex", "convert_exports", "__export", "stringToNumber", "value", "defaultNumber", "_a", "res", "bezier_curve_exports", "__export", "v2CubicBezierBBox", "v2CubicBezierCurve", "v2CubicBezierCurveExtrema", "v2CubicBezierCurveNormal", "v2CubicBezierCurveTangent", "v2QuadraticBezierBBox", "v2QuadraticBezierCurve", "v2QuadraticBezierCurveExtrema", "v2QuadraticBezierCurveNormal", "v2QuadraticBezierCurveTangent", "v3CubicBezierCurve", "v3CubicBezierCurveTangent", "v3QuadraticBezierCurve", "v3QuadraticBezierCurveTangent", "derivative_exports", "__export", "dxArcCos", "dxArcCot", "dxArcSin", "dxArcTan", "dxCos", "dxCot", "dxPolynomial", "dxSin", "dxTan", "dxV2CubicBezierCurve", "dxV2QuadraticBezierCurve", "dxV3CubicBezierCurve", "dxV3QuadraticBezierCurve", "dxPolynomial", "x", "polynomial", "decimalPlaces", "res", "part", "coeff", "power", "setDecimalPlaces", "dxV2QuadraticBezierCurve", "startControlPoint", "centerControlPoint", "endControlPoint", "temp1", "temp2", "temp3", "dxV3QuadraticBezierCurve", "dxV2CubicBezierCurve", "center1ControlPoint", "center2ControlPoint", "temp4", "dxV3CubicBezierCurve", "dxSin", "dxCos", "dxTan", "__pow", "dxCot", "dxArcSin", "dxArcCos", "dxArcTan", "dxArcCot", "linear_equations_exports", "__export", "getLinearEquationBy2Points", "linearEquation", "linearEquationSystem2", "linearEquationSystem3", "linearEquationSystemN", "linearEquation", "equation", "decimalPlaces", "a", "b", "diff", "setDecimalPlaces", "linearEquationSystem2", "equation1", "equation2", "equationParams", "inversed", "m2Inverse", "equationResults", "mMulVector", "linearEquationSystem3", "equation3", "m3Inverse", "linearEquationSystemN", "equations", "mDelLastColumn", "mInverse", "mGetLastColumn", "getLinearEquationBy2Points", "point1", "point2", "deltaX", "deltaY", "v2Sub", "x", "y", "m", "formula", "quadraticEquation", "equation", "decimalPlaces", "a", "b", "c", "d", "res", "linearEquation", "isNumber", "diff", "discriminant", "setDecimalPlaces", "t1", "t2", "v2QuadraticBezierCurve", "startControlPoint", "centerControlPoint", "endControlPoint", "decimalPlaces", "temp1", "temp2", "temp3", "setDecimalPlaces", "v3QuadraticBezierCurve", "v2CubicBezierCurve", "center1ControlPoint", "center2ControlPoint", "temp4", "v3CubicBezierCurve", "v2QuadraticBezierCurveTangent", "dxVector", "dxV2QuadraticBezierCurve", "v2Normalize", "v3QuadraticBezierCurveTangent", "dxV3QuadraticBezierCurve", "v3Normalize", "v2CubicBezierCurveTangent", "dxV2CubicBezierCurve", "v3CubicBezierCurveTangent", "dxV3CubicBezierCurve", "v2QuadraticBezierCurveNormal", "tangent", "v2CubicBezierCurveNormal", "v2QuadraticBezierCurveExtrema", "a1", "b1", "res1", "linearEquation", "a2", "b2", "res2", "res", "isNumber", "v2CubicBezierCurveExtrema", "c1", "equation1", "c2", "equation2", "quadraticEquation", "num", "v2QuadraticBezierBBox", "extrema", "minX", "minY", "maxX", "maxY", "percent", "point", "x", "y", "v2CubicBezierBBox", "path_movement_exports", "__export", "circleMovement", "circleMovementAfterMouse", "ellipseMovement", "ellipseMovementAfterMouse", "lissajousCurve", "sineWaveMovement", "circleMovement", "center", "angle", "radius", "circleMovementAfterMouse", "mouse", "vector", "v2Sub", "getV2Angle", "convertRange", "ellipseMovement", "radius1", "radius2", "ellipseMovementAfterMouse", "radii", "sineWaveMovement", "x", "amplitude", "frequency", "phase", "y", "lissajousCurve", "width", "height", "t", "k", "n", "m", "p", "color_exports", "__export", "getColorsDelta", "getRandomGrayscaleHSLColor", "getRandomHSLColor", "getRandomHSLColorWithHue", "getRandomHSLColorWithLightness", "getRandomHSLColorWithSaturation", "getRandomHSLColorWithinRanges", "getRandomHexColor", "getRandomRGBColor", "getShiftedHue", "getShiftedLightness", "getShiftedSaturation", "hexToRgb", "hslToHex", "hslToRgb", "labToRgb", "rgbToHex", "rgbToHsl", "rgbToLab", "getRandomRGBColor", "hslColor", "getRandomHSLColor", "hslToRgb", "getRandomHexColor", "hslToHex", "h", "getRandom", "s", "l", "getRandomHSLColorWithHue", "getRandomHSLColorWithSaturation", "getRandomHSLColorWithLightness", "getRandomGrayscaleHSLColor", "getRandomHSLColorWithinRanges", "hueStart", "hueEnd", "saturationStart", "saturationEnd", "lightStart", "lightEnd", "convertHueToDegrees", "getHue", "r", "g", "b", "min", "max", "diff", "getLuminance", "getSaturation", "rgbToHsl", "rgb", "decimalPlaces", "setDecimalPlaces", "hslToRgbHelper", "helper1", "helper2", "colorHelper", "hsl", "gray", "rHelper", "gHelper", "bHelper", "hue2rgb", "q", "t", "p", "toHex", "x", "hex", "rgbToHex", "hexToRgb", "shorthandRegex", "_hex", "_m", "result", "rgbToLab", "y", "z", "labToRgb", "lab", "getShiftedHue", "color", "shift", "hue", "mod", "getShiftedLightness", "lightness", "getShiftedSaturation", "saturation", "getColorsDelta", "rgbA", "rgbB", "labA", "labB", "deltaL", "deltaA", "deltaB", "c1", "c2", "deltaC", "deltaH", "sc", "sh", "deltaLKlsl", "deltaCkcsc", "deltaHkhsh", "i", "physics_exports", "id_exports", "__export", "guid", "newId", "c", "collision_detection_exports", "__export", "circleCollide", "convexPolygonsCollide", "rectCollide", "rectCollide", "rect1", "rect2", "circleCollide", "circle1", "circle2", "dx", "dy", "getEdges", "poly", "edges", "i", "nextIndex", "mod", "edge", "convexPolygonsCollide", "poly1", "poly2", "normal", "v2GetNormal", "p1Proj", "projectPolygon", "p2Proj", "polygon", "min", "max", "vertex", "projection", "v2DotProduct", "animation_exports", "__export", "animate", "props", "_duration", "startTime", "animationId", "elapsed", "previousTimeStamp", "animating", "observer", "stop", "restart", "start", "pause", "resume", "step", "timeStamp", "getResult", "observerHandler", "_entries", "_observer", "getElapsedTime", "isAnimating", "getStartTime", "getPercent", "getResizeObserver", "circle_ellipse_exports", "__export", "getCircleCircumference", "getEllipseCircumference", "getSquareInCircleSide", "isAngleInCircleArc", "getCircleCircumference", "radius", "decimalPlaces", "setDecimalPlaces", "getEllipseCircumference", "radius1", "radius2", "__pow", "isAngleInCircleArc", "startAngleDeg", "endAngleDeg", "currentDegrees", "getSquareInCircleSide", "sequence_exports", "__export", "arithmeticSequenceSum", "naturalNumbersSequenceSum", "n", "a", "d", "statistics_exports", "__export", "getArithmeticMean", "getArithmeticMeanFromFrequency", "getMedian", "getMode", "getStandardDeviation", "getVariance", "getVariance1", "getArithmeticMean", "data", "decimalPlaces", "sum", "acc", "val", "setDecimalPlaces", "getArithmeticMeanFromFrequency", "frequencyMap", "mean", "frequency", "getMedian", "copy", "num1", "num2", "mid", "getMode", "num", "maxFrequency", "modes", "getVariance1", "__pow", "getVariance", "getStandardDeviation", "_a", "variance", "ml_exports", "__export", "mlNormalizeArray", "mlNormalizeTestData", "mlNormalizeUnseenData", "mlNormalizeValue", "mlStandardizeArray", "mlStandardizeTestData", "mlStandardizeUnseenData", "mlStandardizeValue", "mlNormalizeValue", "value", "min", "max", "decimalPlaces", "diff", "setDecimalPlaces", "mlNormalizeArray", "data", "copy", "mlNormalizeTestData", "_data", "mlNormalizeUnseenData", "mlStandardizeValue", "mean", "stdDev", "mlStandardizeArray", "mlStandardizeTestData", "_a", "getArithmeticMean", "getStandardDeviation", "mlStandardizeUnseenData", "series_exports", "__export", "naturalNumbersSum1ToN", "naturalNumbersSumMToN", "n", "m", "api", "__spreadValues", "vector_exports", "matrix_exports", "matrix_transformations_exports", "format_exports", "angle_exports", "random_exports", "other_exports", "convert_exports", "bezier_curve_exports", "linear_equations_exports", "path_movement_exports", "color_exports", "physics_exports", "id_exports", "derivative_exports", "collision_detection_exports", "animation_exports", "circle_ellipse_exports", "sequence_exports", "statistics_exports", "ml_exports", "series_exports"] } diff --git a/dist/mz-math.node.cjs b/dist/mz-math.node.cjs index b986a0d0..20f48364 100644 --- a/dist/mz-math.node.cjs +++ b/dist/mz-math.node.cjs @@ -1,14 +1,14 @@ /* -mzMath v3.0.24 +mzMath v3.0.25 A collection of TypeScript-based math helpers. https://github.com/mzusin/mz-math Licensed GPLv3 for open source use, or Commercial License for commercial use - https://github.com/mzusin/index/blob/main/LICENSE.md Copyright (c) 2023-present, Miriam Zusin */ -var _=Object.defineProperty;var ur=Object.getOwnPropertyDescriptor;var xr=Object.getOwnPropertyNames;var mr=Object.prototype.hasOwnProperty;var h=Math.pow;var ar=(t,r)=>{for(var e in r)_(t,e,{get:r[e],enumerable:!0})},fr=(t,r,e,n)=>{if(r&&typeof r=="object"||typeof r=="function")for(let o of xr(r))!mr.call(t,o)&&o!==e&&_(t,o,{get:()=>r[o],enumerable:!(n=ur(r,o))||n.enumerable});return t};var pr=t=>fr(_({},"__esModule",{value:!0}),t);var 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To=t=>t/2*(t+1),Bo=(t,r)=>(r-t+1)*(t+r)/2;0&&(module.exports={animate,arithmeticSequenceSum,circleCollide,circleMovement,circleMovementAfterMouse,convertRange,convexPolygonsCollide,degreesToRadians,doRangesOverlap,dxArcCos,dxArcCot,dxArcSin,dxArcTan,dxCos,dxCot,dxPolynomial,dxSin,dxTan,dxV2CubicBezierCurve,dxV2QuadraticBezierCurve,dxV3CubicBezierCurve,dxV3QuadraticBezierCurve,ellipseMovement,ellipseMovementAfterMouse,getAnglesDistance,getAnglesSub,getArithmeticMean,getArithmeticMeanFromFrequency,getCircleCircumference,getColorsDelta,getEllipseCircumference,getLinearEquationBy2Points,getMedian,getMode,getRandom,getRandomBoolean,getRandomGrayscaleHSLColor,getRandomHSLColor,getRandomHSLColorWithHue,getRandomHSLColorWithLightness,getRandomHSLColorWithSaturation,getRandomHSLColorWithinRanges,getRandomHexColor,getRandomInt,getRandomItemFromArray,getRandomRGBColor,getShiftedHue,getShiftedLightness,getShiftedSaturation,getSquareInCircleSide,getStandardDeviation,getV2Angle,getV2AngleBetween,getV2AngleInEllipse,getV3AngleBetween,getVNAngleBetween,getVariance,getVariance1,guid,hexToRgb,hslToHex,hslToRgb,identity2,identity3,identity4,identityN,isAngleBetween,isAngleInCircleArc,isClockwise,isNumber,isSingularMatrix,labToRgb,linearEquation,linearEquationSystem2,linearEquationSystem3,linearEquationSystemN,lissajousCurve,m2Adjugate,m2AppendRow,m2DeepCopy,m2Determinant,m2DivideScalar,m2Inverse,m2MulScalar,m2PrependRow,m2ReflectionOrigin,m2ReflectionOriginH,m2ReflectionX,m2ReflectionXH,m2ReflectionY,m2ReflectionYH,m2ReflectionYmX,m2Reset,m2RotateAroundPointH,m2Rotation,m2RotationAroundPointH,m2RotationH,m2Scale,m2ScaleAtPointH,m2ScaleAtPointHMatrix,m2ScaleH,m2ScaleX,m2ScaleXH,m2ScaleY,m2ScaleYH,m2ShearingX,m2ShearingY,m2Sub,m2Sum,m2ToCSS,m2Translation,m2TranslationH,m2Transpose,m2hToCSS,m2hToCSS3d,m2x2,m3Adjugate,m3AppendRow,m3DeepCopy,m3Determinant,m3DivideScalar,m3Inverse,m3MulScalar,m3PrependRow,m3ReflectionOrigin,m3ReflectionOriginH,m3ReflectionXY,m3ReflectionXYH,m3ReflectionXZ,m3ReflectionXZH,m3ReflectionYZ,m3ReflectionYZH,m3Reset,m3RotationX,m3RotationXH,m3RotationY,m3RotationYH,m3RotationZ,m3RotationZH,m3Scale,m3ScaleH,m3ScaleX,m3ScaleXH,m3ScaleY,m3ScaleYH,m3ScaleZ,m3ScaleZH,m3Sub,m3Sum,m3Translation,m3TranslationH,m3Transpose,m3hToCSS3d,m3x3,m4x4,mAdjugate,mAppendCol,mAppendRow,mDeepCopy,mDelFirstColumn,mDelFirstRow,mDelLastColumn,mDelLastRow,mDeterminant,mDivideScalar,mEqual,mGetColumn,mGetFirstColumn,mGetLastColumn,mInverse,mMinor,mMul,mMulScalar,mMulVector,mNxM,mPrependCol,mPrependRow,mReset,mSub,mSum,mTranspose,mlNormalizeArray,mlNormalizeTestData,mlNormalizeUnseenData,mlNormalizeValue,mlStandardizeArray,mlStandardizeTestData,mlStandardizeUnseenData,mlStandardizeValue,mod,naturalNumbersSequenceSum,naturalNumbersSum1ToN,naturalNumbersSumMToN,newId,percentToAngle,polarToCartesian,radiansToDegrees,rectCollide,rgbToHex,rgbToHsl,rgbToLab,setDecimalPlaces,setV2Angle,sineWaveMovement,stringToNumber,v2,v2CubicBezierBBox,v2CubicBezierCurve,v2CubicBezierCurveExtrema,v2CubicBezierCurveNormal,v2CubicBezierCurveTangent,v2Distance,v2DivideScalar,v2DotProduct,v2FromPolarCoords,v2GetNormal,v2Length,v2MulScalar,v2Normalize,v2QuadraticBezierBBox,v2QuadraticBezierCurve,v2QuadraticBezierCurveExtrema,v2QuadraticBezierCurveNormal,v2QuadraticBezierCurveTangent,v2Rotate,v2RotateH,v2Scale,v2SetLength,v2Sub,v2Sum,v3,v3CrossProduct,v3CubicBezierCurve,v3CubicBezierCurveTangent,v3Distance,v3DivideScalar,v3DotProduct,v3Length,v3MulScalar,v3Normalize,v3QuadraticBezierCurve,v3QuadraticBezierCurveTangent,v3RotateX,v3RotateY,v3RotateZ,v3Scale,v3Sub,v3Sum,v4,vDistance,vDivideScalar,vDotProduct,vEqual,vLength,vMulScalar,vN,vNormalize,vSub,vSum}); //# sourceMappingURL=mz-math.node.cjs.map diff --git a/dist/mz-math.node.cjs.map b/dist/mz-math.node.cjs.map index 5c312a3b..0fdfdaf5 100644 --- a/dist/mz-math.node.cjs.map +++ b/dist/mz-math.node.cjs.map @@ -1,7 +1,7 @@ { "version": 3, - "sources": ["../src/index-esm.ts", "../src/main/format.ts", "../src/main/other.ts", "../src/main/angle.ts", "../src/main/linear-algebra/vector.ts", "../src/main/linear-algebra/matrix.ts", "../src/main/linear-algebra/matrix-transformations.ts", "../src/main/random.ts", "../src/main/convert.ts", "../src/main/derivative.ts", "../src/main/equations/linear-equations.ts", "../src/main/equations/quadratic-equations.ts", "../src/main/bezier-curves/bezier-curve.ts", "../src/main/path-movement.ts", "../src/main/color.ts", "../src/main/id.ts", "../src/main/collision-detection.ts", "../src/main/animation.ts", "../src/main/circle-ellipse.ts", "../src/main/sequence.ts", "../src/main/statistics.ts", "../src/main/ml.ts"], - "sourcesContent": ["export * from './main/linear-algebra/vector';\nexport * from './main/linear-algebra/matrix';\nexport * from './main/linear-algebra/matrix-transformations';\nexport * from './main/format';\nexport * from './main/angle';\nexport * from './main/random';\nexport * from './main/other';\nexport * from './main/convert';\nexport * from './main/bezier-curves/bezier-curve';\nexport * from './main/equations/linear-equations';\nexport * from './main/path-movement';\nexport * from './main/color';\nexport * from './main/physics';\nexport * from './main/id';\nexport * from './main/derivative';\nexport * from './main/collision-detection';\nexport * from './main/animation';\nexport * from './main/circle-ellipse';\nexport * from './main/sequence';\nexport * from './main/statistics';\nexport * from './main/ml';", "export const setDecimalPlaces = (num: number, decimalPlaces: number | undefined = Infinity) => {\n if(decimalPlaces === Infinity) return num;\n\n if(decimalPlaces < 0){\n decimalPlaces = 0;\n }\n\n const coefficient = 10 ** decimalPlaces;\n return Math.round(num * coefficient) / coefficient;\n};", "import { Vector2 } from '../types';\nimport { setDecimalPlaces } from './format';\n\nexport const mod = (n: number, m: number) => {\n return ((n % m) + m) % m;\n};\n\n/**\n * Convert range [a, b] to [c, d].\n * f(x) = (d - c) * (x - a) / (b - a) + c\n */\nexport const convertRange = (x: number, a: number, b: number, c: number, d: number) => {\n return (d - c) * (x - a) / (b - a) + c;\n};\n\n/**\n * Check if 2 ranges [a,b] and [c,d] overlap.\n */\nexport const doRangesOverlap = (a: number, b: number, c: number, d: number) => {\n return Math.max(a, c) <= Math.min(b, d) ;\n};\n\n// eslint-disable-next-line\nexport const isNumber = (value: any) => {\n return !isNaN(parseFloat(value)) && isFinite(value);\n};\n\n/**\n * Convert polar coordinates to cartesian coordinates.\n */\nexport const polarToCartesian = (center: Vector2, radii: Vector2, angleInRad: number, decimalPlaces = Infinity) : Vector2 => {\n const [cx, cy] = center;\n const [rx, ry] = radii;\n\n return [\n setDecimalPlaces(cx + (rx * Math.cos(angleInRad)), decimalPlaces),\n setDecimalPlaces(cy + (ry * Math.sin(angleInRad)), decimalPlaces),\n ];\n};", "import { Vector, Vector2, Vector3 } from '../types';\nimport { setDecimalPlaces } from './format';\nimport { v2Length, vNormalize, vDotProduct, vSub } from './linear-algebra/vector';\nimport { mod } from './other';\n\nexport const getV2Angle = (v2: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1], v2[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleInEllipse = (v2: Vector2, radii: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1]/radii[1], v2[0]/radii[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const setV2Angle = (v2: Vector2, newAngleRad: number, decimalPlaces = Infinity): Vector2 => {\n const length = v2Length(v2);\n return [\n setDecimalPlaces(Math.cos(newAngleRad) * length, decimalPlaces),\n setDecimalPlaces(Math.sin(newAngleRad) * length, decimalPlaces),\n ];\n};\n\nexport const radiansToDegrees = (radians: number, decimalPlaces = Infinity) => {\n const res = radians * (180 / Math.PI);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\nexport const degreesToRadians = (degrees: number, decimalPlaces = Infinity) => {\n const res = degrees * (Math.PI / 180);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\n/**\n * Returns the range [0, Math.PI]\n * A = Math.acos( dot(v1, v2)/(v1.length()*v2.length()) );\n */\nexport const getVNAngleBetween = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n const unitVector1 = vNormalize(vector1);\n const unitVector2 = vNormalize(vector2);\n const dotProduct = vDotProduct(unitVector1, unitVector2);\n const angle = Math.acos(dotProduct);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleBetween = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) : number => {\n // return getVNAngleBetween(vector1, vector2, decimalPlaces);\n const diff = vSub(vector1, vector2);\n const angle = Math.atan2(diff[1], diff[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV3AngleBetween = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return getVNAngleBetween(vector1, vector2, decimalPlaces);\n};\n\nexport const isAngleBetween = (angleDegrees: number, startAngleDegrees: number, endAngleDegrees: number) : boolean => {\n const distance = getAnglesSub(startAngleDegrees, endAngleDegrees);\n const distance1 = getAnglesSub(startAngleDegrees, angleDegrees);\n const distance2 = getAnglesSub(endAngleDegrees, angleDegrees);\n const totalDistance = distance1 + distance2;\n\n // Use a small threshold for floating point errors\n return Math.abs(totalDistance - distance) <= 0.001;\n}\n\nexport const isClockwise = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n return angle2Deg >= angle1Deg;\n};\n\n/**\n * Shortest distance (angular) between two angles.\n */\nexport const getAnglesSub = (angleDegrees1: number, angleDegrees2: number, decimalPlaces = Infinity) : number => {\n const angleDistance = Math.abs(mod(angleDegrees1, 360) - mod(angleDegrees2, 360));\n return setDecimalPlaces(angleDistance <= 180 ? angleDistance : 360 - angleDistance, decimalPlaces);\n};\n\nexport const getAnglesDistance = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0, decimalPlaces = Infinity) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n if(isClockwise(angle1Deg, angle2Deg, startAngleDeg)) {\n return setDecimalPlaces((angle2Deg - angle1Deg + 360) % 360, decimalPlaces);\n }\n else{\n return setDecimalPlaces((angle1Deg - angle2Deg + 360) % 360, decimalPlaces);\n }\n};\n\nexport const percentToAngle = (percent: number, startAngleDeg: number, endAngleDeg: number, circleStartAngle = 0) => {\n if(percent < 0) {\n percent = 0;\n }\n\n if(percent > 100) {\n percent = 100;\n }\n\n const distance = getAnglesDistance(startAngleDeg, endAngleDeg, circleStartAngle);\n\n const clockwise = isClockwise(startAngleDeg, endAngleDeg, circleStartAngle);\n if(clockwise) {\n return mod(circleStartAngle + (percent * distance / 100), 360);\n }\n else {\n return mod(circleStartAngle - (percent * distance / 100), 360);\n }\n};", "import { Vector, Vector2, Vector3, Vector4 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { getV2Angle, setV2Angle } from '../angle';\n\n// ------------ SUM ------------------------\n\nexport const vSum = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSum(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sum = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSum(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ SUB ------------------------\n\nexport const vSub = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSub(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sub = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSub(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ MUL SCALAR ------------------------\n\nexport const vMulScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n const vector: Vector = [];\n\n for(let i=0; i {\n return vMulScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3MulScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vMulScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ DIVIDE ------------------------\n\nexport const vDivideScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vDivideScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3DivideScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vDivideScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ LENGTH ------------------------\n\nexport const vLength = (vector: Vector, decimalPlaces = Infinity) => {\n let sum = 0;\n\n for(let i=0; i {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v3Length = (vector: Vector3, decimalPlaces = Infinity) => {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v2SetLength = (v2: Vector2, newLength: number, decimalPlaces = Infinity): Vector2 => {\n const angle = getV2Angle(v2);\n return [\n setDecimalPlaces(Math.cos(angle) * newLength, decimalPlaces),\n setDecimalPlaces(Math.sin(angle) * newLength, decimalPlaces),\n ];\n};\n\n// ----------- DISTANCE ------------------------\n\nexport const vDistance = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v2Distance = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v3Distance = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\n// ------------ NORMALIZE ------------------------\n\n/**\n * Normalization creates a unit vector, which is a vector of length 1.\n */\nexport const vNormalize = (v: Vector, decimalPlaces = Infinity) : Vector => {\n const length = vLength(v);\n const unitVector: Vector = [];\n\n for(let i=0; i {\n return vNormalize(v2, decimalPlaces) as Vector2;\n};\n\nexport const v3Normalize = (v3: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vNormalize(v3, decimalPlaces) as Vector3;\n};\n\n// ------------ DOT PRODUCT ------------------------\n\nexport const vDotProduct = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n let sum = 0;\n\n for(let i=0; i {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\nexport const v3DotProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\n// ------------ CROSS PRODUCT ------------------------\n\n/**\n * Cross product is possible on 3D vectors only.\n * The cross product a \u00D7 b is defined as a vector c that is perpendicular (orthogonal) to both a and b.\n */\nexport const v3CrossProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity): Vector3 => {\n return [\n setDecimalPlaces(vector1[1] * vector2[2] - vector1[2] * vector2[1], decimalPlaces),\n setDecimalPlaces(vector1[2] * vector2[0] - vector1[0] * vector2[2], decimalPlaces),\n setDecimalPlaces(vector1[0] * vector2[1] - vector1[1] * vector2[0], decimalPlaces),\n ];\n};\n\n// --------------- INIT VECTOR HELPER -----------------\n\nexport const v2 = (defaultValue = 0): Vector2 => {\n return [defaultValue, defaultValue];\n};\n\nexport const v3 = (defaultValue = 0): Vector3 => {\n return [defaultValue, defaultValue, defaultValue];\n};\n\nexport const v4 = (defaultValue = 0): Vector4 => {\n return [defaultValue, defaultValue, defaultValue, defaultValue];\n};\n\nexport const vN = (N: number, defaultValue = 0): Vector => {\n\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n const vector: Vector = [];\n for(let i=0; i {\n let vector: Vector2 = [0, 0];\n vector = v2SetLength(vector, distance);\n return setV2Angle(vector, angleRad);\n};\n\n// --------------- EQUALITY -------------------------\n\nexport const vEqual = (vector1: Vector, vector2: Vector): boolean => {\n if(vector1.length !== vector2.length) return false;\n\n for(let i=0; i {\n const sub = v2Sub(vector2, vector1);\n return [\n -setDecimalPlaces(sub[1], decimalPlaces),\n setDecimalPlaces(sub[0], decimalPlaces)\n ];\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector, Vector2, Vector3 } from '../../types';\nimport { vMulScalar, vSum, vSub, vDotProduct, vN, vEqual, vDivideScalar } from './vector';\n\n// --------------- SUM ----------------------\n\nexport const mSum = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sum = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- SUB ----------------------\n\nexport const mSub = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sub = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- MUL SCALAR ----------------------\n\nexport const mMulScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vMulScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2MulScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mMulScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3MulScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mMulScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n// --------------- DIVIDE SCALAR ----------------------\n\nexport const mDivideScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vDivideScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2DivideScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mDivideScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3DivideScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mDivideScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n\n// --------------- TRANSPOSE ----------------------\n\nexport const mTranspose = (m: Matrix): Matrix => {\n\n const vectorsCount = m.length;\n if(vectorsCount <= 0) return m;\n\n const vectorLength = m[0].length;\n if(vectorLength <= 0) return m;\n\n const matrix: Matrix = [];\n for(let i=0; i {\n return mTranspose(m2);\n};\n\nexport const m3Transpose = (m3: Matrix3): Matrix => {\n return mTranspose(m3);\n};\n\n// ----------------- RESET ----------------------\n\nexport const mReset = (m: Matrix, defaultValue = 0): Matrix => {\n\n if(m.length <= 0) return [];\n\n const res: Matrix = [];\n\n for(let i=0; i {\n return mReset(m2, defaultValue) as Matrix2;\n};\n\nexport const m3Reset = (m3: Matrix3, defaultValue = 0): Matrix3 => {\n return mReset(m3, defaultValue) as Matrix3;\n};\n\n// --------------- MATRIX INIT HELPERS -----------------\n\nexport const m2x2 = (defaultValue = 0): Matrix2 => {\n return [\n [defaultValue, defaultValue],\n [defaultValue, defaultValue],\n ];\n};\n\nexport const m3x3 = (defaultValue = 0): Matrix3 => {\n return [\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const m4x4 = (defaultValue = 0): Matrix4 => {\n return [\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const mNxM = (N: number, M: number, defaultValue = 0): Matrix => {\n if(N <= 0 || M <= 0){\n throw new Error('M and N must be positive numbers.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return [\n [1, 0],\n [0, 1],\n ];\n};\n\nexport const identity3 = (): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\nexport const identity4 = (): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Identity Matrix (I).\n * M x I = I x M = M for any matrix M.\n * Identity Matrix is a special case of scale matrix.\n */\nexport const identityN = (N: number): Matrix => {\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n if(N === 0) return [];\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mDeepCopy(m2) as Matrix2;\n};\n\nexport const m3DeepCopy = (m3: Matrix3): Matrix3 => {\n return mDeepCopy(m3) as Matrix3;\n};\n\n// -------------- APPEND / PREPEND ROW OR COLUMN ---------------\n\nexport const mAppendCol = (m: Matrix, col: Vector): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n const copy = mDeepCopy(m);\n copy.push(row);\n return copy;\n};\n\nexport const m2AppendRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.push(row);\n return copy;\n};\n\nexport const m3AppendRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.push(row);\n return copy;\n};\n\nexport const mPrependRow = (m: Matrix, row: Vector) : Matrix => {\n const copy = mDeepCopy(m);\n copy.unshift(row);\n return copy;\n};\n\nexport const m2PrependRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.unshift(row);\n return copy;\n};\n\nexport const m3PrependRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.unshift(row);\n return copy;\n};\n\n// ------------ DELETE ROW OR COLUMN ----------------------------\n\nexport const mDelLastRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.pop();\n return copy;\n};\n\nexport const mDelFirstRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.shift();\n return copy;\n};\n\nexport const mDelLastColumn = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const size = m[0].length;\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n\n const matrix: Matrix = [];\n for(let i=0; i {\n\n if(matrix.length < 0) return [];\n\n if(matrix[0].length !== vector.length){\n throw new Error('The number of columns in the matrix must be equal to the length of the vector.');\n }\n\n const res: Vector = [];\n\n for(let i=0; i {\n if(matrix1.length !== matrix2.length) return false;\n\n for(let i=0; i returns matrix N (m-1 x m-1)\n * The matrix must be square.\n */\nconst mMinorHelper = (m: Matrix, row: number, col: number) => {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // prepare the matrix without provided row and column\n const matrix = mMinorHelper(m, row, col);\n\n // calculate the matrix determinant\n return mDeterminant(matrix);\n};\n\n/**\n * Calculate determinant for NxN matrix.\n * Matrix should be square.\n */\nexport const mDeterminant = (matrix: Matrix): number => {\n const size = matrix.length;\n if(size === 0) return 1;\n\n if(size !== matrix[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return matrix[0][0];\n if(size === 2) return m2Determinant(matrix as Matrix2);\n\n let d = 0;\n\n for(let i=0; i {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return m2[0][0] * m2[1][1] - m2[1][0] * m2[0][1];\n};\n\n/**\n * Calculate determinant for 3x3 matrix.\n * Matrix should be square.\n */\nexport const m3Determinant = (m3: Matrix3): number => {\n if(m3.length !== m3[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return mDeterminant(m3);\n};\n\n// ------------------ INVERSE -----------------------\n\nexport const m2Adjugate = (m2: Matrix2): Matrix2|null => {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return [\n [m2[1][1], -m2[0][1]],\n [-m2[1][0], m2[0][0]],\n ];\n};\n\nexport const m3Adjugate = (m3: Matrix3) : Matrix3|null => {\n return mAdjugate(m3) as (Matrix3|null);\n};\n\n/**\n * Adjugate is a transpose of a cofactor matrix\n */\nexport const mAdjugate = (m: Matrix): Matrix|null => {\n\n const size = m.length;\n if(size <= 0) return null;\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return m;\n\n if(size === 2) return m2Adjugate(m as Matrix2);\n\n // build a cofactor matrix ----------------\n const cofactors: Matrix = [];\n\n for(let i=0; i {\n if(m.length > 0 && m.length !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = mDeterminant(m);\n return d === 0;\n};\n\n/**\n * Square matrix A (nxn) is invertible is there is another square matrix B (nxn) so AxB = BxA = I\n * For A (2x2) matrix, the inverse is:\n * (1 / (determinant(A))) * adj(A)\n */\nexport const m2Inverse = (m2: Matrix2, decimalPlaces = Infinity): (Matrix2 | null) => {\n if(m2.length > 0 && m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = m2Determinant(m2);\n if(d === 0) return null;\n\n const adj = m2Adjugate(m2);\n if(adj === null) return null;\n\n return m2DivideScalar(adj, d, decimalPlaces);\n};\n\nexport const m3Inverse = (m3: Matrix3, decimalPlaces = Infinity): (Matrix3 | null) => {\n return mInverse(m3, decimalPlaces) as (Matrix3|null);\n};\n\nexport const mInverse = (m: Matrix, decimalPlaces = Infinity): (Matrix | null) => {\n const size = m.length;\n\n if(size > 0 && size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // find a determinant ----------------------\n const d = mDeterminant(m);\n\n // find an Adjugate - a transpose of a cofactor matrix\n const adj = mAdjugate(m);\n if(adj === null) return null;\n\n return mDivideScalar(adj, d, decimalPlaces);\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector2, Vector3, Vector4 } from '../../types';\nimport { v2Normalize, v3MulScalar, v3Normalize } from './vector';\nimport { mMulVector, mMul } from './matrix';\nimport { setDecimalPlaces } from '../format';\n\n/*\nAny 2D affine transformation can be decomposed\ninto a rotation, followed by a scaling, followed by a\nshearing, and followed by a translation.\n---------------------------------------------------------\nAffine matrix = translation x shearing x scaling x rotation\n */\n\n// ----------------- CSS -------------------------------------\n\n/**\n * Matrix 2D in non-homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2ToCSS = (m: Matrix2) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, 0, 0)`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2hToCSS = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, ${ tx }, ${ ty })`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m2hToCSS3d = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix3d(${ a }, ${ b }, 0, 0, ${ c }, ${ d }, 0, 0, 0, 0, 1, 0, ${ tx }, ${ ty }, 0, 1)`;\n};\n\n/**\n * Matrix 3D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m3hToCSS3d = (m: Matrix4) : string => {\n\n return `matrix3d(\n ${ m[0][0] }, ${ m[0][1] }, ${ m[0][2] }, ${ m[0][3] },\n ${ m[1][0] }, ${ m[1][1] }, ${ m[1][2] }, ${ m[1][3] },\n ${ m[2][0] }, ${ m[2][1] }, ${ m[2][2] }, ${ m[2][3] },\n ${ m[3][0] }, ${ m[3][1] }, ${ m[3][2] }, ${ m[3][3] }\n )`;\n};\n\n// ---------------- TRANSLATION MATRICES ----------------------\n\nexport const m2Translation = (position: Vector2, decimalPlaces = Infinity): Matrix2 => {\n\n return [\n [1, 0],\n [0, 1],\n [setDecimalPlaces(position[0], decimalPlaces), setDecimalPlaces(position[1], decimalPlaces)],\n ];\n};\n\nexport const m3Translation = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n [\n setDecimalPlaces(position[0], decimalPlaces),\n setDecimalPlaces(position[1], decimalPlaces),\n setDecimalPlaces(position[2], decimalPlaces)\n ],\n ];\n};\n\n/**\n * 2D Translation matrix in homogeneous coordinates.\n */\nexport const m2TranslationH = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1],\n ];\n};\n\n/**\n * 3D Translation matrix in homogeneous coordinates.\n */\nexport const m3TranslationH = (position: Vector4, decimalPlaces = Infinity): Matrix4 => {\n\n return [\n [1, 0, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, 0, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1, setDecimalPlaces(position[2], decimalPlaces)],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- ROTATION MATRICES -------------------------\n\n/**\n * Rotation of an angle about the origin.\n */\nexport const m2Rotation = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix2 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin],\n [sin, cos],\n ] :\n [\n [cos, sin],\n [-sin, cos],\n ];\n};\n\n/**\n * Rotation of an angle about the origin in homogeneous coordinates (clockwise).\n */\nexport const m2RotationH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ]:\n [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation of an angle \"angleRad\" around the given point (transformOrigin) in homogeneous coordinates (clockwise).\n * result_vector = TranslationMatrix(x, y) * RotationMatrix() * TranslationMatrix(-x, -y) * position_vector\n */\nexport const m2RotationAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const rotation = m2RotationH(angleRad, isClockwise, decimalPlaces);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, rotation);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2RotateAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n position: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2RotationAroundPointH(angleRad, transformOrigin, isClockwise, decimalPlaces);\n return mMulVector(mat3h, position) as Vector3;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2Rotate = (angleRad: number, vector: Vector2, isClockwise = true, decimalPlaces = Infinity): Vector2 => {\n const unitVector = v2Normalize(vector);\n return mMulVector(m2Rotation(angleRad, isClockwise, decimalPlaces), unitVector) as Vector2;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2RotateH = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m2RotationH(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the X axis (clockwise).\n */\nexport const m3RotationX = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0],\n [0, cos, -sin],\n [0, sin, cos],\n ] :\n [\n [1, 0, 0],\n [0, cos, sin],\n [0, -sin, cos],\n ];\n};\n\n/**\n * Rotation around the X axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationXH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0, 0],\n [0, cos, -sin, 0],\n [0, sin, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [1, 0, 0, 0],\n [0, cos, sin, 0],\n [0, -sin, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateX = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationX(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Y axis (clockwise).\n */\nexport const m3RotationY = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin],\n [0, 1, 0],\n [-sin, 0, cos],\n ] :\n [\n [cos, 0, -sin],\n [0, 1, 0],\n [sin, 0, cos],\n ];\n};\n\n/**\n * Rotation around the Y axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationYH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin, 0],\n [0, 1, 0, 0],\n [-sin, 0, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [cos, 0, -sin, 0],\n [0, 1, 0, 0],\n [sin, 0, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateY = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationY(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Z axis (clockwise).\n */\nexport const m3RotationZ = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ] : [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation around the Z axis (clockwise)- in homogeneous coordinates\n */\nexport const m3RotationZH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0, 0],\n [sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ] : [\n [cos, sin, 0, 0],\n [-sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateZ = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationZ(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n// ---------------- SCALE MATRICES -------------\n\n/**\n * Get matrix for arbitrary scaling pivot point.\n * result_vector = TranslationMatrix(x, y) * ScaleMatrix() * TranslationMatrix(-x, -y) * scale_vector\n */\nexport const m2ScaleAtPointHMatrix = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const scale = m2ScaleH(scaleVector);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, scale);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2ScaleAtPointH = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n point: Vector3,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2ScaleAtPointHMatrix(scaleVector, transformOrigin, decimalPlaces);\n return mMulVector(mat3h, point) as Vector3;\n};\n\nexport const m2Scale = (scaleVector: Vector2): Matrix2 => {\n return [\n [scaleVector[0], 0],\n [0, scaleVector[1]],\n ];\n};\n\nexport const v2Scale = (scaleVector: Vector2, vector: Vector2): Vector2 => {\n return mMulVector(m2Scale(scaleVector), vector) as Vector2;\n};\n\n/**\n * homogeneous coordinates\n */\nexport const m2ScaleH = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, 1],\n ];\n};\n\nexport const m3Scale = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, scaleVector[2]],\n ];\n};\n\nexport const m3ScaleH = (scaleVector: Vector4): Matrix4 => {\n return [\n [scaleVector[0], 0, 0, 0],\n [0, scaleVector[1], 0, 0],\n [0, 0, scaleVector[2], 0],\n [0, 0, 0, 1]\n ];\n};\n\nexport const v3Scale = (scaleVector: Vector3, vector: Vector3): Vector3 => {\n return mMulVector(m3Scale(scaleVector), vector) as Vector3;\n};\n\n/**\n * Stretch, parallel to the x-axis.\n */\nexport const m2ScaleX = (scale: number): Matrix2 => {\n return [\n [scale, 0],\n [0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the x-axis - homogeneous coordinates\n */\nexport const m2ScaleXH = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleX = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleXH = (scale: number): Matrix4 => {\n return [\n [scale, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleY = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleYH = (scale: number): Matrix => {\n return [\n [1, 0, 0, 0],\n [0, scale, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZ = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, scale],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZH = (scale: number): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, scale, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis.\n */\nexport const m2ScaleY = (scale: number): Matrix2 => {\n return [\n [1, 0],\n [0, scale],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis - homogeneous coordinates\n */\nexport const m2ScaleYH = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n// ---------------- REFLECTION MATRICES -------------------------\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOrigin = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOriginH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection about the origin in non-homogeneous coordinates\n */\nexport const m3ReflectionOrigin = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection about the origin in homogeneous coordinates\n */\nexport const m3ReflectionOriginH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection about y=-x\n */\nexport const m2ReflectionYmX = (): Matrix2 => {\n\n return [\n [0, -1],\n [-1, 0],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionX = (): Matrix2 => {\n\n return [\n [1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionXH = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection in the y-axis.\n */\nexport const m2ReflectionY = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, 1],\n ];\n};\n\nexport const m2ReflectionYH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionYZ = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in homogeneous coordinates\n */\nexport const m3ReflectionYZH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXZ = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in homogeneous coordinates\n */\nexport const m3ReflectionXZH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXY = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in homogeneous coordinates\n */\nexport const m3ReflectionXYH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- SHEARING MATRICES -------------------------\n\n\n/**\n * Shearing in y-axis, with x-axis fixed with (0,1) moving to (factor, 1)\n */\nexport const m2ShearingY = (factor: number): Matrix2 => {\n\n return [\n [1, factor],\n [0, 1],\n ];\n};\n\n/**\n * Shearing in x-axis, with y-axis fixed with (1,0) moving to (1, factor)\n */\nexport const m2ShearingX = (factor: number): Matrix2 => {\n\n return [\n [1, 0],\n [factor, 1],\n ];\n};", "import { setDecimalPlaces } from './format';\n\n/**\n * Returns a random number in the [min,max] range.\n */\nexport const getRandom = (min: number, max: number, decimalPlaces = Infinity): number => {\n return setDecimalPlaces(Math.random() * (max - min) + min, decimalPlaces);\n};\n\n/**\n * Returns a random integer number in the [min,max] range.\n */\nexport const getRandomInt = (min: number, max: number): number => {\n return Math.floor(Math.random() * (max - min + 1) + min);\n};\n\nexport const getRandomBoolean = () => Math.random() < 0.5;\n\n/* eslint-disable @typescript-eslint/no-explicit-any */\nexport const getRandomItemFromArray = (array: any[]) => {\n const randomIndex = getRandomInt(0, array.length - 1);\n return array[randomIndex];\n};", "export const stringToNumber = (value: string|undefined|null|number, defaultNumber: number) => {\n if(value === undefined || value === null) return defaultNumber;\n const res = Number(value) ?? defaultNumber;\n return isNaN(res) ? defaultNumber : res;\n};", "import { setDecimalPlaces } from './format';\nimport { Vector2, Vector3 } from '../types';\n\n/**\n * u(x) and v(x) are functions ---------->\n *\n * dx(u + v) = dx(u) + dx(v)\n * dx(u - v) = dx(u) - dx(v)\n * dx(u * v) = dx(u) * v + u * dx(v)\n * dx(u / v) = (dx(u) * v - u * dx(v)) / (v ^ 2), when v(x) != 0\n */\n\n// ------------------ Derivatives of Polynomial ---------------------------\n\n/**\n * y = 3x+2\n * dxPolynomial(10, [[3, 1], [2, 0]])\n */\nexport const dxPolynomial = (x: number, polynomial: number[][], decimalPlaces = Infinity) => {\n let res = 0;\n\n for(const part of polynomial){\n if(part.length !== 2) return NaN;\n\n const coeff = part[0];\n const power = part[1];\n res += coeff * power * Math.pow(x, power - 1);\n }\n\n return setDecimalPlaces(res, decimalPlaces);\n}\n\n// ---------------------- Bezier Curves ---------------------------\n\n/**\n * Derivative of Bezier Curve is another Bezier Curve.\n * t must min in range [0, 1]\n */\nexport const dxV2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n // The derivative: P1 * (2t-2) + (2*P3-4*P2) * t + 2 * P2\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\nexport const dxV2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n\n// ----------------- Derivatives of trigonometry functions ---------------------------\n\nexport const dxSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(Math.cos(x), decimalPlaces);\n};\n\nexport const dxCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-Math.sin(x), decimalPlaces);\n};\n\nexport const dxTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.cos(x) ** 2), decimalPlaces);\n};\n\n/**\n * x != Math.PI * n, where n is an integer\n */\nexport const dxCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sin(x) ** 2), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\nexport const dxArcTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (1 + x ** 2), decimalPlaces);\n};\n\nexport const dxArcCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (1 + x ** 2), decimalPlaces);\n};\n", "import { Matrix, Matrix2, Matrix3, Vector, Vector2, Vector3 } from '../../types';\nimport { m2Inverse, m3Inverse, mInverse, mMulVector, mDelLastColumn, mGetLastColumn } from '../linear-algebra/matrix';\nimport { setDecimalPlaces } from '../format';\nimport { v2Sub } from '../linear-algebra/vector';\n\n/**\n * Linear equation\n * ax + b = c\n * x = (c - b) / a; a != 0\n */\nexport const linearEquation = (equation: Vector3, decimalPlaces = Infinity) : number => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n\n const diff = c - b;\n\n if(a === 0 && diff === 0) return Infinity; // any number is a solution\n if(a === 0) return NaN; // no solution\n\n return setDecimalPlaces(diff / a, decimalPlaces);\n};\n\n/**\n * System of 2 linear equations.\n * [x, y] = inverse(Matrix of equation parameters) x (vector of equation results)\n * ---------------\n * 3x + 2y = 7\n * -6x + 6y = 6\n */\nexport const linearEquationSystem2 = (equation1: Vector3, equation2: Vector3, decimalPlaces = Infinity) : Vector2 | null => {\n const equationParams: Matrix2 = [\n [equation1[0], equation1[1]],\n [equation2[0], equation2[1]],\n ];\n\n const inversed = m2Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector2 = [\n equation1[2],\n equation2[2]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector2;\n};\n\n/**\n * System of 3 linear equations.\n * ---------------------------------------\n * 3x + 2y + 5z = 7\n * -6x + 6y + 6z = 6\n * 2x + 7y - z = 4\n */\nexport const linearEquationSystem3 = (\n equation1: Vector,\n equation2: Vector,\n equation3: Vector,\n decimalPlaces = Infinity) : Vector3 | null => {\n const equationParams: Matrix3 = [\n [equation1[0], equation1[1], equation1[2]],\n [equation2[0], equation2[1], equation2[2]],\n [equation3[0], equation3[1], equation3[2]],\n ];\n\n const inversed = m3Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector3 = [\n equation1[3],\n equation2[3],\n equation3[3]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector3;\n};\n\n/**\n * System of N linear equations.\n */\nexport const linearEquationSystemN = (equations: Matrix, decimalPlaces = Infinity) : Vector | null => {\n if(equations.length <= 0) return null;\n\n const equationParams = mDelLastColumn(equations);\n\n const inversed = mInverse(equationParams);\n if(inversed === null) return null; // no results\n\n // the last column of the equations matrix\n const equationResults = mGetLastColumn(equations);\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector;\n};\n\n/**\n * Calculate the equation of a line given two points in a 2D space.\n * y = ax + b\n * y - y1 = m(x - x1)\n * m = (y2 - y1) / (x2 - x1)\n */\nexport const getLinearEquationBy2Points = (point1: Vector2, point2: Vector2) : {\n slope: number|undefined,\n yIntercept: number|undefined,\n xIntercept: number|undefined,\n formula: string,\n} => {\n const [deltaX, deltaY] = v2Sub(point2, point1);\n const [x, y] = point1;\n\n if(deltaX === 0) {\n return {\n slope: undefined,\n xIntercept: x,\n yIntercept: undefined,\n formula: `x = ${ x }`,\n };\n }\n\n const m = deltaY / deltaX;\n const b = y - m * x;\n let formula = '';\n\n if(m === 0) {\n formula = `y = ${ b }`;\n }\n else{\n formula = `y = ${ m === 1 ? '' : m }x`;\n\n if(b !== 0) {\n formula += ` ${ b < 0 ? '-' : '+' } ${ Math.abs(b) }`;\n }\n }\n\n return {\n slope: m,\n xIntercept: undefined,\n yIntercept: b,\n formula,\n };\n};", "import { Vector } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { linearEquation } from './linear-equations';\nimport { isNumber } from '../other';\n\n/**\n * Quadratic Equation.\n * ax^2 + bx + c = d\n */\nexport const quadraticEquation = (equation: Vector, decimalPlaces = Infinity) : Vector => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n const d = equation[3];\n\n if(a === 0){\n // it's a linear equation -------------------------------------------\n const res = linearEquation([b, c, d], decimalPlaces);\n if(isNumber(res)) return [res];\n return [];\n }\n\n const diff = c - d;\n\n const discriminant = b * b - (4 * a * diff);\n\n if(discriminant < 0){\n return []; // no results\n }\n\n if(discriminant === 0){\n return [ setDecimalPlaces(-b / (2 * a), decimalPlaces) ]; // 1 result\n }\n\n // if(determinant > 0) ---> 2 results\n const t1 = 2 * a;\n const t2 = Math.sqrt(discriminant);\n\n return [\n setDecimalPlaces((-b + t2) / t1, decimalPlaces),\n setDecimalPlaces((-b - t2) / t1, decimalPlaces),\n ];\n};", "import { IBBox, Vector, Vector2, Vector3 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport {\n dxV2CubicBezierCurve,\n dxV2QuadraticBezierCurve,\n dxV3CubicBezierCurve,\n dxV3QuadraticBezierCurve\n} from '../derivative';\nimport { v2Normalize, v3Normalize } from '../linear-algebra/vector';\nimport { linearEquation } from '../equations/linear-equations';\nimport { quadraticEquation } from '../equations/quadratic-equations';\nimport { isNumber } from '../other';\n\n/**\n * B\u00E9zier Curves\n * quadratic: y = P1 * (1-t)\u00B2 + P2 * 2 * (1-t)t + P3 * t\u00B2\n * t in range [0, 1]\n */\n\n// -------------------- GET POINT ON CURVE --------------------------\n\n/**\n * Get a point on a quadratic B\u00E9zier curve as a function of time.\n */\nexport const v2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n/**\n * Get a point on a cubic B\u00E9zier curve as a function of time.\n */\nexport const v2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n// -------------------- TANGENT --------------------------\n\n/**\n * Tangent indicates the direction of travel at specific points along the B\u00E9zier curve,\n * and is literally just the first derivative of our curve.\n */\nexport const v2QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\nexport const v2CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\n// -------------------- NORMAL --------------------------\n\n/**\n * Normal is a vector that runs at a right angle to the direction of the curve, and is typically of length 1.\n * To find it, we take the normalised tangent vector, and then rotate it by a 90 degrees.\n */\nexport const v2QuadraticBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2QuadraticBezierCurveTangent(t, startControlPoint, centerControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\nexport const v2CubicBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2CubicBezierCurveTangent(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\n// -------------------- EXTREMA --------------------------\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2QuadraticBezierCurveExtrema = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector => {\n\n /*\n (-2 * (1 - t)) * startControlPoint[0] + (2 - 4 * t) * centerControlPoint[0] + (2 * t) * endControlPoint[0]\n 2 * t * startControlPoint[0] - 4 * t * centerControlPoint[0] + 2 * t * endControlPoint[0] - 2 * startControlPoint[0] + 2 * centerControlPoint[0]\n t * (2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0]) + (- 2 * startControlPoint[0] + 2 * centerControlPoint[0])\n */\n\n const a1 = 2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0];\n const b1 = -2 * startControlPoint[0] + 2 * centerControlPoint[0];\n const equation1: Vector3 = [a1, b1, 0];\n const res1 = linearEquation(equation1, decimalPlaces);\n\n const a2 = 2 * startControlPoint[1] - 4 * centerControlPoint[1] + 2 * endControlPoint[1];\n const b2 = -2 * startControlPoint[1] + 2 * centerControlPoint[1];\n const equation2: Vector3 = [a2, b2, 0];\n const res2 = linearEquation(equation2, decimalPlaces);\n\n const res: Vector = [];\n\n if(isNumber(res1)){\n res.push(res1);\n }\n\n if(isNumber(res2)){\n res.push(res2);\n }\n\n return res;\n};\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2CubicBezierCurveExtrema = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2|null => {\n\n const a1 = -3 * startControlPoint[0] + 9 * center1ControlPoint[0] - 9 * center2ControlPoint[0] + 3 * endControlPoint[0];\n const b1 = 6 * startControlPoint[0] - 12 * center1ControlPoint[0] + 6 * center2ControlPoint[0];\n const c1 = -3 * startControlPoint[0] + 3 * center1ControlPoint[0];\n const equation1: Vector = [a1, b1, c1, 0];\n\n const a2 = -3 * startControlPoint[1] + 9 * center1ControlPoint[1] - 9 * center2ControlPoint[1] + 3 * endControlPoint[1];\n const b2 = 6 * startControlPoint[1] - 12 * center1ControlPoint[1] + 6 * center2ControlPoint[1];\n const c2 = -3 * startControlPoint[1] + 3 * center1ControlPoint[1];\n const equation2: Vector = [a2, b2, c2, 0];\n\n // Any value between 0 and 1 is a root that matters for B\u00E9zier curves, anything below or above that is irrelevant (because B\u00E9zier curves are only defined over the interval [0,1]).\n const res1 = quadraticEquation(equation1, decimalPlaces).filter(num => num >= 0 && num <= 1);\n const res2 = quadraticEquation(equation2, decimalPlaces).filter(num => num >= 0 && num <= 1);\n\n const res = [...res1, ...res2];\n if(res.length === 2){\n return [...res1, ...res2] as Vector2;\n }\n\n return null;\n};\n\n// -------------------- BOUNDING BOX --------------------------\n\nexport const v2QuadraticBezierBBox = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2QuadraticBezierCurveExtrema(startControlPoint, centerControlPoint, endControlPoint);\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2QuadraticBezierCurve(percent, startControlPoint, centerControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x);\n maxX = Math.max(maxX, x);\n\n minY = Math.min(minY, y);\n maxY = Math.max(maxY, y);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\nexport const v2CubicBezierBBox = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2CubicBezierCurveExtrema(startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint) || [];\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2CubicBezierCurve(percent, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x ?? Infinity);\n maxX = Math.max(maxX, x ?? -Infinity);\n\n minY = Math.min(minY, y ?? Infinity);\n maxY = Math.max(maxY, y ?? -Infinity);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\n\n", "import { Vector2 } from '../types';\nimport { v2Sub } from './linear-algebra/vector';\nimport { getV2Angle } from './angle';\nimport { convertRange } from './other';\n\n/**\n * Circle Equation\n * x^2 + y^2 = radius^2\n * ----------------------\n * Circle Parametric Equation\n * x(t) = radius * cos(t)\n * y(t) = radius * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const circleMovement = (center: Vector2, angle: number, radius: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius,\n center[1] + Math.sin(angle) * radius\n ];\n};\n\n/**\n * Circle Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const circleMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radius: number\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return circleMovement(center, angle, radius);\n};\n\n/**\n * Ellipse Equation\n * (x - centerX)^2 / (radius1^2) + (y - centerY)^2 / (radius2^2) = 1\n * -----------------------------------------------------------------\n * Ellipse Parametric Equation\n * x(t) = radius1 * cos(t)\n * y(t) = radius2 * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const ellipseMovement = (center: Vector2, angle: number, radius1: number, radius2: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius1,\n center[1] + Math.sin(angle) * radius2\n ];\n};\n\n/**\n * Ellipse Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const ellipseMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radii: Vector2\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return ellipseMovement(center, angle, radii[0], radii[1]);\n};\n\n/**\n * Sine Wave Equation (Sinusoid)\n * -----------------------------\n * const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n * amplitude = the peak deviation of the function from zero\n * frequency = number of cycles\n * phase = specifies (in radians) where in its cycle the oscillation is at t = 0.\n * think of it as \"shifting\" the starting point of the function to the right (positive p) or left (negative)\n */\nexport const sineWaveMovement = (x: number, amplitude: number, frequency: number, phase: number) : Vector2 => {\n /*\n example values:\n const amplitude = 50;\n const frequency = 0.005;\n const phase = 0;\n x: [0, 1000]\n */\n const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n\n return [x, y];\n};\n\n/**\n * Lissajous curve (Lissajous figure or Bowditch curve)\n * Parametric equation #1\n * f(t) = A * sin(k * t + m)\n * f(t) = B * sin(n * t)\n * 0 <= m <= PI/2\n * k, n >= 1\n * -----------------------\n * Parametric equation #2\n * f(t) = A * cos(k * t - m)\n * f(t) = B * cos(n * t - p)\n * -----------------------------\n * Shapes:\n * k = 1, n = 1, m = 0, p = 0 ---> line\n * A = B, k = 1, n = 1, m = PI/2, p = PI/2 ----> circle\n * A != B, k = 1, n = 1, m = PI/2, p = PI/2 ----> ellipse\n * k = 2, n = 2, m = PI/2, p = PI/2 ----> section of a parabola\n */\nexport const lissajousCurve = (\n width: number,\n height: number,\n t: number,\n k: number,\n n: number,\n m: number,\n p: number\n) :Vector2 => {\n return [\n width * Math.cos(k * t - m),\n height * Math.cos(n * t - p),\n ];\n};\n", "import { getRandom } from './random';\nimport { HSLColor, LABColor, RGBColor } from '../types';\nimport { mod } from './other';\nimport { setDecimalPlaces } from './format';\n\n// ------------------------ RANDOM COLOR -------------------------------------\n\nexport const getRandomRGBColor = () : RGBColor => {\n const hslColor = getRandomHSLColor();\n return hslToRgb(hslColor);\n};\n\nexport const getRandomHexColor = () : string => {\n const hslColor = getRandomHSLColor();\n return hslToHex(hslColor);\n};\n\nexport const getRandomHSLColor = () : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given hue\n */\nexport const getRandomHSLColorWithHue = (h: number) : HSLColor => {\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given saturation\n */\nexport const getRandomHSLColorWithSaturation = (s: number) : HSLColor => {\n const h = getRandom(1, 360);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given lightness\n */\nexport const getRandomHSLColorWithLightness = (l: number) : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n return [h, s, l];\n};\n\nexport const getRandomGrayscaleHSLColor = () : HSLColor => {\n const l = getRandom(0, 100);\n return [0, 0, l];\n};\n\nexport const getRandomHSLColorWithinRanges = (\n hueStart = 1, hueEnd = 360,\n saturationStart = 0, saturationEnd = 100,\n lightStart = 0, lightEnd = 100\n) : HSLColor => {\n const h = getRandom(hueStart, hueEnd);\n const s = getRandom(saturationStart, saturationEnd);\n const l = getRandom(lightStart, lightEnd);\n return [h, s, l];\n};\n\n// ----------------------- CONVERT COLORS --------------------------------------\n\n/**\n * helper: convert hue value to degrees.\n * @param {number} h\n * @return {number} [0, 360] degrees\n */\nconst convertHueToDegrees = (h : number) : number => {\n\n // the hue value needs to be multiplied by 60 to convert it to degrees\n h *= 60;\n\n // if hue becomes negative, you need to add 360 to, because a circle has 360 degrees\n if(h < 0){\n h += 360;\n }\n\n return h;\n // convert huw to %\n // return h * 100 / 360;\n};\n\n/**\n * get hue from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] % - we use here % instead of [0, 359] degrees\n */\nconst getHue = (r : number, g : number, b : number, min : number | undefined = undefined, max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (max === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no hue, as it's gray\n if(min === max) return 0;\n\n const diff = max - min;\n\n let h = 0;\n\n // if red is max\n if(max === r){\n h = (g - b) / diff + (g < b ? 6 : 0);\n }\n\n // if green is max\n if(max === g){\n h = 2 + (b - r) / diff;\n }\n\n // if blue is max\n if(max === b){\n h = 4 + (r - g) / diff;\n }\n\n return convertHueToDegrees(h);\n};\n\n/**\n * get luminance from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] %\n */\nconst getLuminance = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // calculate the luminance value\n // @ts-ignore\n const l = (min + max) / 2; // [0, 1]\n\n // return l value in %\n return l * 100;\n};\n\n/**\n * get saturation from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @param {number|undefined=} l - luminance in [0, 100] %\n * @return {number} [0, 100] %\n */\nconst getSaturation = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined,\n l : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no saturation, as it's gray\n if(min === max) return 0;\n\n // calculate luminance if it's not provided\n l = (l === undefined) ? getLuminance(r, g, b) : l;\n\n // check the level of luminance\n const s = (l <= 50) ?\n // @ts-ignore\n ((max - min) / (max + min)) : // this formula is used when luminance <= 50%\n // @ts-ignore\n (max - min) / (2.0 - max - min); // this formula is used when luminance > 50%\n\n // return saturation in %\n return s * 100;\n};\n\nexport const rgbToHsl = (rgb: RGBColor, decimalPlaces = Infinity): HSLColor => {\n\n // convert rgb values to the range [0, 1]\n const r = rgb[0] / 255;\n const g = rgb[1] / 255;\n const b = rgb[2] / 255;\n\n // find the minimum and maximum values of r, g, and b\n const min = Math.min(r, g, b);\n const max = Math.max(r, g, b);\n\n // calculate the luminance value in %\n const l = getLuminance(r, g, b, min, max);\n\n // calculate the saturation in %\n const s = getSaturation(r, g, b, min, max, l);\n\n // calculate the hue in % (not in degrees!)\n const h = getHue(r, g, b, min, max);\n\n if(h > 360 || s > 100 || l > 100){\n return [0, 0, 100];\n }\n\n if(h < 0 || s < 0 || l < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(h, decimalPlaces),\n setDecimalPlaces(s, decimalPlaces),\n setDecimalPlaces(l, decimalPlaces),\n ];\n};\n\n/**\n * helper: HSL to RGB\n */\nconst hslToRgbHelper = (helper1 : number, helper2 : number, colorHelper : number) : number => {\n\n // all values need to be between 0 and 1\n // if you get a negative value you need to add 1 to it\n if(colorHelper < 0) colorHelper += 1;\n\n // if you get a value above 1 you need to subtract 1 from it.\n if(colorHelper > 1) colorHelper -= 1;\n\n if(colorHelper * 6 < 1) return helper2 + (helper1 - helper2) * 6 * colorHelper;\n\n if(colorHelper * 2 < 1) return helper1;\n\n if(colorHelper * 3 < 2){\n return helper2 + (helper1 - helper2) * (0.666 - colorHelper) * 6;\n }\n else{\n return helper2;\n }\n};\n\nexport const hslToRgb = (hsl: HSLColor, decimalPlaces = Infinity): RGBColor => {\n\n // convert all values to [0, 1] from %\n const h = hsl[0] / 100;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n // if there is no saturation -> it\u2019s grey\n if(s === 0){\n // convert the luminance from [0, 1] to [0, 255]\n const gray = l * 255;\n return [gray, gray, gray];\n }\n\n // check the level of luminance\n const helper1 = (l < 0.5) ?\n (l * (1.0 + s)) :\n (l + s - l * s);\n\n const helper2 = 2 * l - helper1;\n\n const rHelper = h + 0.333;\n const gHelper = h;\n const bHelper = h - 0.333;\n\n let r = hslToRgbHelper(helper1, helper2, rHelper);\n let g = hslToRgbHelper(helper1, helper2, gHelper);\n let b = hslToRgbHelper(helper1, helper2, bHelper);\n\n // convert rgb to [0, 255]\n r *= 255;\n g *= 255;\n b *= 255;\n\n if(r > 255 || g > 255 || b > 255){\n return [255, 255, 255];\n }\n\n if(r < 0 || g < 0 || b < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(r, decimalPlaces),\n setDecimalPlaces(g, decimalPlaces),\n setDecimalPlaces(b, decimalPlaces),\n ];\n};\n\n/**\n * HSL to hex\n * hslToHex(360, 100, 50) // [360, 100, 5] ==> \"#ff0000\" (red)\n */\nexport const hslToHex = (hsl: HSLColor) => {\n\n if(hsl[0] > 360 || hsl[1] > 100 || hsl[2] > 100){\n return '#ffffff';\n }\n\n if(hsl[0] < 0 || hsl[1] < 0 || hsl[2] < 0){\n return '#000000';\n }\n\n const h = hsl[0] / 360;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n let r, g, b;\n if (s === 0) {\n r = g = b = l; // achromatic\n } else {\n const hue2rgb = (p: number, q: number, t: number) => {\n if (t < 0) t += 1;\n if (t > 1) t -= 1;\n if (t < 1 / 6) return p + (q - p) * 6 * t;\n if (t < 1 / 2) return q;\n if (t < 2 / 3) return p + (q - p) * (2 / 3 - t) * 6;\n return p;\n };\n const q = l < 0.5 ? l * (1 + s) : l + s - l * s;\n const p = 2 * l - q;\n r = hue2rgb(p, q, h + 1 / 3);\n g = hue2rgb(p, q, h);\n b = hue2rgb(p, q, h - 1 / 3);\n }\n const toHex = (x: number) => {\n const hex = Math.round(x * 255).toString(16);\n return hex.length === 1 ? '0' + hex : hex;\n };\n\n return `#${toHex(r)}${toHex(g)}${toHex(b)}`;\n};\n\n/**\n * RGB to HEX\n * rgbToHex([235, 64, 52]) // #eb4034\n */\nexport const rgbToHex = (rgb: RGBColor) => {\n const [r, g, b] = rgb;\n return '#' + (1 << 24 | r << 16 | g << 8 | b).toString(16).slice(1);\n};\n\nexport const hexToRgb = (hex: string) : RGBColor | null => {\n\n const shorthandRegex = /^#?([a-f\\d])([a-f\\d])([a-f\\d])$/i;\n const _hex = hex.replace(shorthandRegex, (_m, r, g, b) => {\n return r + r + g + g + b + b;\n });\n\n const result = /^#?([a-f\\d]{2})([a-f\\d]{2})([a-f\\d]{2})$/i.exec(_hex);\n if(!result) return null;\n\n const r = parseInt(result[1], 16);\n const g = parseInt(result[2], 16);\n const b = parseInt(result[3], 16);\n\n return [r, g, b];\n};\n\nexport const rgbToLab = (rgb: RGBColor, decimalPlaces = Infinity) : LABColor => {\n\n let r = rgb[0] / 255;\n let g = rgb[1] / 255;\n let b = rgb[2] / 255;\n\n r = (r > 0.04045) ? Math.pow((r + 0.055) / 1.055, 2.4) : r / 12.92;\n g = (g > 0.04045) ? Math.pow((g + 0.055) / 1.055, 2.4) : g / 12.92;\n b = (b > 0.04045) ? Math.pow((b + 0.055) / 1.055, 2.4) : b / 12.92;\n\n let x = (r * 0.4124 + g * 0.3576 + b * 0.1805) / 0.95047;\n let y = (r * 0.2126 + g * 0.7152 + b * 0.0722) / 1.00000;\n let z = (r * 0.0193 + g * 0.1192 + b * 0.9505) / 1.08883;\n\n x = (x > 0.008856) ? Math.pow(x, 1/3) : (7.787 * x) + 16/116;\n y = (y > 0.008856) ? Math.pow(y, 1/3) : (7.787 * y) + 16/116;\n z = (z > 0.008856) ? Math.pow(z, 1/3) : (7.787 * z) + 16/116;\n\n return [\n setDecimalPlaces((116 * y) - 16, decimalPlaces),\n setDecimalPlaces(500 * (x - y), decimalPlaces),\n setDecimalPlaces(200 * (y - z), decimalPlaces),\n ];\n};\n\nexport const labToRgb = (lab: LABColor, decimalPlaces = Infinity) : RGBColor => {\n let y = (lab[0] + 16) / 116;\n let x = lab[1] / 500 + y;\n let z = y - lab[2] / 200;\n\n x = 0.95047 * ((x * x * x > 0.008856) ? x * x * x : (x - 16/116) / 7.787);\n y = 1.00000 * ((y * y * y > 0.008856) ? y * y * y : (y - 16/116) / 7.787);\n z = 1.08883 * ((z * z * z > 0.008856) ? z * z * z : (z - 16/116) / 7.787);\n\n let r = x * 3.2406 + y * -1.5372 + z * -0.4986;\n let g = x * -0.9689 + y * 1.8758 + z * 0.0415;\n let b = x * 0.0557 + y * -0.2040 + z * 1.0570;\n\n r = (r > 0.0031308) ? (1.055 * Math.pow(r, 1/2.4) - 0.055) : 12.92 * r;\n g = (g > 0.0031308) ? (1.055 * Math.pow(g, 1/2.4) - 0.055) : 12.92 * g;\n b = (b > 0.0031308) ? (1.055 * Math.pow(b, 1/2.4) - 0.055) : 12.92 * b;\n\n return [\n setDecimalPlaces(Math.max(0, Math.min(1, r)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, g)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, b)) * 255, decimalPlaces),\n ];\n};\n\n// ----------------------- GET SHIFTED COLORS --------------------------------------\n\nexport const getShiftedHue = (color: HSLColor, shift = 180) : HSLColor => {\n let hue = color[0];\n hue += shift;\n\n if (hue > 360 || hue < 0) {\n hue = mod(hue, 360);\n }\n\n return [hue, color[1], color[2]];\n};\n\nexport const getShiftedLightness = (color: HSLColor, shift = 10) : HSLColor => {\n let lightness = color[2];\n lightness += shift;\n\n if (lightness > 100 || lightness < 0) {\n lightness = mod(lightness, 100);\n }\n\n return [color[0], color[1], lightness];\n};\n\nexport const getShiftedSaturation = (color: HSLColor, shift = 10) : HSLColor => {\n let saturation = color[1];\n saturation += shift;\n\n if (saturation > 100) {\n saturation -= 100;\n }\n\n if(saturation < 0){\n saturation += 100;\n }\n\n return [color[0], saturation, color[2]];\n};\n\n// ----------------------- SIMILAR COLORS --------------------------------------\n\n/**\n * Measure the perceptual difference between two RGB colors using the CIE76 color difference formula:\n * delta = Math.sqrt((L2 - L1)^2 + (a2 - a1)^2 + (b2 - b1)^2)\n * https://en.wikipedia.org/wiki/Color_difference\n * https://stackoverflow.com/questions/13586999/color-difference-similarity-between-two-values-with-js\n * <= 1.0 Not perceptible by human eyes.\n * 1 - 2 Perceptible through close observation.\n * 2 - 10 Perceptible at a glance.\n * 11 - 49 Colors are more similar than opposite\n * 100 Colors are exact opposite\n */\nexport const getColorsDelta = (rgbA: RGBColor, rgbB: RGBColor, decimalPlaces = Infinity) => {\n const labA = rgbToLab(rgbA, decimalPlaces);\n const labB = rgbToLab(rgbB, decimalPlaces);\n\n // differences between the LAB components of the two colors\n const deltaL = labA[0] - labB[0];\n const deltaA = labA[1] - labB[1];\n const deltaB = labA[2] - labB[2];\n\n // chroma components\n const c1 = Math.sqrt(labA[1] * labA[1] + labA[2] * labA[2]);\n const c2 = Math.sqrt(labB[1] * labB[1] + labB[2] * labB[2]);\n const deltaC = c1 - c2;\n\n // difference in hue, deltaH, which takes into account both the differences\n // in the a* and b* components of LAB and the differences in chroma.\n let deltaH = deltaA * deltaA + deltaB * deltaB - deltaC * deltaC;\n deltaH = deltaH < 0 ? 0 : Math.sqrt(deltaH);\n\n const sc = 1.0 + 0.045 * c1;\n const sh = 1.0 + 0.015 * c1;\n\n // It applies weighting factors to the differences in lightness (deltaL),\n // chroma (deltaC), and hue (deltaH).\n const deltaLKlsl = deltaL / (1.0);\n const deltaCkcsc = deltaC / (sc);\n const deltaHkhsh = deltaH / (sh);\n\n // It computes the final color difference using the CIE76 formula:\n // deltaE = sqrt(deltaLKlsl^2 + deltaCkcsc^2 + deltaHkhsh^2),\n // where deltaLKlsl is the weighted lightness difference,\n // deltaCkcsc is the weighted chroma difference,\n // and deltaHkhsh is the weighted hue difference.\n const i = deltaLKlsl * deltaLKlsl + deltaCkcsc * deltaCkcsc + deltaHkhsh * deltaHkhsh;\n\n // It returns the calculated color difference,\n // optionally rounded to the specified number of decimal places.\n return i < 0 ? 0 : Math.sqrt(i);\n};\n", "/**\n * guid like '932ade5e-c515-4807-ac01-73b20ab3fb66'\n */\nexport const guid = () => {\n return 'xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx'.replace(/[xy]/g, (c) => {\n const r = Math.random() * 16 | 0;\n return (c == 'x' ? r : r & 0x3 | 0x8).toString(16);\n });\n};\n\n/**\n * id like 'df4unio1opulby2uqh4'\n */\nexport const newId = () => {\n return Math.random().toString(36).substring(2) + (new Date()).getTime().toString(36);\n};\n", "import { ICircle, IPolygon, IRect, Matrix2, Vector2 } from '../types';\nimport { mod } from './other';\nimport { v2GetNormal, v2DotProduct } from './linear-algebra/vector';\n\n/**\n * Rectangles collision detection.\n * Rectangles should not be rotated.\n * The algorithm works by ensuring there is no gap between any of the 4 sides of the rectangles.\n * Any gap means a collision does not exist.\n * Returns true if collision is detected.\n */\nexport const rectCollide = (rect1: IRect, rect2: IRect) : boolean => {\n return rect1.x <= rect2.x + rect2.w &&\n rect1.x + rect1.w >= rect2.x &&\n rect1.y <= rect2.y + rect2.h &&\n rect1.h + rect1.y >= rect2.y;\n};\n\n/**\n * Circles collision detection.\n * This algorithm works by taking the center points of the two circles\n * and ensuring the distance between the center points\n * are less than the two radii added together.\n * Returns true if collision is detected.\n */\nexport const circleCollide = (circle1: ICircle, circle2: ICircle) => {\n const dx = Math.abs(circle1.cx - circle2.cx);\n const dy = Math.abs(circle1.cy - circle2.cy);\n const distance = Math.sqrt(dx * dx + dy * dy);\n return distance <= circle1.r + circle2.r;\n};\n\n//-------------------- Separating Axis Theorem (SAT) Collision detection -------------------------\n\nconst getEdges = (poly: IPolygon) : Matrix2[] => {\n const edges: Matrix2[] = [];\n\n for(let i= 0; i {\n const edges: Matrix2[] = [];\n\n // collect polygon edges, and combine then into a single array\n edges.push(...getEdges(poly1));\n edges.push(...getEdges(poly2));\n\n // for each edge, find the normal vector and project both polygons onto it\n for (const edge of edges) {\n const normal = v2GetNormal(edge[0], edge[1]);\n const p1Proj = projectPolygon(poly1, normal);\n const p2Proj = projectPolygon(poly2, normal);\n\n // Check if the projections overlap\n const isOverlap = p1Proj.max >= p2Proj.min && p2Proj.max >= p1Proj.min;\n\n // Check if the projections overlap; if not, the polygons do not collide\n if (!isOverlap) return false;\n }\n\n // If all tests pass, the polygons overlap and collide\n return true;\n};\n\n/**\n * Project every polygon point onto the normal.\n * Then find min and max.\n */\nconst projectPolygon = (polygon: IPolygon, normal: Vector2): { min: number, max: number } => {\n let min = Infinity;\n let max = -Infinity;\n\n // Project each vertex of the polygon onto the axis\n for (const vertex of polygon) {\n const projection = v2DotProduct(vertex, normal);\n min = Math.min(min, projection);\n max = Math.max(max, projection);\n }\n\n return { min, max };\n};", "export interface IAnimationProps {\n duration?: number;\n callback: (result: IAnimationResult) => void;\n restartOnResize?: boolean;\n resizeCallback?: (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => void;\n}\n\nexport interface IAnimationResult {\n start: () => void;\n stop: () => void;\n pause: () => void;\n resume: () => void;\n restart: () => void;\n isAnimating: () => boolean;\n getStartTime: () => number|undefined;\n getElapsedTime: () => number|undefined;\n getPercent: () => number|undefined;\n getResizeObserver: () => ResizeObserver|undefined;\n}\n\nexport const animate = (props: IAnimationProps) : IAnimationResult => {\n\n const _duration = props.duration !== undefined ? props.duration : Infinity;\n\n let startTime: number|undefined = undefined; // in milliseconds\n let animationId: number|undefined = undefined;\n\n // the time elapsed since the start of the animation (in milliseconds)\n let elapsed: number|undefined = undefined;\n let previousTimeStamp: number|undefined = undefined;\n\n let animating = false;\n let observer: ResizeObserver|undefined = undefined;\n\n // -------------------- COMMANDS ---------------------\n\n const stop = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = false;\n\n /*if(observer !== undefined){\n observer.disconnect();\n observer = undefined;\n }*/\n\n if(animationId === undefined) return;\n window.cancelAnimationFrame(animationId);\n };\n\n const restart = () => {\n stop();\n start();\n };\n\n const pause = () => {\n animating = false;\n };\n\n const resume = () => {\n animating = true;\n };\n\n /**\n * Animation Step.\n * @param {number} timeStamp in milliseconds\n */\n const step = (timeStamp: DOMHighResTimeStamp) => {\n\n if (startTime === undefined) {\n startTime = timeStamp;\n }\n\n // the time elapsed since the start of the animation (in milliseconds)\n elapsed = timeStamp - startTime;\n\n if (animating && previousTimeStamp !== timeStamp && typeof props.callback === 'function') {\n\n // do the rendering .............\n props.callback(getResult());\n }\n\n if(elapsed <= _duration){\n previousTimeStamp = timeStamp;\n animationId = window.requestAnimationFrame(step);\n }\n else{\n stop();\n }\n };\n\n const observerHandler = (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => {\n restart();\n\n if(typeof props.resizeCallback === 'function'){\n props.resizeCallback(_entries, _observer);\n }\n };\n\n const start = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = true;\n\n if(props.restartOnResize && window.ResizeObserver && observer === undefined){\n observer = new ResizeObserver(observerHandler);\n observer.observe(document.body, { box: 'border-box' });\n }\n else{\n animationId = window.requestAnimationFrame(step);\n }\n };\n\n // --------------- GET INFO ----------------------\n\n /**\n * the time elapsed since the start of the animation (in milliseconds)\n */\n const getElapsedTime = () : number|undefined => {\n return elapsed;\n };\n\n const isAnimating = () => {\n return animating;\n };\n\n const getStartTime = () => {\n return startTime;\n };\n\n const getPercent = () => {\n if(_duration === Infinity || elapsed === undefined) return undefined;\n return elapsed * 100 / _duration;\n };\n\n const getResizeObserver = () => {\n return observer;\n };\n\n const getResult = () : IAnimationResult => {\n return {\n\n // commands --------------\n start,\n stop,\n pause,\n resume,\n restart,\n\n // information -------\n isAnimating,\n getElapsedTime,\n getStartTime,\n getPercent,\n getResizeObserver,\n };\n };\n\n return getResult();\n};\n", "import { setDecimalPlaces } from './format';\n\nexport const getCircleCircumference = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * radius, decimalPlaces);\n};\n\nexport const getEllipseCircumference = (radius1: number, radius2: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * Math.sqrt((radius1 ** 2 + radius2 ** 2) / 2), decimalPlaces);\n};\n\nexport const isAngleInCircleArc = (startAngleDeg: number, endAngleDeg: number, currentDegrees: number) : boolean => {\n\n if(startAngleDeg > endAngleDeg) {\n endAngleDeg += 360;\n }\n\n return currentDegrees >= startAngleDeg && currentDegrees <= endAngleDeg ||\n (currentDegrees + 360) >= startAngleDeg && (currentDegrees + 360) <= endAngleDeg;\n};\n\n/**\n * get the side of a square inscribed in a circle\n */\nexport const getSquareInCircleSide = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(radius * 2 / Math.sqrt(2), decimalPlaces);\n};\n", "/**\n * 1 + 2 + ... + n = n * (n + 1) / 2\n */\nexport const naturalNumbersSequenceSum = (n: number) => {\n return n * (n + 1) / 2;\n};\n\n/**\n * n = the number of terms to be added\n * a = the first term in the sequence\n * d = the constant value between terms\n */\nexport const arithmeticSequenceSum = (n: number, a: number, d: number) => {\n return (n / 2) * (2 * a + (n - 1) * d);\n};", "import { setDecimalPlaces } from './format';\n\n// -------------------- CENTRAL TENDENCY ----------------------------\n\n/**\n * Central tendency: Calculate the Average (mean = \u03BC)\n * Sum of all numbers divided by the array length.\n */\nexport const getArithmeticMean = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const sum = data.reduce((acc, val) => acc + val, 0);\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Frequency map: number ---> it's frequency\n */\nexport const getArithmeticMeanFromFrequency = (frequencyMap: Map, decimalPlaces = Infinity) => {\n\n let mean = 0;\n\n for(const [val, frequency] of frequencyMap) {\n mean += val * frequency;\n }\n\n return setDecimalPlaces(mean, decimalPlaces);\n};\n\n/**\n * Central tendency: What is the central number in the sorted array?\n * Good for lists like [3, 3, 3, 3, 3, 3, 100] - 100 here is called \"Outlier\"\n */\nexport const getMedian = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const copy = [...data].sort((num1, num2) => num1 - num2);\n const mid = Math.floor(copy.length / 2);\n\n if(copy.length % 2 === 0) {\n return setDecimalPlaces((copy[mid] + copy[mid - 1]) / 2, decimalPlaces);\n }\n else {\n return setDecimalPlaces(copy[mid], decimalPlaces);\n }\n};\n\n/**\n * Central tendency: What number is most common in the set.\n * If all numbers have the same frequency, there is no mode.\n */\nexport const getMode = (data: number[]) : number[]|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n // Count frequency of each number in the data array.\n const frequencyMap: Map = new Map();\n for (const num of data) {\n frequencyMap.set(num, (frequencyMap.get(num) || 0) + 1);\n }\n\n let maxFrequency = 0;\n let modes: number[] = [];\n\n // Find the maximum frequency\n for (const [num, frequency] of frequencyMap) {\n if (frequency > maxFrequency) {\n maxFrequency = frequency;\n modes = [num];\n }\n else if (frequency === maxFrequency) {\n modes.push(num);\n }\n }\n\n // If all numbers have the same frequency, there is no mode\n if (modes.length === data.length) {\n return undefined;\n }\n\n // Return the mode(s)\n return modes.length === 1 ? [modes[0]] : modes;\n};\n\n/*\nTODO:\n- geometric mean\n- harmonic mean\n */\n\n// -------------------- DISPERSION ----------------------------\n\n/**\n * Dispersion: the average square distance from the mean.\n * Sum of (x - mean)^2 / N\n */\nexport const getVariance1 = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + ((val - mean) ** 2), 0);\n\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Another formula of dispersion - the average square distance from the mean.\n * (Sum of x^2) / N - (mean ^ 2)\n */\nexport const getVariance = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + (val ** 2), 0);\n\n return setDecimalPlaces((sum / data.length) - (mean ** 2), decimalPlaces);\n};\n\n/**\n * \u03C3\n */\nexport const getStandardDeviation = (data: number[], decimalPlaces = Infinity) => {\n const variance = getVariance(data) ?? 0;\n return setDecimalPlaces(Math.sqrt(variance), decimalPlaces);\n};", "import { setDecimalPlaces } from './format';\nimport { getArithmeticMean, getStandardDeviation } from './statistics';\nimport { IMlNormalizeResult, IMlStandardizeResult } from '../types';\n\n// --------------------- NORMALIZE --------------------------------\n\n/**\n * Changes value to be in the range [0, 1].\n */\nexport const mlNormalizeValue = (value: number, min: number, max: number, decimalPlaces = Infinity) : number => {\n const diff = max - min;\n if(diff === 0) return 0;\n return setDecimalPlaces((value - min) / diff, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [0, 1].\n */\nexport const mlNormalizeArray = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n const copy = [...data];\n\n for(let i=0; i {\n const min = Math.min(...data);\n const max = Math.max(...data);\n const _data = mlNormalizeArray(data, min, max, decimalPlaces);\n\n return {\n min: setDecimalPlaces(min, decimalPlaces),\n max: setDecimalPlaces(max, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlNormalizeUnseenData = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n return mlNormalizeArray(data, min, max, decimalPlaces);\n};\n\n// --------------------- STANDARDIZE --------------------------------\n\n/**\n * Changes value to be in the range [-1, 1].\n */\nexport const mlStandardizeValue = (value: number, mean: number, stdDev: number, decimalPlaces = Infinity) : number => {\n if(stdDev === 0) return 0;\n return setDecimalPlaces((value - mean) / stdDev, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [-1, 1].\n */\nexport const mlStandardizeArray = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity) : number[] => {\n return [...data].map(value => mlStandardizeValue(value, mean, stdDev, decimalPlaces));\n};\n\nexport const mlStandardizeTestData = (data: number[], decimalPlaces = Infinity): IMlStandardizeResult => {\n const mean = getArithmeticMean(data) ?? 0;\n const stdDev = getStandardDeviation(data);\n const _data = mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n\n return {\n mean: setDecimalPlaces(mean, decimalPlaces),\n stdDev: setDecimalPlaces(stdDev, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlStandardizeUnseenData = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity): number[] => {\n return mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n};"], - "mappings": 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"unitVector2", "dotProduct", "vDotProduct", "getV2AngleBetween", "diff", "vSub", "getV3AngleBetween", "isAngleBetween", "angleDegrees", "startAngleDegrees", "endAngleDegrees", "distance", "getAnglesSub", "distance1", "distance2", "totalDistance", "isClockwise", "angle1Deg", "angle2Deg", "startAngleDeg", "angleDegrees1", "angleDegrees2", "angleDistance", "mod", "getAnglesDistance", "percentToAngle", "percent", "endAngleDeg", "circleStartAngle", "vSum", "vector1", "vector2", "decimalPlaces", "vector", "i", "setDecimalPlaces", "v2Sum", "v3Sum", "vSub", "v2Sub", "v3Sub", "vMulScalar", "v", "scalar", "v2MulScalar", "v2", "v3MulScalar", "v3", "vDivideScalar", "v2DivideScalar", "v3DivideScalar", "vLength", "sum", "v2Length", "v3Length", "v2SetLength", "newLength", "angle", "getV2Angle", "vDistance", "diff", "v2Distance", "v3Distance", "vNormalize", "length", "unitVector", "v2Normalize", "v3Normalize", "vDotProduct", "v2DotProduct", "v3DotProduct", "v3CrossProduct", "defaultValue", "v4", "vN", "N", "v2FromPolarCoords", "distance", "angleRad", "setV2Angle", "vEqual", "v2GetNormal", "sub", "mSum", "matrix1", "matrix2", "decimalPlaces", "matrix", "i", "vSum", "m2Sum", "m3Sum", "mSub", "vSub", "m2Sub", "m3Sub", "mMulScalar", "m", "scalar", "v", "vMulScalar", "m2MulScalar", "m2", "m3MulScalar", "m3", "mDivideScalar", "vDivideScalar", "m2DivideScalar", "m3DivideScalar", "mTranspose", "vectorsCount", "vectorLength", "j", "m2Transpose", "m3Transpose", "mReset", "defaultValue", "res", "size", "vector", "m2Reset", "m3Reset", "m2x2", "m3x3", "m4x4", "mNxM", "N", "M", "vN", "identity2", "identity3", "identity4", "identityN", "mDeepCopy", "m2DeepCopy", "m3DeepCopy", "mAppendCol", "col", "copy", "mPrependCol", "mAppendRow", "row", "m2AppendRow", "m3AppendRow", "mPrependRow", "m2PrependRow", "m3PrependRow", "mDelLastRow", "mDelFirstRow", "mDelLastColumn", "mDelFirstColumn", "mGetFirstColumn", "mGetLastColumn", "mGetColumn", "colIndex", "mMul", "transposed", "vector1", "vector2", "product", "vDotProduct", "mMulVector", "mEqual", "vEqual", "mMinorHelper", "mMinor", "mDeterminant", "m2Determinant", "d", "minor", "param", "m3Determinant", "m2Adjugate", "m3Adjugate", "mAdjugate", "cofactors", "sign", "isSingularMatrix", "m2Inverse", "adj", "m3Inverse", "mInverse", "m2ToCSS", "m", "a", "b", "c", "d", "m2hToCSS", "tx", "ty", "m2hToCSS3d", "m3hToCSS3d", "m2Translation", "position", "decimalPlaces", "setDecimalPlaces", "m3Translation", "m2TranslationH", "m3TranslationH", "m2Rotation", "angleRad", "isClockwise", "cos", "sin", "m2RotationH", "m2RotationAroundPointH", "transformOrigin", "translation", "rotation", "translationBack", "v3MulScalar", "temp1", "mMul", "m2RotateAroundPointH", "mat3h", "mMulVector", "v2Rotate", "vector", "unitVector", "v2Normalize", "v2RotateH", "v3Normalize", "m3RotationX", "m3RotationXH", "v3RotateX", "m3RotationY", "m3RotationYH", "v3RotateY", "m3RotationZ", "m3RotationZH", "v3RotateZ", "m2ScaleAtPointHMatrix", "scaleVector", "scale", "m2ScaleH", "m2ScaleAtPointH", "point", "m2Scale", "v2Scale", "m3Scale", "m3ScaleH", "v3Scale", "m2ScaleX", "m2ScaleXH", "m3ScaleX", "m3ScaleXH", "m3ScaleY", "m3ScaleYH", "m3ScaleZ", "m3ScaleZH", "m2ScaleY", "m2ScaleYH", "m2ReflectionOrigin", "m2ReflectionOriginH", "m3ReflectionOrigin", "m3ReflectionOriginH", "m2ReflectionYmX", "m2ReflectionX", "m2ReflectionXH", "m2ReflectionY", "m2ReflectionYH", "m3ReflectionYZ", "m3ReflectionYZH", "m3ReflectionXZ", "m3ReflectionXZH", "m3ReflectionXY", "m3ReflectionXYH", "m2ShearingY", "factor", "m2ShearingX", "getRandom", "min", "max", "decimalPlaces", "setDecimalPlaces", "getRandomInt", "getRandomBoolean", "getRandomItemFromArray", "array", "randomIndex", "stringToNumber", "value", "defaultNumber", "_a", "res", "dxPolynomial", "x", "polynomial", "decimalPlaces", "res", "part", "coeff", "power", "setDecimalPlaces", "dxV2QuadraticBezierCurve", "startControlPoint", "centerControlPoint", "endControlPoint", "temp1", "temp2", "temp3", "dxV3QuadraticBezierCurve", "dxV2CubicBezierCurve", "center1ControlPoint", "center2ControlPoint", "temp4", "dxV3CubicBezierCurve", "dxSin", "dxCos", "dxTan", "__pow", "dxCot", "dxArcSin", "dxArcCos", "dxArcTan", "dxArcCot", "linearEquation", "equation", "decimalPlaces", "a", "b", "diff", "setDecimalPlaces", "linearEquationSystem2", "equation1", "equation2", "equationParams", "inversed", "m2Inverse", "equationResults", "mMulVector", "linearEquationSystem3", "equation3", "m3Inverse", "linearEquationSystemN", "equations", "mDelLastColumn", "mInverse", "mGetLastColumn", "getLinearEquationBy2Points", "point1", "point2", "deltaX", "deltaY", "v2Sub", "x", "y", "m", "formula", "quadraticEquation", "equation", "decimalPlaces", "a", "b", "c", "d", "res", "linearEquation", "isNumber", "diff", "discriminant", "setDecimalPlaces", "t1", "t2", "v2QuadraticBezierCurve", "startControlPoint", "centerControlPoint", "endControlPoint", "decimalPlaces", "temp1", "temp2", "temp3", "setDecimalPlaces", "v3QuadraticBezierCurve", "v2CubicBezierCurve", "center1ControlPoint", "center2ControlPoint", "temp4", "v3CubicBezierCurve", "v2QuadraticBezierCurveTangent", "dxVector", "dxV2QuadraticBezierCurve", "v2Normalize", "v3QuadraticBezierCurveTangent", "dxV3QuadraticBezierCurve", "v3Normalize", "v2CubicBezierCurveTangent", "dxV2CubicBezierCurve", "v3CubicBezierCurveTangent", "dxV3CubicBezierCurve", "v2QuadraticBezierCurveNormal", "tangent", "v2CubicBezierCurveNormal", "v2QuadraticBezierCurveExtrema", "a1", "b1", "res1", "linearEquation", "a2", "b2", "res2", "res", "isNumber", "v2CubicBezierCurveExtrema", "c1", "equation1", "c2", "equation2", "quadraticEquation", "num", "v2QuadraticBezierBBox", "extrema", "minX", "minY", "maxX", "maxY", "percent", "point", "x", "y", "v2CubicBezierBBox", "circleMovement", "center", "angle", "radius", "circleMovementAfterMouse", "mouse", "vector", "v2Sub", "getV2Angle", "convertRange", "ellipseMovement", "radius1", "radius2", "ellipseMovementAfterMouse", "radii", "sineWaveMovement", "x", "amplitude", "frequency", "phase", "y", "lissajousCurve", "width", "height", "t", "k", "n", "m", "p", "getRandomRGBColor", "hslColor", "getRandomHSLColor", "hslToRgb", "getRandomHexColor", "hslToHex", "h", "getRandom", "s", "l", "getRandomHSLColorWithHue", "getRandomHSLColorWithSaturation", "getRandomHSLColorWithLightness", "getRandomGrayscaleHSLColor", "getRandomHSLColorWithinRanges", "hueStart", "hueEnd", "saturationStart", "saturationEnd", "lightStart", "lightEnd", "convertHueToDegrees", "getHue", "r", "g", "b", "min", "max", "diff", "getLuminance", "getSaturation", "rgbToHsl", "rgb", "decimalPlaces", "setDecimalPlaces", "hslToRgbHelper", "helper1", "helper2", "colorHelper", "hsl", "gray", "rHelper", "gHelper", "bHelper", "hue2rgb", "q", "t", "p", "toHex", "hex", "rgbToHex", "hexToRgb", "shorthandRegex", "_hex", "_m", "result", "rgbToLab", "x", "y", "z", "labToRgb", "lab", "getShiftedHue", "color", "shift", "hue", "mod", "getShiftedLightness", "lightness", "getShiftedSaturation", "saturation", "getColorsDelta", "rgbA", "rgbB", "labA", "labB", "deltaL", "deltaA", "deltaB", "c1", "c2", "deltaC", "deltaH", "sc", "sh", "deltaLKlsl", "deltaCkcsc", "deltaHkhsh", "i", "guid", "c", "newId", "rectCollide", "rect1", "rect2", "circleCollide", "circle1", "circle2", "dx", "dy", "getEdges", "poly", "edges", "i", "nextIndex", "mod", "edge", "convexPolygonsCollide", "poly1", "poly2", "normal", "v2GetNormal", "p1Proj", "projectPolygon", "p2Proj", "polygon", "min", "max", "vertex", "projection", "v2DotProduct", "animate", "props", "_duration", "startTime", "animationId", "elapsed", "previousTimeStamp", "animating", "observer", "stop", "restart", "start", "pause", "resume", "step", "timeStamp", "getResult", "observerHandler", "_entries", "_observer", "getElapsedTime", "isAnimating", "getStartTime", "getPercent", "getResizeObserver", "getCircleCircumference", "radius", "decimalPlaces", "setDecimalPlaces", "getEllipseCircumference", "radius1", "radius2", "__pow", "isAngleInCircleArc", "startAngleDeg", "endAngleDeg", "currentDegrees", "getSquareInCircleSide", "naturalNumbersSequenceSum", "n", "arithmeticSequenceSum", "a", "d", "getArithmeticMean", "data", "decimalPlaces", "sum", "acc", "val", "setDecimalPlaces", "getArithmeticMeanFromFrequency", "frequencyMap", "mean", "frequency", "getMedian", "copy", "num1", "num2", "mid", "getMode", "num", "maxFrequency", "modes", "getVariance1", "__pow", "getVariance", "getStandardDeviation", "_a", "variance", "mlNormalizeValue", "value", "min", "max", "decimalPlaces", "diff", "setDecimalPlaces", "mlNormalizeArray", "data", "copy", "mlNormalizeTestData", "_data", "mlNormalizeUnseenData", "mlStandardizeValue", "mean", "stdDev", "mlStandardizeArray", "mlStandardizeTestData", "_a", "getArithmeticMean", "getStandardDeviation", "mlStandardizeUnseenData"] + "sources": ["../src/index-esm.ts", "../src/main/format.ts", "../src/main/other.ts", "../src/main/angle.ts", "../src/main/linear-algebra/vector.ts", "../src/main/linear-algebra/matrix.ts", "../src/main/linear-algebra/matrix-transformations.ts", "../src/main/random.ts", "../src/main/convert.ts", "../src/main/derivative.ts", "../src/main/equations/linear-equations.ts", "../src/main/equations/quadratic-equations.ts", "../src/main/bezier-curves/bezier-curve.ts", "../src/main/path-movement.ts", "../src/main/color.ts", "../src/main/id.ts", "../src/main/collision-detection.ts", "../src/main/animation.ts", "../src/main/circle-ellipse.ts", "../src/main/sequence.ts", "../src/main/statistics.ts", "../src/main/ml.ts", "../src/main/series.ts"], + "sourcesContent": ["export * from './main/linear-algebra/vector';\nexport * from './main/linear-algebra/matrix';\nexport * from './main/linear-algebra/matrix-transformations';\nexport * from './main/format';\nexport * from './main/angle';\nexport * from './main/random';\nexport * from './main/other';\nexport * from './main/convert';\nexport * from './main/bezier-curves/bezier-curve';\nexport * from './main/equations/linear-equations';\nexport * from './main/path-movement';\nexport * from './main/color';\nexport * from './main/physics';\nexport * from './main/id';\nexport * from './main/derivative';\nexport * from './main/collision-detection';\nexport * from './main/animation';\nexport * from './main/circle-ellipse';\nexport * from './main/sequence';\nexport * from './main/statistics';\nexport * from './main/ml';\nexport * from './main/series';", "export const setDecimalPlaces = (num: number, decimalPlaces: number | undefined = Infinity) => {\n if(decimalPlaces === Infinity) return num;\n\n if(decimalPlaces < 0){\n decimalPlaces = 0;\n }\n\n const coefficient = 10 ** decimalPlaces;\n return Math.round(num * coefficient) / coefficient;\n};", "import { Vector2 } from '../types';\nimport { setDecimalPlaces } from './format';\n\nexport const mod = (n: number, m: number) => {\n return ((n % m) + m) % m;\n};\n\n/**\n * Convert range [a, b] to [c, d].\n * f(x) = (d - c) * (x - a) / (b - a) + c\n */\nexport const convertRange = (x: number, a: number, b: number, c: number, d: number) => {\n return (d - c) * (x - a) / (b - a) + c;\n};\n\n/**\n * Check if 2 ranges [a,b] and [c,d] overlap.\n */\nexport const doRangesOverlap = (a: number, b: number, c: number, d: number) => {\n return Math.max(a, c) <= Math.min(b, d) ;\n};\n\n// eslint-disable-next-line\nexport const isNumber = (value: any) => {\n return !isNaN(parseFloat(value)) && isFinite(value);\n};\n\n/**\n * Convert polar coordinates to cartesian coordinates.\n */\nexport const polarToCartesian = (center: Vector2, radii: Vector2, angleInRad: number, decimalPlaces = Infinity) : Vector2 => {\n const [cx, cy] = center;\n const [rx, ry] = radii;\n\n return [\n setDecimalPlaces(cx + (rx * Math.cos(angleInRad)), decimalPlaces),\n setDecimalPlaces(cy + (ry * Math.sin(angleInRad)), decimalPlaces),\n ];\n};", "import { Vector, Vector2, Vector3 } from '../types';\nimport { setDecimalPlaces } from './format';\nimport { v2Length, vNormalize, vDotProduct, vSub } from './linear-algebra/vector';\nimport { mod } from './other';\n\nexport const getV2Angle = (v2: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1], v2[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleInEllipse = (v2: Vector2, radii: Vector2, decimalPlaces = Infinity) => {\n const angle = Math.atan2(v2[1]/radii[1], v2[0]/radii[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const setV2Angle = (v2: Vector2, newAngleRad: number, decimalPlaces = Infinity): Vector2 => {\n const length = v2Length(v2);\n return [\n setDecimalPlaces(Math.cos(newAngleRad) * length, decimalPlaces),\n setDecimalPlaces(Math.sin(newAngleRad) * length, decimalPlaces),\n ];\n};\n\nexport const radiansToDegrees = (radians: number, decimalPlaces = Infinity) => {\n const res = radians * (180 / Math.PI);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\nexport const degreesToRadians = (degrees: number, decimalPlaces = Infinity) => {\n const res = degrees * (Math.PI / 180);\n return setDecimalPlaces(res, decimalPlaces);\n};\n\n/**\n * Returns the range [0, Math.PI]\n * A = Math.acos( dot(v1, v2)/(v1.length()*v2.length()) );\n */\nexport const getVNAngleBetween = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n const unitVector1 = vNormalize(vector1);\n const unitVector2 = vNormalize(vector2);\n const dotProduct = vDotProduct(unitVector1, unitVector2);\n const angle = Math.acos(dotProduct);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV2AngleBetween = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) : number => {\n // return getVNAngleBetween(vector1, vector2, decimalPlaces);\n const diff = vSub(vector1, vector2);\n const angle = Math.atan2(diff[1], diff[0]);\n return setDecimalPlaces(angle, decimalPlaces);\n};\n\nexport const getV3AngleBetween = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return getVNAngleBetween(vector1, vector2, decimalPlaces);\n};\n\nexport const isAngleBetween = (angleDegrees: number, startAngleDegrees: number, endAngleDegrees: number) : boolean => {\n const distance = getAnglesSub(startAngleDegrees, endAngleDegrees);\n const distance1 = getAnglesSub(startAngleDegrees, angleDegrees);\n const distance2 = getAnglesSub(endAngleDegrees, angleDegrees);\n const totalDistance = distance1 + distance2;\n\n // Use a small threshold for floating point errors\n return Math.abs(totalDistance - distance) <= 0.001;\n}\n\nexport const isClockwise = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n return angle2Deg >= angle1Deg;\n};\n\n/**\n * Shortest distance (angular) between two angles.\n */\nexport const getAnglesSub = (angleDegrees1: number, angleDegrees2: number, decimalPlaces = Infinity) : number => {\n const angleDistance = Math.abs(mod(angleDegrees1, 360) - mod(angleDegrees2, 360));\n return setDecimalPlaces(angleDistance <= 180 ? angleDistance : 360 - angleDistance, decimalPlaces);\n};\n\nexport const getAnglesDistance = (angle1Deg: number, angle2Deg: number, startAngleDeg = 0, decimalPlaces = Infinity) => {\n angle1Deg = angle1Deg % 360;\n angle2Deg = angle2Deg % 360;\n\n if(angle1Deg < startAngleDeg) {\n angle1Deg += 360;\n }\n\n if(angle2Deg < startAngleDeg) {\n angle2Deg += 360;\n }\n\n if(isClockwise(angle1Deg, angle2Deg, startAngleDeg)) {\n return setDecimalPlaces((angle2Deg - angle1Deg + 360) % 360, decimalPlaces);\n }\n else{\n return setDecimalPlaces((angle1Deg - angle2Deg + 360) % 360, decimalPlaces);\n }\n};\n\nexport const percentToAngle = (percent: number, startAngleDeg: number, endAngleDeg: number, circleStartAngle = 0) => {\n if(percent < 0) {\n percent = 0;\n }\n\n if(percent > 100) {\n percent = 100;\n }\n\n const distance = getAnglesDistance(startAngleDeg, endAngleDeg, circleStartAngle);\n\n const clockwise = isClockwise(startAngleDeg, endAngleDeg, circleStartAngle);\n if(clockwise) {\n return mod(circleStartAngle + (percent * distance / 100), 360);\n }\n else {\n return mod(circleStartAngle - (percent * distance / 100), 360);\n }\n};", "import { Vector, Vector2, Vector3, Vector4 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { getV2Angle, setV2Angle } from '../angle';\n\n// ------------ SUM ------------------------\n\nexport const vSum = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSum(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sum = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSum(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ SUB ------------------------\n\nexport const vSub = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : Vector => {\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vSub(vector1, vector2, decimalPlaces) as Vector2;\n};\n\nexport const v3Sub = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vSub(vector1, vector2, decimalPlaces) as Vector3;\n};\n\n// ------------ MUL SCALAR ------------------------\n\nexport const vMulScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n const vector: Vector = [];\n\n for(let i=0; i {\n return vMulScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3MulScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vMulScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ DIVIDE ------------------------\n\nexport const vDivideScalar = (v: Vector, scalar: number, decimalPlaces = Infinity): Vector => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const vector: Vector = [];\n\n for(let i=0; i {\n return vDivideScalar(v2, scalar, decimalPlaces) as Vector2;\n};\n\nexport const v3DivideScalar = (v3: Vector3, scalar: number, decimalPlaces = Infinity): Vector3 => {\n return vDivideScalar(v3, scalar, decimalPlaces) as Vector3;\n};\n\n// ------------ LENGTH ------------------------\n\nexport const vLength = (vector: Vector, decimalPlaces = Infinity) => {\n let sum = 0;\n\n for(let i=0; i {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v3Length = (vector: Vector3, decimalPlaces = Infinity) => {\n return vLength(vector, decimalPlaces);\n};\n\nexport const v2SetLength = (v2: Vector2, newLength: number, decimalPlaces = Infinity): Vector2 => {\n const angle = getV2Angle(v2);\n return [\n setDecimalPlaces(Math.cos(angle) * newLength, decimalPlaces),\n setDecimalPlaces(Math.sin(angle) * newLength, decimalPlaces),\n ];\n};\n\n// ----------- DISTANCE ------------------------\n\nexport const vDistance = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v2Distance = (vector1: Vector2, vector2: Vector2, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\nexport const v3Distance = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) => {\n const diff = vSub(vector1, vector2);\n return vLength(diff, decimalPlaces);\n};\n\n// ------------ NORMALIZE ------------------------\n\n/**\n * Normalization creates a unit vector, which is a vector of length 1.\n */\nexport const vNormalize = (v: Vector, decimalPlaces = Infinity) : Vector => {\n const length = vLength(v);\n const unitVector: Vector = [];\n\n for(let i=0; i {\n return vNormalize(v2, decimalPlaces) as Vector2;\n};\n\nexport const v3Normalize = (v3: Vector3, decimalPlaces = Infinity) : Vector3 => {\n return vNormalize(v3, decimalPlaces) as Vector3;\n};\n\n// ------------ DOT PRODUCT ------------------------\n\nexport const vDotProduct = (vector1: Vector, vector2: Vector, decimalPlaces = Infinity) : number => {\n let sum = 0;\n\n for(let i=0; i {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\nexport const v3DotProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity) : number => {\n return vDotProduct(vector1, vector2, decimalPlaces);\n};\n\n// ------------ CROSS PRODUCT ------------------------\n\n/**\n * Cross product is possible on 3D vectors only.\n * The cross product a \u00D7 b is defined as a vector c that is perpendicular (orthogonal) to both a and b.\n */\nexport const v3CrossProduct = (vector1: Vector3, vector2: Vector3, decimalPlaces = Infinity): Vector3 => {\n return [\n setDecimalPlaces(vector1[1] * vector2[2] - vector1[2] * vector2[1], decimalPlaces),\n setDecimalPlaces(vector1[2] * vector2[0] - vector1[0] * vector2[2], decimalPlaces),\n setDecimalPlaces(vector1[0] * vector2[1] - vector1[1] * vector2[0], decimalPlaces),\n ];\n};\n\n// --------------- INIT VECTOR HELPER -----------------\n\nexport const v2 = (defaultValue = 0): Vector2 => {\n return [defaultValue, defaultValue];\n};\n\nexport const v3 = (defaultValue = 0): Vector3 => {\n return [defaultValue, defaultValue, defaultValue];\n};\n\nexport const v4 = (defaultValue = 0): Vector4 => {\n return [defaultValue, defaultValue, defaultValue, defaultValue];\n};\n\nexport const vN = (N: number, defaultValue = 0): Vector => {\n\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n const vector: Vector = [];\n for(let i=0; i {\n let vector: Vector2 = [0, 0];\n vector = v2SetLength(vector, distance);\n return setV2Angle(vector, angleRad);\n};\n\n// --------------- EQUALITY -------------------------\n\nexport const vEqual = (vector1: Vector, vector2: Vector): boolean => {\n if(vector1.length !== vector2.length) return false;\n\n for(let i=0; i {\n const sub = v2Sub(vector2, vector1);\n return [\n -setDecimalPlaces(sub[1], decimalPlaces),\n setDecimalPlaces(sub[0], decimalPlaces)\n ];\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector, Vector2, Vector3 } from '../../types';\nimport { vMulScalar, vSum, vSub, vDotProduct, vN, vEqual, vDivideScalar } from './vector';\n\n// --------------- SUM ----------------------\n\nexport const mSum = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sum = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSum(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- SUB ----------------------\n\nexport const mSub = (matrix1: Matrix, matrix2: Matrix, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix2;\n};\n\nexport const m3Sub = (matrix1: Matrix3, matrix2: Matrix3, decimalPlaces = Infinity): Matrix3 => {\n return mSub(matrix1, matrix2, decimalPlaces) as Matrix3;\n};\n\n// --------------- MUL SCALAR ----------------------\n\nexport const mMulScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vMulScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2MulScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mMulScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3MulScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mMulScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n// --------------- DIVIDE SCALAR ----------------------\n\nexport const mDivideScalar = (m: Matrix, scalar: number, decimalPlaces = Infinity): Matrix => {\n if(scalar === 0){\n throw new Error('Division by zero error.');\n }\n\n const matrix: Matrix = [];\n\n for(const v of m){\n matrix.push(vDivideScalar(v, scalar, decimalPlaces));\n }\n\n return matrix;\n};\n\nexport const m2DivideScalar = (m2: Matrix2, scalar: number, decimalPlaces = Infinity): Matrix2 => {\n return mDivideScalar(m2, scalar, decimalPlaces) as Matrix2;\n};\n\nexport const m3DivideScalar = (m3: Matrix3, scalar: number, decimalPlaces = Infinity): Matrix3 => {\n return mDivideScalar(m3, scalar, decimalPlaces) as Matrix3;\n};\n\n\n// --------------- TRANSPOSE ----------------------\n\nexport const mTranspose = (m: Matrix): Matrix => {\n\n const vectorsCount = m.length;\n if(vectorsCount <= 0) return m;\n\n const vectorLength = m[0].length;\n if(vectorLength <= 0) return m;\n\n const matrix: Matrix = [];\n for(let i=0; i {\n return mTranspose(m2);\n};\n\nexport const m3Transpose = (m3: Matrix3): Matrix => {\n return mTranspose(m3);\n};\n\n// ----------------- RESET ----------------------\n\nexport const mReset = (m: Matrix, defaultValue = 0): Matrix => {\n\n if(m.length <= 0) return [];\n\n const res: Matrix = [];\n\n for(let i=0; i {\n return mReset(m2, defaultValue) as Matrix2;\n};\n\nexport const m3Reset = (m3: Matrix3, defaultValue = 0): Matrix3 => {\n return mReset(m3, defaultValue) as Matrix3;\n};\n\n// --------------- MATRIX INIT HELPERS -----------------\n\nexport const m2x2 = (defaultValue = 0): Matrix2 => {\n return [\n [defaultValue, defaultValue],\n [defaultValue, defaultValue],\n ];\n};\n\nexport const m3x3 = (defaultValue = 0): Matrix3 => {\n return [\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const m4x4 = (defaultValue = 0): Matrix4 => {\n return [\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n [defaultValue, defaultValue, defaultValue, defaultValue],\n ];\n};\n\nexport const mNxM = (N: number, M: number, defaultValue = 0): Matrix => {\n if(N <= 0 || M <= 0){\n throw new Error('M and N must be positive numbers.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return [\n [1, 0],\n [0, 1],\n ];\n};\n\nexport const identity3 = (): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\nexport const identity4 = (): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Identity Matrix (I).\n * M x I = I x M = M for any matrix M.\n * Identity Matrix is a special case of scale matrix.\n */\nexport const identityN = (N: number): Matrix => {\n if(N < 0){\n throw new Error('N must be a non-negative number.');\n }\n\n if(N === 0) return [];\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const matrix: Matrix = [];\n\n for(let i=0; i {\n return mDeepCopy(m2) as Matrix2;\n};\n\nexport const m3DeepCopy = (m3: Matrix3): Matrix3 => {\n return mDeepCopy(m3) as Matrix3;\n};\n\n// -------------- APPEND / PREPEND ROW OR COLUMN ---------------\n\nexport const mAppendCol = (m: Matrix, col: Vector): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n const copy = mDeepCopy(m);\n copy.push(row);\n return copy;\n};\n\nexport const m2AppendRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.push(row);\n return copy;\n};\n\nexport const m3AppendRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.push(row);\n return copy;\n};\n\nexport const mPrependRow = (m: Matrix, row: Vector) : Matrix => {\n const copy = mDeepCopy(m);\n copy.unshift(row);\n return copy;\n};\n\nexport const m2PrependRow = (m2: Matrix2, row: Vector2) : Matrix2 => {\n const copy = m2DeepCopy(m2);\n copy.unshift(row);\n return copy;\n};\n\nexport const m3PrependRow = (m3: Matrix3, row: Vector3) : Matrix3 => {\n const copy = m3DeepCopy(m3);\n copy.unshift(row);\n return copy;\n};\n\n// ------------ DELETE ROW OR COLUMN ----------------------------\n\nexport const mDelLastRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.pop();\n return copy;\n};\n\nexport const mDelFirstRow = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n copy.shift();\n return copy;\n};\n\nexport const mDelLastColumn = (m: Matrix): Matrix => {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const copy = mDeepCopy(m);\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const size = m[0].length;\n\n const vector: Vector = [];\n for(let i=0; i {\n if(m.length <= 0) return [];\n\n const vector: Vector = [];\n for(let i=0; i {\n\n const matrix: Matrix = [];\n for(let i=0; i {\n\n if(matrix.length < 0) return [];\n\n if(matrix[0].length !== vector.length){\n throw new Error('The number of columns in the matrix must be equal to the length of the vector.');\n }\n\n const res: Vector = [];\n\n for(let i=0; i {\n if(matrix1.length !== matrix2.length) return false;\n\n for(let i=0; i returns matrix N (m-1 x m-1)\n * The matrix must be square.\n */\nconst mMinorHelper = (m: Matrix, row: number, col: number) => {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const matrix: Matrix = [];\n\n for(let i=0; i {\n const size = m.length;\n\n if(size <= 0){\n throw new Error('The matrix should not be empty.');\n }\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // prepare the matrix without provided row and column\n const matrix = mMinorHelper(m, row, col);\n\n // calculate the matrix determinant\n return mDeterminant(matrix);\n};\n\n/**\n * Calculate determinant for NxN matrix.\n * Matrix should be square.\n */\nexport const mDeterminant = (matrix: Matrix): number => {\n const size = matrix.length;\n if(size === 0) return 1;\n\n if(size !== matrix[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return matrix[0][0];\n if(size === 2) return m2Determinant(matrix as Matrix2);\n\n let d = 0;\n\n for(let i=0; i {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return m2[0][0] * m2[1][1] - m2[1][0] * m2[0][1];\n};\n\n/**\n * Calculate determinant for 3x3 matrix.\n * Matrix should be square.\n */\nexport const m3Determinant = (m3: Matrix3): number => {\n if(m3.length !== m3[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return mDeterminant(m3);\n};\n\n// ------------------ INVERSE -----------------------\n\nexport const m2Adjugate = (m2: Matrix2): Matrix2|null => {\n if(m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n return [\n [m2[1][1], -m2[0][1]],\n [-m2[1][0], m2[0][0]],\n ];\n};\n\nexport const m3Adjugate = (m3: Matrix3) : Matrix3|null => {\n return mAdjugate(m3) as (Matrix3|null);\n};\n\n/**\n * Adjugate is a transpose of a cofactor matrix\n */\nexport const mAdjugate = (m: Matrix): Matrix|null => {\n\n const size = m.length;\n if(size <= 0) return null;\n\n if(size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n if(size === 1) return m;\n\n if(size === 2) return m2Adjugate(m as Matrix2);\n\n // build a cofactor matrix ----------------\n const cofactors: Matrix = [];\n\n for(let i=0; i {\n if(m.length > 0 && m.length !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = mDeterminant(m);\n return d === 0;\n};\n\n/**\n * Square matrix A (nxn) is invertible is there is another square matrix B (nxn) so AxB = BxA = I\n * For A (2x2) matrix, the inverse is:\n * (1 / (determinant(A))) * adj(A)\n */\nexport const m2Inverse = (m2: Matrix2, decimalPlaces = Infinity): (Matrix2 | null) => {\n if(m2.length > 0 && m2.length !== m2[0].length){\n throw new Error('The matrix must be square.');\n }\n\n const d = m2Determinant(m2);\n if(d === 0) return null;\n\n const adj = m2Adjugate(m2);\n if(adj === null) return null;\n\n return m2DivideScalar(adj, d, decimalPlaces);\n};\n\nexport const m3Inverse = (m3: Matrix3, decimalPlaces = Infinity): (Matrix3 | null) => {\n return mInverse(m3, decimalPlaces) as (Matrix3|null);\n};\n\nexport const mInverse = (m: Matrix, decimalPlaces = Infinity): (Matrix | null) => {\n const size = m.length;\n\n if(size > 0 && size !== m[0].length){\n throw new Error('The matrix must be square.');\n }\n\n // find a determinant ----------------------\n const d = mDeterminant(m);\n\n // find an Adjugate - a transpose of a cofactor matrix\n const adj = mAdjugate(m);\n if(adj === null) return null;\n\n return mDivideScalar(adj, d, decimalPlaces);\n};", "import { Matrix2, Matrix3, Matrix4, Matrix, Vector2, Vector3, Vector4 } from '../../types';\nimport { v2Normalize, v3MulScalar, v3Normalize } from './vector';\nimport { mMulVector, mMul } from './matrix';\nimport { setDecimalPlaces } from '../format';\n\n/*\nAny 2D affine transformation can be decomposed\ninto a rotation, followed by a scaling, followed by a\nshearing, and followed by a translation.\n---------------------------------------------------------\nAffine matrix = translation x shearing x scaling x rotation\n */\n\n// ----------------- CSS -------------------------------------\n\n/**\n * Matrix 2D in non-homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2ToCSS = (m: Matrix2) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, 0, 0)`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix\n */\nexport const m2hToCSS = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix(${ a }, ${ b }, ${ c }, ${ d }, ${ tx }, ${ ty })`;\n};\n\n/**\n * Matrix 2D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m2hToCSS3d = (m: Matrix3) : string => {\n const a = m[0][0];\n const b = m[1][0];\n const c = m[0][1];\n const d = m[1][1];\n const tx = m[0][2];\n const ty = m[1][2];\n\n return `matrix3d(${ a }, ${ b }, 0, 0, ${ c }, ${ d }, 0, 0, 0, 0, 1, 0, ${ tx }, ${ ty }, 0, 1)`;\n};\n\n/**\n * Matrix 3D in homogeneous coordinates to CSS matrix3d() function\n * https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function/matrix3d\n */\nexport const m3hToCSS3d = (m: Matrix4) : string => {\n\n return `matrix3d(\n ${ m[0][0] }, ${ m[0][1] }, ${ m[0][2] }, ${ m[0][3] },\n ${ m[1][0] }, ${ m[1][1] }, ${ m[1][2] }, ${ m[1][3] },\n ${ m[2][0] }, ${ m[2][1] }, ${ m[2][2] }, ${ m[2][3] },\n ${ m[3][0] }, ${ m[3][1] }, ${ m[3][2] }, ${ m[3][3] }\n )`;\n};\n\n// ---------------- TRANSLATION MATRICES ----------------------\n\nexport const m2Translation = (position: Vector2, decimalPlaces = Infinity): Matrix2 => {\n\n return [\n [1, 0],\n [0, 1],\n [setDecimalPlaces(position[0], decimalPlaces), setDecimalPlaces(position[1], decimalPlaces)],\n ];\n};\n\nexport const m3Translation = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n [\n setDecimalPlaces(position[0], decimalPlaces),\n setDecimalPlaces(position[1], decimalPlaces),\n setDecimalPlaces(position[2], decimalPlaces)\n ],\n ];\n};\n\n/**\n * 2D Translation matrix in homogeneous coordinates.\n */\nexport const m2TranslationH = (position: Vector3, decimalPlaces = Infinity): Matrix3 => {\n\n return [\n [1, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1],\n ];\n};\n\n/**\n * 3D Translation matrix in homogeneous coordinates.\n */\nexport const m3TranslationH = (position: Vector4, decimalPlaces = Infinity): Matrix4 => {\n\n return [\n [1, 0, 0, setDecimalPlaces(position[0], decimalPlaces)],\n [0, 1, 0, setDecimalPlaces(position[1], decimalPlaces)],\n [0, 0, 1, setDecimalPlaces(position[2], decimalPlaces)],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- ROTATION MATRICES -------------------------\n\n/**\n * Rotation of an angle about the origin.\n */\nexport const m2Rotation = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix2 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin],\n [sin, cos],\n ] :\n [\n [cos, sin],\n [-sin, cos],\n ];\n};\n\n/**\n * Rotation of an angle about the origin in homogeneous coordinates (clockwise).\n */\nexport const m2RotationH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ]:\n [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation of an angle \"angleRad\" around the given point (transformOrigin) in homogeneous coordinates (clockwise).\n * result_vector = TranslationMatrix(x, y) * RotationMatrix() * TranslationMatrix(-x, -y) * position_vector\n */\nexport const m2RotationAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const rotation = m2RotationH(angleRad, isClockwise, decimalPlaces);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, rotation);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2RotateAroundPointH = (\n angleRad: number,\n transformOrigin: Vector3,\n position: Vector3,\n isClockwise = true,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2RotationAroundPointH(angleRad, transformOrigin, isClockwise, decimalPlaces);\n return mMulVector(mat3h, position) as Vector3;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2Rotate = (angleRad: number, vector: Vector2, isClockwise = true, decimalPlaces = Infinity): Vector2 => {\n const unitVector = v2Normalize(vector);\n return mMulVector(m2Rotation(angleRad, isClockwise, decimalPlaces), unitVector) as Vector2;\n};\n\n/**\n * Rotate vector around the origin by angle \"angleRad\" (clockwise).\n */\nexport const v2RotateH = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m2RotationH(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the X axis (clockwise).\n */\nexport const m3RotationX = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0],\n [0, cos, -sin],\n [0, sin, cos],\n ] :\n [\n [1, 0, 0],\n [0, cos, sin],\n [0, -sin, cos],\n ];\n};\n\n/**\n * Rotation around the X axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationXH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [1, 0, 0, 0],\n [0, cos, -sin, 0],\n [0, sin, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [1, 0, 0, 0],\n [0, cos, sin, 0],\n [0, -sin, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateX = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationX(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Y axis (clockwise).\n */\nexport const m3RotationY = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin],\n [0, 1, 0],\n [-sin, 0, cos],\n ] :\n [\n [cos, 0, -sin],\n [0, 1, 0],\n [sin, 0, cos],\n ];\n};\n\n/**\n * Rotation around the Y axis (clockwise) - in homogeneous coordinates\n */\nexport const m3RotationYH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, 0, sin, 0],\n [0, 1, 0, 0],\n [-sin, 0, cos, 0],\n [0, 0, 0, 1],\n ] :\n [\n [cos, 0, -sin, 0],\n [0, 1, 0, 0],\n [sin, 0, cos, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateY = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationY(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n/**\n * Rotation around the Z axis (clockwise).\n */\nexport const m3RotationZ = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix3 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0],\n [sin, cos, 0],\n [0, 0, 1],\n ] : [\n [cos, sin, 0],\n [-sin, cos, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Rotation around the Z axis (clockwise)- in homogeneous coordinates\n */\nexport const m3RotationZH = (angleRad: number, isClockwise = true, decimalPlaces = Infinity): Matrix4 => {\n\n const cos = setDecimalPlaces(Math.cos(angleRad), decimalPlaces);\n const sin = setDecimalPlaces(Math.sin(angleRad), decimalPlaces);\n\n return isClockwise ? [\n [cos, -sin, 0, 0],\n [sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ] : [\n [cos, sin, 0, 0],\n [-sin, cos, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\nexport const v3RotateZ = (angleRad: number, vector: Vector3, isClockwise = true, decimalPlaces = Infinity): Vector3 => {\n const unitVector = v3Normalize(vector);\n return mMulVector(m3RotationZ(angleRad, isClockwise, decimalPlaces), unitVector) as Vector3;\n};\n\n// ---------------- SCALE MATRICES -------------\n\n/**\n * Get matrix for arbitrary scaling pivot point.\n * result_vector = TranslationMatrix(x, y) * ScaleMatrix() * TranslationMatrix(-x, -y) * scale_vector\n */\nexport const m2ScaleAtPointHMatrix = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n decimalPlaces = Infinity): Matrix3 => {\n\n const translation = m2TranslationH(transformOrigin, decimalPlaces);\n const scale = m2ScaleH(scaleVector);\n const translationBack = m2TranslationH(v3MulScalar(transformOrigin, -1), decimalPlaces);\n const temp1 = mMul(translation, scale);\n return mMul(temp1, translationBack) as Matrix3;\n};\n\nexport const m2ScaleAtPointH = (\n scaleVector: Vector3,\n transformOrigin: Vector3,\n point: Vector3,\n decimalPlaces = Infinity): Vector3 => {\n\n const mat3h = m2ScaleAtPointHMatrix(scaleVector, transformOrigin, decimalPlaces);\n return mMulVector(mat3h, point) as Vector3;\n};\n\nexport const m2Scale = (scaleVector: Vector2): Matrix2 => {\n return [\n [scaleVector[0], 0],\n [0, scaleVector[1]],\n ];\n};\n\nexport const v2Scale = (scaleVector: Vector2, vector: Vector2): Vector2 => {\n return mMulVector(m2Scale(scaleVector), vector) as Vector2;\n};\n\n/**\n * homogeneous coordinates\n */\nexport const m2ScaleH = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, 1],\n ];\n};\n\nexport const m3Scale = (scaleVector: Vector3): Matrix3 => {\n return [\n [scaleVector[0], 0, 0],\n [0, scaleVector[1], 0],\n [0, 0, scaleVector[2]],\n ];\n};\n\nexport const m3ScaleH = (scaleVector: Vector4): Matrix4 => {\n return [\n [scaleVector[0], 0, 0, 0],\n [0, scaleVector[1], 0, 0],\n [0, 0, scaleVector[2], 0],\n [0, 0, 0, 1]\n ];\n};\n\nexport const v3Scale = (scaleVector: Vector3, vector: Vector3): Vector3 => {\n return mMulVector(m3Scale(scaleVector), vector) as Vector3;\n};\n\n/**\n * Stretch, parallel to the x-axis.\n */\nexport const m2ScaleX = (scale: number): Matrix2 => {\n return [\n [scale, 0],\n [0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the x-axis - homogeneous coordinates\n */\nexport const m2ScaleXH = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleX = (scale: number): Matrix3 => {\n return [\n [scale, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in x-direction\n */\nexport const m3ScaleXH = (scale: number): Matrix4 => {\n return [\n [scale, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleY = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Stretch in y-direction\n */\nexport const m3ScaleYH = (scale: number): Matrix => {\n return [\n [1, 0, 0, 0],\n [0, scale, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZ = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, scale],\n ];\n};\n\n/**\n * Stretch in z-direction\n */\nexport const m3ScaleZH = (scale: number): Matrix4 => {\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, scale, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis.\n */\nexport const m2ScaleY = (scale: number): Matrix2 => {\n return [\n [1, 0],\n [0, scale],\n ];\n};\n\n/**\n * Stretch, parallel to the y-axis - homogeneous coordinates\n */\nexport const m2ScaleYH = (scale: number): Matrix3 => {\n return [\n [1, 0, 0],\n [0, scale, 0],\n [0, 0, 1],\n ];\n};\n\n// ---------------- REFLECTION MATRICES -------------------------\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOrigin = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection about the origin.\n */\nexport const m2ReflectionOriginH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection about the origin in non-homogeneous coordinates\n */\nexport const m3ReflectionOrigin = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, -1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection about the origin in homogeneous coordinates\n */\nexport const m3ReflectionOriginH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection about y=-x\n */\nexport const m2ReflectionYmX = (): Matrix2 => {\n\n return [\n [0, -1],\n [-1, 0],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionX = (): Matrix2 => {\n\n return [\n [1, 0],\n [0, -1],\n ];\n};\n\n/**\n * Reflection in the x-axis.\n */\nexport const m2ReflectionXH = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection in the y-axis.\n */\nexport const m2ReflectionY = (): Matrix2 => {\n\n return [\n [-1, 0],\n [0, 1],\n ];\n};\n\nexport const m2ReflectionYH = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionYZ = (): Matrix3 => {\n\n return [\n [-1, 0, 0],\n [0, 1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to YZ plane in homogeneous coordinates\n */\nexport const m3ReflectionYZH = (): Matrix4 => {\n\n return [\n [-1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXZ = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, -1, 0],\n [0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XZ plane in homogeneous coordinates\n */\nexport const m3ReflectionXZH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, -1, 0, 0],\n [0, 0, 1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in non-homogeneous coordinates\n */\nexport const m3ReflectionXY = (): Matrix3 => {\n\n return [\n [1, 0, 0],\n [0, 1, 0],\n [0, 0, -1],\n ];\n};\n\n/**\n * Reflection relative to XY plane in homogeneous coordinates\n */\nexport const m3ReflectionXYH = (): Matrix4 => {\n\n return [\n [1, 0, 0, 0],\n [0, 1, 0, 0],\n [0, 0, -1, 0],\n [0, 0, 0, 1],\n ];\n};\n\n// ---------------- SHEARING MATRICES -------------------------\n\n\n/**\n * Shearing in y-axis, with x-axis fixed with (0,1) moving to (factor, 1)\n */\nexport const m2ShearingY = (factor: number): Matrix2 => {\n\n return [\n [1, factor],\n [0, 1],\n ];\n};\n\n/**\n * Shearing in x-axis, with y-axis fixed with (1,0) moving to (1, factor)\n */\nexport const m2ShearingX = (factor: number): Matrix2 => {\n\n return [\n [1, 0],\n [factor, 1],\n ];\n};", "import { setDecimalPlaces } from './format';\n\n/**\n * Returns a random number in the [min,max] range.\n */\nexport const getRandom = (min: number, max: number, decimalPlaces = Infinity): number => {\n return setDecimalPlaces(Math.random() * (max - min) + min, decimalPlaces);\n};\n\n/**\n * Returns a random integer number in the [min,max] range.\n */\nexport const getRandomInt = (min: number, max: number): number => {\n return Math.floor(Math.random() * (max - min + 1) + min);\n};\n\nexport const getRandomBoolean = () => Math.random() < 0.5;\n\n/* eslint-disable @typescript-eslint/no-explicit-any */\nexport const getRandomItemFromArray = (array: any[]) => {\n const randomIndex = getRandomInt(0, array.length - 1);\n return array[randomIndex];\n};", "export const stringToNumber = (value: string|undefined|null|number, defaultNumber: number) => {\n if(value === undefined || value === null) return defaultNumber;\n const res = Number(value) ?? defaultNumber;\n return isNaN(res) ? defaultNumber : res;\n};", "import { setDecimalPlaces } from './format';\nimport { Vector2, Vector3 } from '../types';\n\n/**\n * u(x) and v(x) are functions ---------->\n *\n * dx(u + v) = dx(u) + dx(v)\n * dx(u - v) = dx(u) - dx(v)\n * dx(u * v) = dx(u) * v + u * dx(v)\n * dx(u / v) = (dx(u) * v - u * dx(v)) / (v ^ 2), when v(x) != 0\n */\n\n// ------------------ Derivatives of Polynomial ---------------------------\n\n/**\n * y = 3x+2\n * dxPolynomial(10, [[3, 1], [2, 0]])\n */\nexport const dxPolynomial = (x: number, polynomial: number[][], decimalPlaces = Infinity) => {\n let res = 0;\n\n for(const part of polynomial){\n if(part.length !== 2) return NaN;\n\n const coeff = part[0];\n const power = part[1];\n res += coeff * power * Math.pow(x, power - 1);\n }\n\n return setDecimalPlaces(res, decimalPlaces);\n}\n\n// ---------------------- Bezier Curves ---------------------------\n\n/**\n * Derivative of Bezier Curve is another Bezier Curve.\n * t must min in range [0, 1]\n */\nexport const dxV2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n // The derivative: P1 * (2t-2) + (2*P3-4*P2) * t + 2 * P2\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -2 * (1 - t); // Math.pow(1 - t, 2)\n const temp2 = 2 - 4 * t; // (1 - t) * 2 * t\n const temp3 = 2 * t; //t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\nexport const dxV2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const dxV3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = -3 * Math.pow(1 - t, 2); //Math.pow(1 - t, 3);\n const temp2 = 3 * (t - 1) * (3 * t - 1); //Math.pow(1 - t, 2) * 3 * t;\n const temp3 = 6 * t - 9 * t * t; // (1 - t) * 3 * t * t;\n const temp4 = 3 * t * t; //t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n\n// ----------------- Derivatives of trigonometry functions ---------------------------\n\nexport const dxSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(Math.cos(x), decimalPlaces);\n};\n\nexport const dxCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-Math.sin(x), decimalPlaces);\n};\n\nexport const dxTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.cos(x) ** 2), decimalPlaces);\n};\n\n/**\n * x != Math.PI * n, where n is an integer\n */\nexport const dxCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sin(x) ** 2), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcSin = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\n/**\n * -1 < x < 1\n */\nexport const dxArcCos = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (Math.sqrt(1 - x ** 2)), decimalPlaces);\n};\n\nexport const dxArcTan = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(1 / (1 + x ** 2), decimalPlaces);\n};\n\nexport const dxArcCot = (x: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(-1 / (1 + x ** 2), decimalPlaces);\n};\n", "import { Matrix, Matrix2, Matrix3, Vector, Vector2, Vector3 } from '../../types';\nimport { m2Inverse, m3Inverse, mInverse, mMulVector, mDelLastColumn, mGetLastColumn } from '../linear-algebra/matrix';\nimport { setDecimalPlaces } from '../format';\nimport { v2Sub } from '../linear-algebra/vector';\n\n/**\n * Linear equation\n * ax + b = c\n * x = (c - b) / a; a != 0\n */\nexport const linearEquation = (equation: Vector3, decimalPlaces = Infinity) : number => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n\n const diff = c - b;\n\n if(a === 0 && diff === 0) return Infinity; // any number is a solution\n if(a === 0) return NaN; // no solution\n\n return setDecimalPlaces(diff / a, decimalPlaces);\n};\n\n/**\n * System of 2 linear equations.\n * [x, y] = inverse(Matrix of equation parameters) x (vector of equation results)\n * ---------------\n * 3x + 2y = 7\n * -6x + 6y = 6\n */\nexport const linearEquationSystem2 = (equation1: Vector3, equation2: Vector3, decimalPlaces = Infinity) : Vector2 | null => {\n const equationParams: Matrix2 = [\n [equation1[0], equation1[1]],\n [equation2[0], equation2[1]],\n ];\n\n const inversed = m2Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector2 = [\n equation1[2],\n equation2[2]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector2;\n};\n\n/**\n * System of 3 linear equations.\n * ---------------------------------------\n * 3x + 2y + 5z = 7\n * -6x + 6y + 6z = 6\n * 2x + 7y - z = 4\n */\nexport const linearEquationSystem3 = (\n equation1: Vector,\n equation2: Vector,\n equation3: Vector,\n decimalPlaces = Infinity) : Vector3 | null => {\n const equationParams: Matrix3 = [\n [equation1[0], equation1[1], equation1[2]],\n [equation2[0], equation2[1], equation2[2]],\n [equation3[0], equation3[1], equation3[2]],\n ];\n\n const inversed = m3Inverse(equationParams);\n if(inversed === null) return null; // no results\n\n const equationResults: Vector3 = [\n equation1[3],\n equation2[3],\n equation3[3]\n ];\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector3;\n};\n\n/**\n * System of N linear equations.\n */\nexport const linearEquationSystemN = (equations: Matrix, decimalPlaces = Infinity) : Vector | null => {\n if(equations.length <= 0) return null;\n\n const equationParams = mDelLastColumn(equations);\n\n const inversed = mInverse(equationParams);\n if(inversed === null) return null; // no results\n\n // the last column of the equations matrix\n const equationResults = mGetLastColumn(equations);\n\n return mMulVector(inversed, equationResults, decimalPlaces) as Vector;\n};\n\n/**\n * Calculate the equation of a line given two points in a 2D space.\n * y = ax + b\n * y - y1 = m(x - x1)\n * m = (y2 - y1) / (x2 - x1)\n */\nexport const getLinearEquationBy2Points = (point1: Vector2, point2: Vector2) : {\n slope: number|undefined,\n yIntercept: number|undefined,\n xIntercept: number|undefined,\n formula: string,\n} => {\n const [deltaX, deltaY] = v2Sub(point2, point1);\n const [x, y] = point1;\n\n if(deltaX === 0) {\n return {\n slope: undefined,\n xIntercept: x,\n yIntercept: undefined,\n formula: `x = ${ x }`,\n };\n }\n\n const m = deltaY / deltaX;\n const b = y - m * x;\n let formula = '';\n\n if(m === 0) {\n formula = `y = ${ b }`;\n }\n else{\n formula = `y = ${ m === 1 ? '' : m }x`;\n\n if(b !== 0) {\n formula += ` ${ b < 0 ? '-' : '+' } ${ Math.abs(b) }`;\n }\n }\n\n return {\n slope: m,\n xIntercept: undefined,\n yIntercept: b,\n formula,\n };\n};", "import { Vector } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport { linearEquation } from './linear-equations';\nimport { isNumber } from '../other';\n\n/**\n * Quadratic Equation.\n * ax^2 + bx + c = d\n */\nexport const quadraticEquation = (equation: Vector, decimalPlaces = Infinity) : Vector => {\n const a = equation[0];\n const b = equation[1];\n const c = equation[2];\n const d = equation[3];\n\n if(a === 0){\n // it's a linear equation -------------------------------------------\n const res = linearEquation([b, c, d], decimalPlaces);\n if(isNumber(res)) return [res];\n return [];\n }\n\n const diff = c - d;\n\n const discriminant = b * b - (4 * a * diff);\n\n if(discriminant < 0){\n return []; // no results\n }\n\n if(discriminant === 0){\n return [ setDecimalPlaces(-b / (2 * a), decimalPlaces) ]; // 1 result\n }\n\n // if(determinant > 0) ---> 2 results\n const t1 = 2 * a;\n const t2 = Math.sqrt(discriminant);\n\n return [\n setDecimalPlaces((-b + t2) / t1, decimalPlaces),\n setDecimalPlaces((-b - t2) / t1, decimalPlaces),\n ];\n};", "import { IBBox, Vector, Vector2, Vector3 } from '../../types';\nimport { setDecimalPlaces } from '../format';\nimport {\n dxV2CubicBezierCurve,\n dxV2QuadraticBezierCurve,\n dxV3CubicBezierCurve,\n dxV3QuadraticBezierCurve\n} from '../derivative';\nimport { v2Normalize, v3Normalize } from '../linear-algebra/vector';\nimport { linearEquation } from '../equations/linear-equations';\nimport { quadraticEquation } from '../equations/quadratic-equations';\nimport { isNumber } from '../other';\n\n/**\n * B\u00E9zier Curves\n * quadratic: y = P1 * (1-t)\u00B2 + P2 * 2 * (1-t)t + P3 * t\u00B2\n * t in range [0, 1]\n */\n\n// -------------------- GET POINT ON CURVE --------------------------\n\n/**\n * Get a point on a quadratic B\u00E9zier curve as a function of time.\n */\nexport const v2QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3QuadraticBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 2);\n const temp2 = (1 - t) * 2 * t;\n const temp3 = t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * centerControlPoint[0] + temp3 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * centerControlPoint[1] + temp3 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * centerControlPoint[2] + temp3 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n/**\n * Get a point on a cubic B\u00E9zier curve as a function of time.\n */\nexport const v2CubicBezierCurve = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n ];\n};\n\nexport const v3CubicBezierCurve = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n\n const temp1 = Math.pow(1 - t, 3);\n const temp2 = Math.pow(1 - t, 2) * 3 * t;\n const temp3 = (1 - t) * 3 * t * t;\n const temp4 = t * t * t;\n\n return [\n setDecimalPlaces(temp1 * startControlPoint[0] + temp2 * center1ControlPoint[0] + temp3 * center2ControlPoint[0] + temp4 * endControlPoint[0], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[1] + temp2 * center1ControlPoint[1] + temp3 * center2ControlPoint[1] + temp4 * endControlPoint[1], decimalPlaces),\n setDecimalPlaces(temp1 * startControlPoint[2] + temp2 * center1ControlPoint[2] + temp3 * center2ControlPoint[2] + temp4 * endControlPoint[2], decimalPlaces),\n ];\n};\n\n// -------------------- TANGENT --------------------------\n\n/**\n * Tangent indicates the direction of travel at specific points along the B\u00E9zier curve,\n * and is literally just the first derivative of our curve.\n */\nexport const v2QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3QuadraticBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n centerControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3QuadraticBezierCurve(t, startControlPoint, centerControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\nexport const v2CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n const dxVector = dxV2CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v2Normalize(dxVector, decimalPlaces);\n};\n\nexport const v3CubicBezierCurveTangent = (\n t: number,\n startControlPoint: Vector3,\n center1ControlPoint: Vector3,\n center2ControlPoint: Vector3,\n endControlPoint: Vector3,\n decimalPlaces = Infinity\n) : Vector3 => {\n const dxVector = dxV3CubicBezierCurve(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n return v3Normalize(dxVector, decimalPlaces);\n};\n\n// -------------------- NORMAL --------------------------\n\n/**\n * Normal is a vector that runs at a right angle to the direction of the curve, and is typically of length 1.\n * To find it, we take the normalised tangent vector, and then rotate it by a 90 degrees.\n */\nexport const v2QuadraticBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2QuadraticBezierCurveTangent(t, startControlPoint, centerControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\nexport const v2CubicBezierCurveNormal = (\n t: number,\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2 => {\n\n const tangent = v2CubicBezierCurveTangent(t, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint, decimalPlaces);\n return [-tangent[1], tangent[0]];\n};\n\n// -------------------- EXTREMA --------------------------\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2QuadraticBezierCurveExtrema = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector => {\n\n /*\n (-2 * (1 - t)) * startControlPoint[0] + (2 - 4 * t) * centerControlPoint[0] + (2 * t) * endControlPoint[0]\n 2 * t * startControlPoint[0] - 4 * t * centerControlPoint[0] + 2 * t * endControlPoint[0] - 2 * startControlPoint[0] + 2 * centerControlPoint[0]\n t * (2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0]) + (- 2 * startControlPoint[0] + 2 * centerControlPoint[0])\n */\n\n const a1 = 2 * startControlPoint[0] - 4 * centerControlPoint[0] + 2 * endControlPoint[0];\n const b1 = -2 * startControlPoint[0] + 2 * centerControlPoint[0];\n const equation1: Vector3 = [a1, b1, 0];\n const res1 = linearEquation(equation1, decimalPlaces);\n\n const a2 = 2 * startControlPoint[1] - 4 * centerControlPoint[1] + 2 * endControlPoint[1];\n const b2 = -2 * startControlPoint[1] + 2 * centerControlPoint[1];\n const equation2: Vector3 = [a2, b2, 0];\n const res2 = linearEquation(equation2, decimalPlaces);\n\n const res: Vector = [];\n\n if(isNumber(res1)){\n res.push(res1);\n }\n\n if(isNumber(res2)){\n res.push(res2);\n }\n\n return res;\n};\n\n/**\n * Find maxima and minima by solving the equation B'(t) = 0\n * Returns result in [0, 1] range.\n */\nexport const v2CubicBezierCurveExtrema = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : Vector2|null => {\n\n const a1 = -3 * startControlPoint[0] + 9 * center1ControlPoint[0] - 9 * center2ControlPoint[0] + 3 * endControlPoint[0];\n const b1 = 6 * startControlPoint[0] - 12 * center1ControlPoint[0] + 6 * center2ControlPoint[0];\n const c1 = -3 * startControlPoint[0] + 3 * center1ControlPoint[0];\n const equation1: Vector = [a1, b1, c1, 0];\n\n const a2 = -3 * startControlPoint[1] + 9 * center1ControlPoint[1] - 9 * center2ControlPoint[1] + 3 * endControlPoint[1];\n const b2 = 6 * startControlPoint[1] - 12 * center1ControlPoint[1] + 6 * center2ControlPoint[1];\n const c2 = -3 * startControlPoint[1] + 3 * center1ControlPoint[1];\n const equation2: Vector = [a2, b2, c2, 0];\n\n // Any value between 0 and 1 is a root that matters for B\u00E9zier curves, anything below or above that is irrelevant (because B\u00E9zier curves are only defined over the interval [0,1]).\n const res1 = quadraticEquation(equation1, decimalPlaces).filter(num => num >= 0 && num <= 1);\n const res2 = quadraticEquation(equation2, decimalPlaces).filter(num => num >= 0 && num <= 1);\n\n const res = [...res1, ...res2];\n if(res.length === 2){\n return [...res1, ...res2] as Vector2;\n }\n\n return null;\n};\n\n// -------------------- BOUNDING BOX --------------------------\n\nexport const v2QuadraticBezierBBox = (\n startControlPoint: Vector2,\n centerControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2QuadraticBezierCurveExtrema(startControlPoint, centerControlPoint, endControlPoint);\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2QuadraticBezierCurve(percent, startControlPoint, centerControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x);\n maxX = Math.max(maxX, x);\n\n minY = Math.min(minY, y);\n maxY = Math.max(maxY, y);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\nexport const v2CubicBezierBBox = (\n startControlPoint: Vector2,\n center1ControlPoint: Vector2,\n center2ControlPoint: Vector2,\n endControlPoint: Vector2,\n decimalPlaces = Infinity\n) : IBBox => {\n\n const extrema = v2CubicBezierCurveExtrema(startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint) || [];\n\n let minX = Infinity;\n let minY = Infinity;\n let maxX = -Infinity;\n let maxY = -Infinity;\n\n for(const percent of extrema){\n const point = v2CubicBezierCurve(percent, startControlPoint, center1ControlPoint, center2ControlPoint, endControlPoint);\n\n const x = point[0];\n const y = point[1];\n\n minX = Math.min(minX, x ?? Infinity);\n maxX = Math.max(maxX, x ?? -Infinity);\n\n minY = Math.min(minY, y ?? Infinity);\n maxY = Math.max(maxY, y ?? -Infinity);\n }\n\n minX = setDecimalPlaces(Math.min(minX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n maxX = setDecimalPlaces(Math.max(maxX, startControlPoint[0], endControlPoint[0]), decimalPlaces);\n minY = setDecimalPlaces(Math.min(minY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n maxY = setDecimalPlaces(Math.max(maxY, startControlPoint[1], endControlPoint[1]), decimalPlaces);\n\n return {\n x: minX,\n y: minY,\n w: Math.abs(maxX - minX),\n h: Math.abs(maxY - minY),\n x2: maxX,\n y2: maxY,\n }\n};\n\n\n", "import { Vector2 } from '../types';\nimport { v2Sub } from './linear-algebra/vector';\nimport { getV2Angle } from './angle';\nimport { convertRange } from './other';\n\n/**\n * Circle Equation\n * x^2 + y^2 = radius^2\n * ----------------------\n * Circle Parametric Equation\n * x(t) = radius * cos(t)\n * y(t) = radius * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const circleMovement = (center: Vector2, angle: number, radius: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius,\n center[1] + Math.sin(angle) * radius\n ];\n};\n\n/**\n * Circle Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const circleMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radius: number\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return circleMovement(center, angle, radius);\n};\n\n/**\n * Ellipse Equation\n * (x - centerX)^2 / (radius1^2) + (y - centerY)^2 / (radius2^2) = 1\n * -----------------------------------------------------------------\n * Ellipse Parametric Equation\n * x(t) = radius1 * cos(t)\n * y(t) = radius2 * sin(t)\n * t is the parameter = angle\n *\n * Angle should be in the range [0, Math.PI]\n */\nexport const ellipseMovement = (center: Vector2, angle: number, radius1: number, radius2: number): Vector2 => {\n angle = angle % Math.PI * 2;\n\n return [\n center[0] + Math.cos(angle) * radius1,\n center[1] + Math.sin(angle) * radius2\n ];\n};\n\n/**\n * Ellipse Movement After Mouse.\n * Mouse Positions:\n * - pageX/Y coordinates are relative to the top left corner of the whole rendered page (including parts hidden by scrolling),\n * - screenX and screenY: Relative to the top left of the physical screen/monitor, this reference point only moves if you increase or decrease the number of monitors or the monitor resolution.\n * - clientX/Y coordinates are relative to the top left corner of the visible part of the page, \"seen\" through browser window.\n * - offsetX and offsetY are relative to the parent container,\n */\nexport const ellipseMovementAfterMouse = (\n mouse: Vector2,\n center: Vector2,\n radii: Vector2\n): Vector2 => {\n\n const vector = v2Sub(mouse, center);\n\n let angle = getV2Angle(vector);\n\n // convert the angle from the range [0, Math.PI*2] to the range [0, Math.PI]\n angle = convertRange(angle, 0, Math.PI*2, 0, Math.PI);\n\n return ellipseMovement(center, angle, radii[0], radii[1]);\n};\n\n/**\n * Sine Wave Equation (Sinusoid)\n * -----------------------------\n * const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n * amplitude = the peak deviation of the function from zero\n * frequency = number of cycles\n * phase = specifies (in radians) where in its cycle the oscillation is at t = 0.\n * think of it as \"shifting\" the starting point of the function to the right (positive p) or left (negative)\n */\nexport const sineWaveMovement = (x: number, amplitude: number, frequency: number, phase: number) : Vector2 => {\n /*\n example values:\n const amplitude = 50;\n const frequency = 0.005;\n const phase = 0;\n x: [0, 1000]\n */\n const y = amplitude * Math.sin(2 * Math.PI * frequency * x + phase);\n\n return [x, y];\n};\n\n/**\n * Lissajous curve (Lissajous figure or Bowditch curve)\n * Parametric equation #1\n * f(t) = A * sin(k * t + m)\n * f(t) = B * sin(n * t)\n * 0 <= m <= PI/2\n * k, n >= 1\n * -----------------------\n * Parametric equation #2\n * f(t) = A * cos(k * t - m)\n * f(t) = B * cos(n * t - p)\n * -----------------------------\n * Shapes:\n * k = 1, n = 1, m = 0, p = 0 ---> line\n * A = B, k = 1, n = 1, m = PI/2, p = PI/2 ----> circle\n * A != B, k = 1, n = 1, m = PI/2, p = PI/2 ----> ellipse\n * k = 2, n = 2, m = PI/2, p = PI/2 ----> section of a parabola\n */\nexport const lissajousCurve = (\n width: number,\n height: number,\n t: number,\n k: number,\n n: number,\n m: number,\n p: number\n) :Vector2 => {\n return [\n width * Math.cos(k * t - m),\n height * Math.cos(n * t - p),\n ];\n};\n", "import { getRandom } from './random';\nimport { HSLColor, LABColor, RGBColor } from '../types';\nimport { mod } from './other';\nimport { setDecimalPlaces } from './format';\n\n// ------------------------ RANDOM COLOR -------------------------------------\n\nexport const getRandomRGBColor = () : RGBColor => {\n const hslColor = getRandomHSLColor();\n return hslToRgb(hslColor);\n};\n\nexport const getRandomHexColor = () : string => {\n const hslColor = getRandomHSLColor();\n return hslToHex(hslColor);\n};\n\nexport const getRandomHSLColor = () : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given hue\n */\nexport const getRandomHSLColorWithHue = (h: number) : HSLColor => {\n const s = getRandom(0, 100);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given saturation\n */\nexport const getRandomHSLColorWithSaturation = (s: number) : HSLColor => {\n const h = getRandom(1, 360);\n const l = getRandom(0, 100);\n return [h, s, l];\n};\n\n/**\n * generate random color with the given lightness\n */\nexport const getRandomHSLColorWithLightness = (l: number) : HSLColor => {\n const h = getRandom(1, 360);\n const s = getRandom(0, 100);\n return [h, s, l];\n};\n\nexport const getRandomGrayscaleHSLColor = () : HSLColor => {\n const l = getRandom(0, 100);\n return [0, 0, l];\n};\n\nexport const getRandomHSLColorWithinRanges = (\n hueStart = 1, hueEnd = 360,\n saturationStart = 0, saturationEnd = 100,\n lightStart = 0, lightEnd = 100\n) : HSLColor => {\n const h = getRandom(hueStart, hueEnd);\n const s = getRandom(saturationStart, saturationEnd);\n const l = getRandom(lightStart, lightEnd);\n return [h, s, l];\n};\n\n// ----------------------- CONVERT COLORS --------------------------------------\n\n/**\n * helper: convert hue value to degrees.\n * @param {number} h\n * @return {number} [0, 360] degrees\n */\nconst convertHueToDegrees = (h : number) : number => {\n\n // the hue value needs to be multiplied by 60 to convert it to degrees\n h *= 60;\n\n // if hue becomes negative, you need to add 360 to, because a circle has 360 degrees\n if(h < 0){\n h += 360;\n }\n\n return h;\n // convert huw to %\n // return h * 100 / 360;\n};\n\n/**\n * get hue from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] % - we use here % instead of [0, 359] degrees\n */\nconst getHue = (r : number, g : number, b : number, min : number | undefined = undefined, max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (max === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no hue, as it's gray\n if(min === max) return 0;\n\n const diff = max - min;\n\n let h = 0;\n\n // if red is max\n if(max === r){\n h = (g - b) / diff + (g < b ? 6 : 0);\n }\n\n // if green is max\n if(max === g){\n h = 2 + (b - r) / diff;\n }\n\n // if blue is max\n if(max === b){\n h = 4 + (r - g) / diff;\n }\n\n return convertHueToDegrees(h);\n};\n\n/**\n * get luminance from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @return {number} [0, 100] %\n */\nconst getLuminance = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // calculate the luminance value\n // @ts-ignore\n const l = (min + max) / 2; // [0, 1]\n\n // return l value in %\n return l * 100;\n};\n\n/**\n * get saturation from RGB\n * @param {number} r [0, 255]\n * @param {number} g [0, 255]\n * @param {number} b [0, 255]\n * @param {number|undefined=} min - min number of [r, g, b]\n * @param {number|undefined=} max - max number of [r, g, b]\n * @param {number|undefined=} l - luminance in [0, 100] %\n * @return {number} [0, 100] %\n */\nconst getSaturation = (\n r : number,\n g : number,\n b : number,\n min : number | undefined = undefined,\n max : number | undefined = undefined,\n l : number | undefined = undefined) : number => {\n\n // find the minimum and maximum values of r, g, and b if they are not provided\n min = (min === undefined) ? Math.min(r, g, b) : min;\n max = (min === undefined) ? Math.max(r, g, b) : max;\n\n // if the min and max value are the same -> no saturation, as it's gray\n if(min === max) return 0;\n\n // calculate luminance if it's not provided\n l = (l === undefined) ? getLuminance(r, g, b) : l;\n\n // check the level of luminance\n const s = (l <= 50) ?\n // @ts-ignore\n ((max - min) / (max + min)) : // this formula is used when luminance <= 50%\n // @ts-ignore\n (max - min) / (2.0 - max - min); // this formula is used when luminance > 50%\n\n // return saturation in %\n return s * 100;\n};\n\nexport const rgbToHsl = (rgb: RGBColor, decimalPlaces = Infinity): HSLColor => {\n\n // convert rgb values to the range [0, 1]\n const r = rgb[0] / 255;\n const g = rgb[1] / 255;\n const b = rgb[2] / 255;\n\n // find the minimum and maximum values of r, g, and b\n const min = Math.min(r, g, b);\n const max = Math.max(r, g, b);\n\n // calculate the luminance value in %\n const l = getLuminance(r, g, b, min, max);\n\n // calculate the saturation in %\n const s = getSaturation(r, g, b, min, max, l);\n\n // calculate the hue in % (not in degrees!)\n const h = getHue(r, g, b, min, max);\n\n if(h > 360 || s > 100 || l > 100){\n return [0, 0, 100];\n }\n\n if(h < 0 || s < 0 || l < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(h, decimalPlaces),\n setDecimalPlaces(s, decimalPlaces),\n setDecimalPlaces(l, decimalPlaces),\n ];\n};\n\n/**\n * helper: HSL to RGB\n */\nconst hslToRgbHelper = (helper1 : number, helper2 : number, colorHelper : number) : number => {\n\n // all values need to be between 0 and 1\n // if you get a negative value you need to add 1 to it\n if(colorHelper < 0) colorHelper += 1;\n\n // if you get a value above 1 you need to subtract 1 from it.\n if(colorHelper > 1) colorHelper -= 1;\n\n if(colorHelper * 6 < 1) return helper2 + (helper1 - helper2) * 6 * colorHelper;\n\n if(colorHelper * 2 < 1) return helper1;\n\n if(colorHelper * 3 < 2){\n return helper2 + (helper1 - helper2) * (0.666 - colorHelper) * 6;\n }\n else{\n return helper2;\n }\n};\n\nexport const hslToRgb = (hsl: HSLColor, decimalPlaces = Infinity): RGBColor => {\n\n // convert all values to [0, 1] from %\n const h = hsl[0] / 100;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n // if there is no saturation -> it\u2019s grey\n if(s === 0){\n // convert the luminance from [0, 1] to [0, 255]\n const gray = l * 255;\n return [gray, gray, gray];\n }\n\n // check the level of luminance\n const helper1 = (l < 0.5) ?\n (l * (1.0 + s)) :\n (l + s - l * s);\n\n const helper2 = 2 * l - helper1;\n\n const rHelper = h + 0.333;\n const gHelper = h;\n const bHelper = h - 0.333;\n\n let r = hslToRgbHelper(helper1, helper2, rHelper);\n let g = hslToRgbHelper(helper1, helper2, gHelper);\n let b = hslToRgbHelper(helper1, helper2, bHelper);\n\n // convert rgb to [0, 255]\n r *= 255;\n g *= 255;\n b *= 255;\n\n if(r > 255 || g > 255 || b > 255){\n return [255, 255, 255];\n }\n\n if(r < 0 || g < 0 || b < 0){\n return [0, 0, 0];\n }\n\n return [\n setDecimalPlaces(r, decimalPlaces),\n setDecimalPlaces(g, decimalPlaces),\n setDecimalPlaces(b, decimalPlaces),\n ];\n};\n\n/**\n * HSL to hex\n * hslToHex(360, 100, 50) // [360, 100, 5] ==> \"#ff0000\" (red)\n */\nexport const hslToHex = (hsl: HSLColor) => {\n\n if(hsl[0] > 360 || hsl[1] > 100 || hsl[2] > 100){\n return '#ffffff';\n }\n\n if(hsl[0] < 0 || hsl[1] < 0 || hsl[2] < 0){\n return '#000000';\n }\n\n const h = hsl[0] / 360;\n const s = hsl[1] / 100;\n const l = hsl[2] / 100;\n\n let r, g, b;\n if (s === 0) {\n r = g = b = l; // achromatic\n } else {\n const hue2rgb = (p: number, q: number, t: number) => {\n if (t < 0) t += 1;\n if (t > 1) t -= 1;\n if (t < 1 / 6) return p + (q - p) * 6 * t;\n if (t < 1 / 2) return q;\n if (t < 2 / 3) return p + (q - p) * (2 / 3 - t) * 6;\n return p;\n };\n const q = l < 0.5 ? l * (1 + s) : l + s - l * s;\n const p = 2 * l - q;\n r = hue2rgb(p, q, h + 1 / 3);\n g = hue2rgb(p, q, h);\n b = hue2rgb(p, q, h - 1 / 3);\n }\n const toHex = (x: number) => {\n const hex = Math.round(x * 255).toString(16);\n return hex.length === 1 ? '0' + hex : hex;\n };\n\n return `#${toHex(r)}${toHex(g)}${toHex(b)}`;\n};\n\n/**\n * RGB to HEX\n * rgbToHex([235, 64, 52]) // #eb4034\n */\nexport const rgbToHex = (rgb: RGBColor) => {\n const [r, g, b] = rgb;\n return '#' + (1 << 24 | r << 16 | g << 8 | b).toString(16).slice(1);\n};\n\nexport const hexToRgb = (hex: string) : RGBColor | null => {\n\n const shorthandRegex = /^#?([a-f\\d])([a-f\\d])([a-f\\d])$/i;\n const _hex = hex.replace(shorthandRegex, (_m, r, g, b) => {\n return r + r + g + g + b + b;\n });\n\n const result = /^#?([a-f\\d]{2})([a-f\\d]{2})([a-f\\d]{2})$/i.exec(_hex);\n if(!result) return null;\n\n const r = parseInt(result[1], 16);\n const g = parseInt(result[2], 16);\n const b = parseInt(result[3], 16);\n\n return [r, g, b];\n};\n\nexport const rgbToLab = (rgb: RGBColor, decimalPlaces = Infinity) : LABColor => {\n\n let r = rgb[0] / 255;\n let g = rgb[1] / 255;\n let b = rgb[2] / 255;\n\n r = (r > 0.04045) ? Math.pow((r + 0.055) / 1.055, 2.4) : r / 12.92;\n g = (g > 0.04045) ? Math.pow((g + 0.055) / 1.055, 2.4) : g / 12.92;\n b = (b > 0.04045) ? Math.pow((b + 0.055) / 1.055, 2.4) : b / 12.92;\n\n let x = (r * 0.4124 + g * 0.3576 + b * 0.1805) / 0.95047;\n let y = (r * 0.2126 + g * 0.7152 + b * 0.0722) / 1.00000;\n let z = (r * 0.0193 + g * 0.1192 + b * 0.9505) / 1.08883;\n\n x = (x > 0.008856) ? Math.pow(x, 1/3) : (7.787 * x) + 16/116;\n y = (y > 0.008856) ? Math.pow(y, 1/3) : (7.787 * y) + 16/116;\n z = (z > 0.008856) ? Math.pow(z, 1/3) : (7.787 * z) + 16/116;\n\n return [\n setDecimalPlaces((116 * y) - 16, decimalPlaces),\n setDecimalPlaces(500 * (x - y), decimalPlaces),\n setDecimalPlaces(200 * (y - z), decimalPlaces),\n ];\n};\n\nexport const labToRgb = (lab: LABColor, decimalPlaces = Infinity) : RGBColor => {\n let y = (lab[0] + 16) / 116;\n let x = lab[1] / 500 + y;\n let z = y - lab[2] / 200;\n\n x = 0.95047 * ((x * x * x > 0.008856) ? x * x * x : (x - 16/116) / 7.787);\n y = 1.00000 * ((y * y * y > 0.008856) ? y * y * y : (y - 16/116) / 7.787);\n z = 1.08883 * ((z * z * z > 0.008856) ? z * z * z : (z - 16/116) / 7.787);\n\n let r = x * 3.2406 + y * -1.5372 + z * -0.4986;\n let g = x * -0.9689 + y * 1.8758 + z * 0.0415;\n let b = x * 0.0557 + y * -0.2040 + z * 1.0570;\n\n r = (r > 0.0031308) ? (1.055 * Math.pow(r, 1/2.4) - 0.055) : 12.92 * r;\n g = (g > 0.0031308) ? (1.055 * Math.pow(g, 1/2.4) - 0.055) : 12.92 * g;\n b = (b > 0.0031308) ? (1.055 * Math.pow(b, 1/2.4) - 0.055) : 12.92 * b;\n\n return [\n setDecimalPlaces(Math.max(0, Math.min(1, r)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, g)) * 255, decimalPlaces),\n setDecimalPlaces(Math.max(0, Math.min(1, b)) * 255, decimalPlaces),\n ];\n};\n\n// ----------------------- GET SHIFTED COLORS --------------------------------------\n\nexport const getShiftedHue = (color: HSLColor, shift = 180) : HSLColor => {\n let hue = color[0];\n hue += shift;\n\n if (hue > 360 || hue < 0) {\n hue = mod(hue, 360);\n }\n\n return [hue, color[1], color[2]];\n};\n\nexport const getShiftedLightness = (color: HSLColor, shift = 10) : HSLColor => {\n let lightness = color[2];\n lightness += shift;\n\n if (lightness > 100 || lightness < 0) {\n lightness = mod(lightness, 100);\n }\n\n return [color[0], color[1], lightness];\n};\n\nexport const getShiftedSaturation = (color: HSLColor, shift = 10) : HSLColor => {\n let saturation = color[1];\n saturation += shift;\n\n if (saturation > 100) {\n saturation -= 100;\n }\n\n if(saturation < 0){\n saturation += 100;\n }\n\n return [color[0], saturation, color[2]];\n};\n\n// ----------------------- SIMILAR COLORS --------------------------------------\n\n/**\n * Measure the perceptual difference between two RGB colors using the CIE76 color difference formula:\n * delta = Math.sqrt((L2 - L1)^2 + (a2 - a1)^2 + (b2 - b1)^2)\n * https://en.wikipedia.org/wiki/Color_difference\n * https://stackoverflow.com/questions/13586999/color-difference-similarity-between-two-values-with-js\n * <= 1.0 Not perceptible by human eyes.\n * 1 - 2 Perceptible through close observation.\n * 2 - 10 Perceptible at a glance.\n * 11 - 49 Colors are more similar than opposite\n * 100 Colors are exact opposite\n */\nexport const getColorsDelta = (rgbA: RGBColor, rgbB: RGBColor, decimalPlaces = Infinity) => {\n const labA = rgbToLab(rgbA, decimalPlaces);\n const labB = rgbToLab(rgbB, decimalPlaces);\n\n // differences between the LAB components of the two colors\n const deltaL = labA[0] - labB[0];\n const deltaA = labA[1] - labB[1];\n const deltaB = labA[2] - labB[2];\n\n // chroma components\n const c1 = Math.sqrt(labA[1] * labA[1] + labA[2] * labA[2]);\n const c2 = Math.sqrt(labB[1] * labB[1] + labB[2] * labB[2]);\n const deltaC = c1 - c2;\n\n // difference in hue, deltaH, which takes into account both the differences\n // in the a* and b* components of LAB and the differences in chroma.\n let deltaH = deltaA * deltaA + deltaB * deltaB - deltaC * deltaC;\n deltaH = deltaH < 0 ? 0 : Math.sqrt(deltaH);\n\n const sc = 1.0 + 0.045 * c1;\n const sh = 1.0 + 0.015 * c1;\n\n // It applies weighting factors to the differences in lightness (deltaL),\n // chroma (deltaC), and hue (deltaH).\n const deltaLKlsl = deltaL / (1.0);\n const deltaCkcsc = deltaC / (sc);\n const deltaHkhsh = deltaH / (sh);\n\n // It computes the final color difference using the CIE76 formula:\n // deltaE = sqrt(deltaLKlsl^2 + deltaCkcsc^2 + deltaHkhsh^2),\n // where deltaLKlsl is the weighted lightness difference,\n // deltaCkcsc is the weighted chroma difference,\n // and deltaHkhsh is the weighted hue difference.\n const i = deltaLKlsl * deltaLKlsl + deltaCkcsc * deltaCkcsc + deltaHkhsh * deltaHkhsh;\n\n // It returns the calculated color difference,\n // optionally rounded to the specified number of decimal places.\n return i < 0 ? 0 : Math.sqrt(i);\n};\n", "/**\n * guid like '932ade5e-c515-4807-ac01-73b20ab3fb66'\n */\nexport const guid = () => {\n return 'xxxxxxxx-xxxx-4xxx-yxxx-xxxxxxxxxxxx'.replace(/[xy]/g, (c) => {\n const r = Math.random() * 16 | 0;\n return (c == 'x' ? r : r & 0x3 | 0x8).toString(16);\n });\n};\n\n/**\n * id like 'df4unio1opulby2uqh4'\n */\nexport const newId = () => {\n return Math.random().toString(36).substring(2) + (new Date()).getTime().toString(36);\n};\n", "import { ICircle, IPolygon, IRect, Matrix2, Vector2 } from '../types';\nimport { mod } from './other';\nimport { v2GetNormal, v2DotProduct } from './linear-algebra/vector';\n\n/**\n * Rectangles collision detection.\n * Rectangles should not be rotated.\n * The algorithm works by ensuring there is no gap between any of the 4 sides of the rectangles.\n * Any gap means a collision does not exist.\n * Returns true if collision is detected.\n */\nexport const rectCollide = (rect1: IRect, rect2: IRect) : boolean => {\n return rect1.x <= rect2.x + rect2.w &&\n rect1.x + rect1.w >= rect2.x &&\n rect1.y <= rect2.y + rect2.h &&\n rect1.h + rect1.y >= rect2.y;\n};\n\n/**\n * Circles collision detection.\n * This algorithm works by taking the center points of the two circles\n * and ensuring the distance between the center points\n * are less than the two radii added together.\n * Returns true if collision is detected.\n */\nexport const circleCollide = (circle1: ICircle, circle2: ICircle) => {\n const dx = Math.abs(circle1.cx - circle2.cx);\n const dy = Math.abs(circle1.cy - circle2.cy);\n const distance = Math.sqrt(dx * dx + dy * dy);\n return distance <= circle1.r + circle2.r;\n};\n\n//-------------------- Separating Axis Theorem (SAT) Collision detection -------------------------\n\nconst getEdges = (poly: IPolygon) : Matrix2[] => {\n const edges: Matrix2[] = [];\n\n for(let i= 0; i {\n const edges: Matrix2[] = [];\n\n // collect polygon edges, and combine then into a single array\n edges.push(...getEdges(poly1));\n edges.push(...getEdges(poly2));\n\n // for each edge, find the normal vector and project both polygons onto it\n for (const edge of edges) {\n const normal = v2GetNormal(edge[0], edge[1]);\n const p1Proj = projectPolygon(poly1, normal);\n const p2Proj = projectPolygon(poly2, normal);\n\n // Check if the projections overlap\n const isOverlap = p1Proj.max >= p2Proj.min && p2Proj.max >= p1Proj.min;\n\n // Check if the projections overlap; if not, the polygons do not collide\n if (!isOverlap) return false;\n }\n\n // If all tests pass, the polygons overlap and collide\n return true;\n};\n\n/**\n * Project every polygon point onto the normal.\n * Then find min and max.\n */\nconst projectPolygon = (polygon: IPolygon, normal: Vector2): { min: number, max: number } => {\n let min = Infinity;\n let max = -Infinity;\n\n // Project each vertex of the polygon onto the axis\n for (const vertex of polygon) {\n const projection = v2DotProduct(vertex, normal);\n min = Math.min(min, projection);\n max = Math.max(max, projection);\n }\n\n return { min, max };\n};", "export interface IAnimationProps {\n duration?: number;\n callback: (result: IAnimationResult) => void;\n restartOnResize?: boolean;\n resizeCallback?: (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => void;\n}\n\nexport interface IAnimationResult {\n start: () => void;\n stop: () => void;\n pause: () => void;\n resume: () => void;\n restart: () => void;\n isAnimating: () => boolean;\n getStartTime: () => number|undefined;\n getElapsedTime: () => number|undefined;\n getPercent: () => number|undefined;\n getResizeObserver: () => ResizeObserver|undefined;\n}\n\nexport const animate = (props: IAnimationProps) : IAnimationResult => {\n\n const _duration = props.duration !== undefined ? props.duration : Infinity;\n\n let startTime: number|undefined = undefined; // in milliseconds\n let animationId: number|undefined = undefined;\n\n // the time elapsed since the start of the animation (in milliseconds)\n let elapsed: number|undefined = undefined;\n let previousTimeStamp: number|undefined = undefined;\n\n let animating = false;\n let observer: ResizeObserver|undefined = undefined;\n\n // -------------------- COMMANDS ---------------------\n\n const stop = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = false;\n\n /*if(observer !== undefined){\n observer.disconnect();\n observer = undefined;\n }*/\n\n if(animationId === undefined) return;\n window.cancelAnimationFrame(animationId);\n };\n\n const restart = () => {\n stop();\n start();\n };\n\n const pause = () => {\n animating = false;\n };\n\n const resume = () => {\n animating = true;\n };\n\n /**\n * Animation Step.\n * @param {number} timeStamp in milliseconds\n */\n const step = (timeStamp: DOMHighResTimeStamp) => {\n\n if (startTime === undefined) {\n startTime = timeStamp;\n }\n\n // the time elapsed since the start of the animation (in milliseconds)\n elapsed = timeStamp - startTime;\n\n if (animating && previousTimeStamp !== timeStamp && typeof props.callback === 'function') {\n\n // do the rendering .............\n props.callback(getResult());\n }\n\n if(elapsed <= _duration){\n previousTimeStamp = timeStamp;\n animationId = window.requestAnimationFrame(step);\n }\n else{\n stop();\n }\n };\n\n const observerHandler = (_entries: ResizeObserverEntry[], _observer: ResizeObserver) => {\n restart();\n\n if(typeof props.resizeCallback === 'function'){\n props.resizeCallback(_entries, _observer);\n }\n };\n\n const start = () => {\n startTime = undefined;\n elapsed = undefined;\n previousTimeStamp = undefined;\n animating = true;\n\n if(props.restartOnResize && window.ResizeObserver && observer === undefined){\n observer = new ResizeObserver(observerHandler);\n observer.observe(document.body, { box: 'border-box' });\n }\n else{\n animationId = window.requestAnimationFrame(step);\n }\n };\n\n // --------------- GET INFO ----------------------\n\n /**\n * the time elapsed since the start of the animation (in milliseconds)\n */\n const getElapsedTime = () : number|undefined => {\n return elapsed;\n };\n\n const isAnimating = () => {\n return animating;\n };\n\n const getStartTime = () => {\n return startTime;\n };\n\n const getPercent = () => {\n if(_duration === Infinity || elapsed === undefined) return undefined;\n return elapsed * 100 / _duration;\n };\n\n const getResizeObserver = () => {\n return observer;\n };\n\n const getResult = () : IAnimationResult => {\n return {\n\n // commands --------------\n start,\n stop,\n pause,\n resume,\n restart,\n\n // information -------\n isAnimating,\n getElapsedTime,\n getStartTime,\n getPercent,\n getResizeObserver,\n };\n };\n\n return getResult();\n};\n", "import { setDecimalPlaces } from './format';\n\nexport const getCircleCircumference = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * radius, decimalPlaces);\n};\n\nexport const getEllipseCircumference = (radius1: number, radius2: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(2 * Math.PI * Math.sqrt((radius1 ** 2 + radius2 ** 2) / 2), decimalPlaces);\n};\n\nexport const isAngleInCircleArc = (startAngleDeg: number, endAngleDeg: number, currentDegrees: number) : boolean => {\n\n if(startAngleDeg > endAngleDeg) {\n endAngleDeg += 360;\n }\n\n return currentDegrees >= startAngleDeg && currentDegrees <= endAngleDeg ||\n (currentDegrees + 360) >= startAngleDeg && (currentDegrees + 360) <= endAngleDeg;\n};\n\n/**\n * get the side of a square inscribed in a circle\n */\nexport const getSquareInCircleSide = (radius: number, decimalPlaces = Infinity) => {\n return setDecimalPlaces(radius * 2 / Math.sqrt(2), decimalPlaces);\n};\n", "/**\n * 1 + 2 + ... + n = n * (n + 1) / 2\n */\nexport const naturalNumbersSequenceSum = (n: number) => {\n return n * (n + 1) / 2;\n};\n\n/**\n * n = the number of terms to be added\n * a = the first term in the sequence\n * d = the constant value between terms\n */\nexport const arithmeticSequenceSum = (n: number, a: number, d: number) => {\n return (n / 2) * (2 * a + (n - 1) * d);\n};", "import { setDecimalPlaces } from './format';\n\n// -------------------- CENTRAL TENDENCY ----------------------------\n\n/**\n * Central tendency: Calculate the Average (mean = \u03BC)\n * Sum of all numbers divided by the array length.\n */\nexport const getArithmeticMean = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const sum = data.reduce((acc, val) => acc + val, 0);\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Frequency map: number ---> it's frequency\n */\nexport const getArithmeticMeanFromFrequency = (frequencyMap: Map, decimalPlaces = Infinity) => {\n\n let mean = 0;\n\n for(const [val, frequency] of frequencyMap) {\n mean += val * frequency;\n }\n\n return setDecimalPlaces(mean, decimalPlaces);\n};\n\n/**\n * Central tendency: What is the central number in the sorted array?\n * Good for lists like [3, 3, 3, 3, 3, 3, 100] - 100 here is called \"Outlier\"\n */\nexport const getMedian = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const copy = [...data].sort((num1, num2) => num1 - num2);\n const mid = Math.floor(copy.length / 2);\n\n if(copy.length % 2 === 0) {\n return setDecimalPlaces((copy[mid] + copy[mid - 1]) / 2, decimalPlaces);\n }\n else {\n return setDecimalPlaces(copy[mid], decimalPlaces);\n }\n};\n\n/**\n * Central tendency: What number is most common in the set.\n * If all numbers have the same frequency, there is no mode.\n */\nexport const getMode = (data: number[]) : number[]|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n // Count frequency of each number in the data array.\n const frequencyMap: Map = new Map();\n for (const num of data) {\n frequencyMap.set(num, (frequencyMap.get(num) || 0) + 1);\n }\n\n let maxFrequency = 0;\n let modes: number[] = [];\n\n // Find the maximum frequency\n for (const [num, frequency] of frequencyMap) {\n if (frequency > maxFrequency) {\n maxFrequency = frequency;\n modes = [num];\n }\n else if (frequency === maxFrequency) {\n modes.push(num);\n }\n }\n\n // If all numbers have the same frequency, there is no mode\n if (modes.length === data.length) {\n return undefined;\n }\n\n // Return the mode(s)\n return modes.length === 1 ? [modes[0]] : modes;\n};\n\n/*\nTODO:\n- geometric mean\n- harmonic mean\n */\n\n// -------------------- DISPERSION ----------------------------\n\n/**\n * Dispersion: the average square distance from the mean.\n * Sum of (x - mean)^2 / N\n */\nexport const getVariance1 = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + ((val - mean) ** 2), 0);\n\n return setDecimalPlaces(sum / data.length, decimalPlaces);\n};\n\n/**\n * Another formula of dispersion - the average square distance from the mean.\n * (Sum of x^2) / N - (mean ^ 2)\n */\nexport const getVariance = (data: number[], decimalPlaces = Infinity) : number|undefined => {\n if(!data || data.length <= 0) return undefined;\n\n const mean = getArithmeticMean(data);\n if(mean === undefined) return undefined;\n\n const sum = data.reduce((acc, val) => acc + (val ** 2), 0);\n\n return setDecimalPlaces((sum / data.length) - (mean ** 2), decimalPlaces);\n};\n\n/**\n * \u03C3\n */\nexport const getStandardDeviation = (data: number[], decimalPlaces = Infinity) => {\n const variance = getVariance(data) ?? 0;\n return setDecimalPlaces(Math.sqrt(variance), decimalPlaces);\n};", "import { setDecimalPlaces } from './format';\nimport { getArithmeticMean, getStandardDeviation } from './statistics';\nimport { IMlNormalizeResult, IMlStandardizeResult } from '../types';\n\n// --------------------- NORMALIZE --------------------------------\n\n/**\n * Changes value to be in the range [0, 1].\n */\nexport const mlNormalizeValue = (value: number, min: number, max: number, decimalPlaces = Infinity) : number => {\n const diff = max - min;\n if(diff === 0) return 0;\n return setDecimalPlaces((value - min) / diff, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [0, 1].\n */\nexport const mlNormalizeArray = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n const copy = [...data];\n\n for(let i=0; i {\n const min = Math.min(...data);\n const max = Math.max(...data);\n const _data = mlNormalizeArray(data, min, max, decimalPlaces);\n\n return {\n min: setDecimalPlaces(min, decimalPlaces),\n max: setDecimalPlaces(max, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlNormalizeUnseenData = (data: number[], min: number, max: number, decimalPlaces = Infinity): number[] => {\n return mlNormalizeArray(data, min, max, decimalPlaces);\n};\n\n// --------------------- STANDARDIZE --------------------------------\n\n/**\n * Changes value to be in the range [-1, 1].\n */\nexport const mlStandardizeValue = (value: number, mean: number, stdDev: number, decimalPlaces = Infinity) : number => {\n if(stdDev === 0) return 0;\n return setDecimalPlaces((value - mean) / stdDev, decimalPlaces);\n};\n\n/**\n * Returns a copy of array, where each value will be in the range [-1, 1].\n */\nexport const mlStandardizeArray = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity) : number[] => {\n return [...data].map(value => mlStandardizeValue(value, mean, stdDev, decimalPlaces));\n};\n\nexport const mlStandardizeTestData = (data: number[], decimalPlaces = Infinity): IMlStandardizeResult => {\n const mean = getArithmeticMean(data) ?? 0;\n const stdDev = getStandardDeviation(data);\n const _data = mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n\n return {\n mean: setDecimalPlaces(mean, decimalPlaces),\n stdDev: setDecimalPlaces(stdDev, decimalPlaces),\n data: _data,\n };\n};\n\n/**\n * Alias.\n */\nexport const mlStandardizeUnseenData = (data: number[], mean: number, stdDev: number, decimalPlaces = Infinity): number[] => {\n return mlStandardizeArray(data, mean, stdDev, decimalPlaces);\n};", "/**\n * Sum of 1 to n numbers:\n * (n * (n + 1)) / 2\n */\nexport const naturalNumbersSum1ToN 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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -299,6 +299,6 @@ - + \ No newline at end of file diff --git a/docs/pages/angles-distance.html b/docs/pages/angles-distance.html index b8f7eebb..d1b8b4f8 100644 --- a/docs/pages/angles-distance.html +++ b/docs/pages/angles-distance.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -306,6 +306,6 @@

Angles Subtraction (Angular Distance)

- + \ No newline at end of file diff --git a/docs/pages/animation.html b/docs/pages/animation.html index cc3cca3b..294cb822 100644 --- a/docs/pages/animation.html +++ b/docs/pages/animation.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -333,6 +333,6 @@ - + \ No newline at end of file diff --git a/docs/pages/append-or-prepend-column.html b/docs/pages/append-or-prepend-column.html index 29ceaeac..03084370 100644 --- a/docs/pages/append-or-prepend-column.html +++ b/docs/pages/append-or-prepend-column.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -298,6 +298,6 @@ - + \ No newline at end of file diff --git a/docs/pages/append-or-prepend-row.html b/docs/pages/append-or-prepend-row.html index 754a09bc..fdd963a4 100644 --- a/docs/pages/append-or-prepend-row.html +++ b/docs/pages/append-or-prepend-row.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -347,6 +347,6 @@ - + \ No newline at end of file diff --git a/docs/pages/arithmetic-sequence-sum.html b/docs/pages/arithmetic-sequence-sum.html index cb54b472..d35072b9 100644 --- a/docs/pages/arithmetic-sequence-sum.html +++ b/docs/pages/arithmetic-sequence-sum.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -290,6 +290,6 @@ - + \ No newline at end of file diff --git a/docs/pages/bezier-curves.html b/docs/pages/bezier-curves.html index d07c6cd1..0d3ed632 100644 --- a/docs/pages/bezier-curves.html +++ b/docs/pages/bezier-curves.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -343,6 +343,6 @@ - + \ No newline at end of file diff --git a/docs/pages/bounding-box.html b/docs/pages/bounding-box.html index 00f9a523..d0c4126c 100644 --- a/docs/pages/bounding-box.html +++ b/docs/pages/bounding-box.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -316,6 +316,6 @@ - + \ No newline at end of file diff --git a/docs/pages/browser-usage.html b/docs/pages/browser-usage.html index 2a3cdf7c..ec3d1fd5 100644 --- a/docs/pages/browser-usage.html +++ b/docs/pages/browser-usage.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -289,6 +289,6 @@ - + \ No newline at end of file diff --git a/docs/pages/check-if-ranges-overlap.html b/docs/pages/check-if-ranges-overlap.html index 177ede41..36909b01 100644 --- a/docs/pages/check-if-ranges-overlap.html +++ b/docs/pages/check-if-ranges-overlap.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -284,6 +284,6 @@ - + \ No newline at end of file diff --git a/docs/pages/circle-movement.html b/docs/pages/circle-movement.html index 6507e151..361bf7d0 100644 --- a/docs/pages/circle-movement.html +++ b/docs/pages/circle-movement.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -293,6 +293,6 @@

Circle movement after mouse

- + \ No newline at end of file diff --git a/docs/pages/circles-collision.html b/docs/pages/circles-collision.html index da36d7c2..73838a92 100644 --- a/docs/pages/circles-collision.html +++ b/docs/pages/circles-collision.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -290,6 +290,6 @@ - + \ No newline at end of file diff --git a/docs/pages/circumference.html b/docs/pages/circumference.html index 24253c96..49f3cd70 100644 --- a/docs/pages/circumference.html +++ b/docs/pages/circumference.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -292,6 +292,6 @@ - + \ No newline at end of file diff --git a/docs/pages/color.html b/docs/pages/color.html index 2b2ea683..55a4566c 100644 --- a/docs/pages/color.html +++ b/docs/pages/color.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -288,6 +288,6 @@ - + \ No newline at end of file diff --git a/docs/pages/convert-colors.html b/docs/pages/convert-colors.html index 8ec03983..3536286a 100644 --- a/docs/pages/convert-colors.html +++ b/docs/pages/convert-colors.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -306,6 +306,6 @@ - + \ No newline at end of file diff --git a/docs/pages/convert-range.html b/docs/pages/convert-range.html index 14e3ea25..738cb5d9 100644 --- a/docs/pages/convert-range.html +++ b/docs/pages/convert-range.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -282,6 +282,6 @@ - + \ No newline at end of file diff --git a/docs/pages/convert-string-to-number.html b/docs/pages/convert-string-to-number.html index afa963de..6cd04ed8 100644 --- a/docs/pages/convert-string-to-number.html +++ b/docs/pages/convert-string-to-number.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -284,6 +284,6 @@ - + \ No newline at end of file diff --git a/docs/pages/convex-polygons-collision.html b/docs/pages/convex-polygons-collision.html index e1c4bf55..84de5a7b 100644 --- a/docs/pages/convex-polygons-collision.html +++ b/docs/pages/convex-polygons-collision.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -286,6 +286,6 @@ - + \ No newline at end of file diff --git a/docs/pages/cross-product.html b/docs/pages/cross-product.html index d34d0104..5769ac59 100644 --- a/docs/pages/cross-product.html +++ b/docs/pages/cross-product.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -287,6 +287,6 @@ - + \ No newline at end of file diff --git a/docs/pages/degrees-and-radians.html b/docs/pages/degrees-and-radians.html index 16b05db8..dee30942 100644 --- a/docs/pages/degrees-and-radians.html +++ b/docs/pages/degrees-and-radians.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -288,6 +288,6 @@

Radians to degrees

- + \ No newline at end of file diff --git a/docs/pages/distance-between-vectors.html b/docs/pages/distance-between-vectors.html index 98b69aab..3913d9a3 100644 --- a/docs/pages/distance-between-vectors.html +++ b/docs/pages/distance-between-vectors.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -295,6 +295,6 @@ - + \ No newline at end of file diff --git a/docs/pages/divide-by-scalar.html b/docs/pages/divide-by-scalar.html index dc8382a1..400a6321 100644 --- a/docs/pages/divide-by-scalar.html +++ b/docs/pages/divide-by-scalar.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -351,6 +351,6 @@ - + \ No newline at end of file diff --git a/docs/pages/divide-vector-by-scalar.html b/docs/pages/divide-vector-by-scalar.html index 7bbce3fa..f82a3e93 100644 --- a/docs/pages/divide-vector-by-scalar.html +++ b/docs/pages/divide-vector-by-scalar.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -296,6 +296,6 @@ - + \ No newline at end of file diff --git a/docs/pages/dot-product.html b/docs/pages/dot-product.html index 96eb4a68..3ebcd475 100644 --- a/docs/pages/dot-product.html +++ b/docs/pages/dot-product.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -291,6 +291,6 @@ - + \ No newline at end of file diff --git a/docs/pages/ellipse-movement.html b/docs/pages/ellipse-movement.html index 7ed1110e..b7cde41c 100644 --- a/docs/pages/ellipse-movement.html +++ b/docs/pages/ellipse-movement.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -293,6 +293,6 @@

Ellipse movement after mouse

- + \ No newline at end of file diff --git a/docs/pages/extrema.html b/docs/pages/extrema.html index aa082423..5b8116a4 100644 --- a/docs/pages/extrema.html +++ b/docs/pages/extrema.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -307,6 +307,6 @@ - + \ No newline at end of file diff --git a/docs/pages/general-case.html b/docs/pages/general-case.html index 4218177c..5357624d 100644 --- a/docs/pages/general-case.html +++ b/docs/pages/general-case.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -286,6 +286,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-animation-data.html b/docs/pages/get-animation-data.html index 6b5f320e..31f63d7d 100644 --- a/docs/pages/get-animation-data.html +++ b/docs/pages/get-animation-data.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -290,6 +290,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-column.html b/docs/pages/get-column.html index d96410d6..6254eb6c 100644 --- a/docs/pages/get-column.html +++ b/docs/pages/get-column.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -289,6 +289,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-linear-equation-by-2-points.html b/docs/pages/get-linear-equation-by-2-points.html index cc11c8a6..d9e3c9f5 100644 --- a/docs/pages/get-linear-equation-by-2-points.html +++ b/docs/pages/get-linear-equation-by-2-points.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -326,6 +326,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-matrix-minor.html b/docs/pages/get-matrix-minor.html index f374a1bf..8bfee0e2 100644 --- a/docs/pages/get-matrix-minor.html +++ b/docs/pages/get-matrix-minor.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -288,6 +288,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-normal.html b/docs/pages/get-normal.html index 930dd9e8..7b045a72 100644 --- a/docs/pages/get-normal.html +++ b/docs/pages/get-normal.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -284,6 +284,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-point-on-cubic-bezier-curve.html b/docs/pages/get-point-on-cubic-bezier-curve.html index e8c87132..be1b00f4 100644 --- a/docs/pages/get-point-on-cubic-bezier-curve.html +++ b/docs/pages/get-point-on-cubic-bezier-curve.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -340,6 +340,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-point-on-quadratic-bezier-curve.html b/docs/pages/get-point-on-quadratic-bezier-curve.html index d666dace..4ec0f2a6 100644 --- a/docs/pages/get-point-on-quadratic-bezier-curve.html +++ b/docs/pages/get-point-on-quadratic-bezier-curve.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -334,6 +334,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-random-boolean.html b/docs/pages/get-random-boolean.html index 1fbb2c29..50e8437b 100644 --- a/docs/pages/get-random-boolean.html +++ b/docs/pages/get-random-boolean.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -280,6 +280,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-random-integer.html b/docs/pages/get-random-integer.html index 4aef7009..7322c902 100644 --- a/docs/pages/get-random-integer.html +++ b/docs/pages/get-random-integer.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -281,6 +281,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-random-item-from-array.html b/docs/pages/get-random-item-from-array.html index 85cf08fd..a1d3f31f 100644 --- a/docs/pages/get-random-item-from-array.html +++ b/docs/pages/get-random-item-from-array.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -282,6 +282,6 @@ - + \ No newline at end of file diff --git a/docs/pages/get-random-number-in-range.html b/docs/pages/get-random-number-in-range.html index 238c2f26..f97c4e62 100644 --- a/docs/pages/get-random-number-in-range.html +++ b/docs/pages/get-random-number-in-range.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -282,6 +282,6 @@ - + \ No newline at end of file diff --git a/docs/pages/inverse-matrix.html b/docs/pages/inverse-matrix.html index 10c6ffe1..0dbe8f97 100644 --- a/docs/pages/inverse-matrix.html +++ b/docs/pages/inverse-matrix.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -329,6 +329,6 @@ - + \ No newline at end of file diff --git a/docs/pages/is-angle-between.html b/docs/pages/is-angle-between.html index 176e2e1c..d6f5b730 100644 --- a/docs/pages/is-angle-between.html +++ b/docs/pages/is-angle-between.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -282,6 +282,6 @@ - + \ No newline at end of file diff --git a/docs/pages/is-angle-in-circle-arc.html b/docs/pages/is-angle-in-circle-arc.html index 53d77f14..3ee6f8a5 100644 --- a/docs/pages/is-angle-in-circle-arc.html +++ b/docs/pages/is-angle-in-circle-arc.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -292,6 +292,6 @@ - + \ No newline at end of file diff --git a/docs/pages/is-clockwise.html b/docs/pages/is-clockwise.html index e7f3a8a2..8c66273a 100644 --- a/docs/pages/is-clockwise.html +++ b/docs/pages/is-clockwise.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -290,6 +290,6 @@ - + \ No newline at end of file diff --git a/docs/pages/lerp.html b/docs/pages/lerp.html index 62e68720..6f95d332 100644 --- a/docs/pages/lerp.html +++ b/docs/pages/lerp.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -361,6 +361,6 @@ - + \ No newline at end of file diff --git a/docs/pages/linear-equation.html b/docs/pages/linear-equation.html index faa2466d..6ca402d0 100644 --- a/docs/pages/linear-equation.html +++ b/docs/pages/linear-equation.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -284,6 +284,6 @@ - + \ No newline at end of file diff --git a/docs/pages/lissajous-curve.html b/docs/pages/lissajous-curve.html index 7c4f454a..2583ca2f 100644 --- a/docs/pages/lissajous-curve.html +++ b/docs/pages/lissajous-curve.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -305,6 +305,6 @@ - + \ No newline at end of file diff --git a/docs/pages/matrix-deep-copy.html b/docs/pages/matrix-deep-copy.html index e1761ea8..297cee1f 100644 --- a/docs/pages/matrix-deep-copy.html +++ b/docs/pages/matrix-deep-copy.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -308,6 +308,6 @@ - + \ No newline at end of file diff --git a/docs/pages/matrix-equality.html b/docs/pages/matrix-equality.html index 2795c480..0468a9d7 100644 --- a/docs/pages/matrix-equality.html +++ b/docs/pages/matrix-equality.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -380,6 +380,6 @@

Identity Matrix

- + \ No newline at end of file diff --git a/docs/pages/matrix-multiplication.html b/docs/pages/matrix-multiplication.html index 3791c59d..f4754cdd 100644 --- a/docs/pages/matrix-multiplication.html +++ b/docs/pages/matrix-multiplication.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -319,6 +319,6 @@ - + \ No newline at end of file diff --git a/docs/pages/matrix-singularity.html b/docs/pages/matrix-singularity.html index 1b342d46..75ab5233 100644 --- a/docs/pages/matrix-singularity.html +++ b/docs/pages/matrix-singularity.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -294,6 +294,6 @@ - + \ No newline at end of file diff --git a/docs/pages/matrix-subtraction.html b/docs/pages/matrix-subtraction.html index 4f4382d3..45a0c3fc 100644 --- a/docs/pages/matrix-subtraction.html +++ b/docs/pages/matrix-subtraction.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -338,6 +338,6 @@ - + \ No newline at end of file diff --git a/docs/pages/matrix-sum.html b/docs/pages/matrix-sum.html index 0f7d103f..2c038765 100644 --- a/docs/pages/matrix-sum.html +++ b/docs/pages/matrix-sum.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -338,6 +338,6 @@ - + \ No newline at end of file diff --git a/docs/pages/matrix-to-CSS-transform.html b/docs/pages/matrix-to-CSS-transform.html index b8542d28..f159259f 100644 --- a/docs/pages/matrix-to-CSS-transform.html +++ b/docs/pages/matrix-to-CSS-transform.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -330,6 +330,6 @@ - + \ No newline at end of file diff --git a/docs/pages/matrix-transposition.html b/docs/pages/matrix-transposition.html index bc16fa4a..3a1d9494 100644 --- a/docs/pages/matrix-transposition.html +++ b/docs/pages/matrix-transposition.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -357,6 +357,6 @@ - + \ No newline at end of file diff --git a/docs/pages/modulo.html b/docs/pages/modulo.html index a09f7ca0..31f9651f 100644 --- a/docs/pages/modulo.html +++ b/docs/pages/modulo.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -282,6 +282,6 @@ - + \ No newline at end of file diff --git a/docs/pages/multiply-by-scalar.html b/docs/pages/multiply-by-scalar.html index af252368..0d6ac296 100644 --- a/docs/pages/multiply-by-scalar.html +++ b/docs/pages/multiply-by-scalar.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
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Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -288,6 +288,6 @@ - + \ No newline at end of file diff --git a/docs/pages/multiply-vector-by-scalar.html b/docs/pages/multiply-vector-by-scalar.html index e6d47e88..d6996523 100644 --- a/docs/pages/multiply-vector-by-scalar.html +++ b/docs/pages/multiply-vector-by-scalar.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -296,6 +296,6 @@ - + \ No newline at end of file diff --git a/docs/pages/natural-numbers-sequence-sum.html b/docs/pages/natural-numbers-sequence-sum.html index 66c00f15..9f936ff8 100644 --- a/docs/pages/natural-numbers-sequence-sum.html +++ b/docs/pages/natural-numbers-sequence-sum.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -280,6 +280,6 @@ - + \ No newline at end of file diff --git a/docs/pages/nodejs-usage.html b/docs/pages/nodejs-usage.html index 05d6265d..8ff5ef45 100644 --- a/docs/pages/nodejs-usage.html +++ b/docs/pages/nodejs-usage.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -286,6 +286,6 @@ - + \ No newline at end of file diff --git a/docs/pages/normal.html b/docs/pages/normal.html index d38de630..de4ff66a 100644 --- a/docs/pages/normal.html +++ b/docs/pages/normal.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -311,6 +311,6 @@ - + \ No newline at end of file diff --git a/docs/pages/normalize-vector.html b/docs/pages/normalize-vector.html index cb787415..44fc06e7 100644 --- a/docs/pages/normalize-vector.html +++ b/docs/pages/normalize-vector.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -291,6 +291,6 @@ - + \ No newline at end of file diff --git a/docs/pages/percent-to-angle.html b/docs/pages/percent-to-angle.html index 9263e97f..a38cf0fb 100644 --- a/docs/pages/percent-to-angle.html +++ b/docs/pages/percent-to-angle.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -291,6 +291,6 @@ - + \ No newline at end of file diff --git a/docs/pages/polar-to-cartesian.html b/docs/pages/polar-to-cartesian.html index 91eaa629..92d5af23 100644 --- a/docs/pages/polar-to-cartesian.html +++ b/docs/pages/polar-to-cartesian.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -285,6 +285,6 @@ - + \ No newline at end of file diff --git a/docs/pages/polynomial.html b/docs/pages/polynomial.html index f7483cbf..4feebbd7 100644 --- a/docs/pages/polynomial.html +++ b/docs/pages/polynomial.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -289,6 +289,6 @@ - + \ No newline at end of file diff --git a/docs/pages/quadratic-equation.html b/docs/pages/quadratic-equation.html index 7aa2ec01..07b75520 100644 --- a/docs/pages/quadratic-equation.html +++ b/docs/pages/quadratic-equation.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -306,6 +306,6 @@ - + \ No newline at end of file diff --git a/docs/pages/random-color.html b/docs/pages/random-color.html index 3e9a26e0..9f5d5ab9 100644 --- a/docs/pages/random-color.html +++ b/docs/pages/random-color.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -312,6 +312,6 @@ - + \ No newline at end of file diff --git a/docs/pages/random-id-or-GUID.html b/docs/pages/random-id-or-GUID.html index de397519..272134fc 100644 --- a/docs/pages/random-id-or-GUID.html +++ b/docs/pages/random-id-or-GUID.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -281,6 +281,6 @@ - + \ No newline at end of file diff --git a/docs/pages/rectangles-collision.html b/docs/pages/rectangles-collision.html index f60721a0..5ecddde5 100644 --- a/docs/pages/rectangles-collision.html +++ b/docs/pages/rectangles-collision.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -291,6 +291,6 @@ - + \ No newline at end of file diff --git a/docs/pages/reflection-matrix.html b/docs/pages/reflection-matrix.html index 0d9a918f..5280ecf1 100644 --- a/docs/pages/reflection-matrix.html +++ b/docs/pages/reflection-matrix.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -454,6 +454,6 @@ - + \ No newline at end of file diff --git a/docs/pages/remove-row-or-column.html b/docs/pages/remove-row-or-column.html index c41446d1..acdf6703 100644 --- a/docs/pages/remove-row-or-column.html +++ b/docs/pages/remove-row-or-column.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -335,6 +335,6 @@ - + \ No newline at end of file diff --git a/docs/pages/reset-matrix.html b/docs/pages/reset-matrix.html index 8d39d337..ac6607b5 100644 --- a/docs/pages/reset-matrix.html +++ b/docs/pages/reset-matrix.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -365,6 +365,6 @@ - + \ No newline at end of file diff --git a/docs/pages/rotate-around-point.html b/docs/pages/rotate-around-point.html index 2553377f..680cd379 100644 --- a/docs/pages/rotate-around-point.html +++ b/docs/pages/rotate-around-point.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -303,6 +303,6 @@ - + \ No newline at end of file diff --git a/docs/pages/rotation-matrix.html b/docs/pages/rotation-matrix.html index 5b862fbb..86f520d1 100644 --- a/docs/pages/rotation-matrix.html +++ b/docs/pages/rotation-matrix.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -387,6 +387,6 @@ - + \ No newline at end of file diff --git a/docs/pages/scale-and-stretch-matrix.html b/docs/pages/scale-and-stretch-matrix.html index 1c8fc78d..6be6a690 100644 --- a/docs/pages/scale-and-stretch-matrix.html +++ b/docs/pages/scale-and-stretch-matrix.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -436,6 +436,6 @@ - + \ No newline at end of file diff --git a/docs/pages/scale-around-point.html b/docs/pages/scale-around-point.html index 5e5c89be..126a772e 100644 --- a/docs/pages/scale-around-point.html +++ b/docs/pages/scale-around-point.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -299,6 +299,6 @@ - + \ No newline at end of file diff --git a/docs/pages/series.html b/docs/pages/series.html new file mode 100644 index 00000000..b6067e9c --- /dev/null +++ b/docs/pages/series.html @@ -0,0 +1,275 @@ + + + + mzMath Documentation + + + + + + + + + + + + + + + + + + + + +
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+ +
+ + + + + + + mzMath on GitHub + +
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+
+ +
+
+ + + + +
+ Main + + + + + +
Typescript UsageBrowser UsageNode.js Usage
+ Vectors + + + + + +
VectorsVectors SumVectors SubtractionMultiply by ScalarDivide by ScalarVector LengthNormalized (Unit) VectorDot ProductCross ProductDistance Between VectorsVector InitializationVectors EqualityGet Normal
+ Matrix + + + + + +
MatrixMatrix SumMatrix SubtractionMultiply By ScalarDivide By ScalarMatrix TranspositionMatrix MultiplicationMultiply Matrix By VectorMatrix DeterminantInverse MatrixMatrix SingularityAdjugate MatrixGet Matrix Minor
+ Matrix Manipulation + + + + + +
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+ Transformation Matrices + + + + + +
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Natural Numbers Sequence SumArithmetic Sequence Sum
+ Other + + + + + +
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
+
+
+ +
+

Series

+
import { naturalNumbersSum1ToN } from 'mz-math';
+
+// 1 + 2 + 3
+const sum = naturalNumbersSum1ToN(3); // 6;
+
import { naturalNumbersSumMToN } from 'mz-math';
+
+// 5 + 6 + 7
+const sum = naturalNumbersSumMToN(5, 7); // 18
+
+ +
+
+ + + + + + +
+
Previous
+ Temperature Conversion +
+
+
+
+ +
+
+ + + + \ No newline at end of file diff --git a/docs/pages/set-decimal-places.html b/docs/pages/set-decimal-places.html index f559d318..2d4b4818 100644 --- a/docs/pages/set-decimal-places.html +++ b/docs/pages/set-decimal-places.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -285,6 +285,6 @@ - + \ No newline at end of file diff --git a/docs/pages/shearing-matrix.html b/docs/pages/shearing-matrix.html index 347839db..2e935992 100644 --- a/docs/pages/shearing-matrix.html +++ b/docs/pages/shearing-matrix.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -299,6 +299,6 @@ - + \ No newline at end of file diff --git a/docs/pages/shift-colors.html b/docs/pages/shift-colors.html index 02586244..48d437b7 100644 --- a/docs/pages/shift-colors.html +++ b/docs/pages/shift-colors.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -287,6 +287,6 @@ - + \ No newline at end of file diff --git a/docs/pages/similar-colors.html b/docs/pages/similar-colors.html index 0a88cd5c..2a9051cc 100644 --- a/docs/pages/similar-colors.html +++ b/docs/pages/similar-colors.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -318,6 +318,6 @@ - + \ No newline at end of file diff --git a/docs/pages/sine-wave-movement.html b/docs/pages/sine-wave-movement.html index 068c9cf4..5e985dee 100644 --- a/docs/pages/sine-wave-movement.html +++ b/docs/pages/sine-wave-movement.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -285,6 +285,6 @@ - + \ No newline at end of file diff --git a/docs/pages/square-in-circle.html b/docs/pages/square-in-circle.html index 18e1a82f..4bf63a60 100644 --- a/docs/pages/square-in-circle.html +++ b/docs/pages/square-in-circle.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -284,6 +284,6 @@ - + \ No newline at end of file diff --git a/docs/pages/system-of-linear-equations.html b/docs/pages/system-of-linear-equations.html index 0c36340c..a394e16b 100644 --- a/docs/pages/system-of-linear-equations.html +++ b/docs/pages/system-of-linear-equations.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -326,6 +326,6 @@ - + \ No newline at end of file diff --git a/docs/pages/tangent.html b/docs/pages/tangent.html index bd69cbd6..2048acf2 100644 --- a/docs/pages/tangent.html +++ b/docs/pages/tangent.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -345,6 +345,6 @@ - + \ No newline at end of file diff --git a/docs/pages/temperature-conversion.html b/docs/pages/temperature-conversion.html index 46d5d5dd..135ea7ed 100644 --- a/docs/pages/temperature-conversion.html +++ b/docs/pages/temperature-conversion.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -264,7 +264,7 @@ const fahrenheit = kelvinToFahrenheit(273.15); // 32 -
+
@@ -277,12 +277,27 @@ Polar To Cartesian
+ +
+ +
+
Next
+ Series +
+ + + + + + + +
- + \ No newline at end of file diff --git a/docs/pages/translation-matrix.html b/docs/pages/translation-matrix.html index ee188d4a..cbabe981 100644 --- a/docs/pages/translation-matrix.html +++ b/docs/pages/translation-matrix.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -328,6 +328,6 @@ - + \ No newline at end of file diff --git a/docs/pages/trigonometric-functions.html b/docs/pages/trigonometric-functions.html index a97ee250..13f71114 100644 --- a/docs/pages/trigonometric-functions.html +++ b/docs/pages/trigonometric-functions.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -317,6 +317,6 @@ - + \ No newline at end of file diff --git a/docs/pages/typescript-usage.html b/docs/pages/typescript-usage.html index 5bd58c07..f9106fd5 100644 --- a/docs/pages/typescript-usage.html +++ b/docs/pages/typescript-usage.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -274,6 +274,6 @@ - + \ No newline at end of file diff --git a/docs/pages/vector-angle.html b/docs/pages/vector-angle.html index 1957694e..775d0dd5 100644 --- a/docs/pages/vector-angle.html +++ b/docs/pages/vector-angle.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -296,6 +296,6 @@

getV2AngleInEllipse()

- + \ No newline at end of file diff --git a/docs/pages/vector-initialization.html b/docs/pages/vector-initialization.html index 487f98af..f35d9d26 100644 --- a/docs/pages/vector-initialization.html +++ b/docs/pages/vector-initialization.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -297,6 +297,6 @@ - + \ No newline at end of file diff --git a/docs/pages/vector-length.html b/docs/pages/vector-length.html index d021badc..ede10913 100644 --- a/docs/pages/vector-length.html +++ b/docs/pages/vector-length.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -297,6 +297,6 @@

Set Vector Length

- + \ No newline at end of file diff --git a/docs/pages/vectors-equality.html b/docs/pages/vectors-equality.html index 7bfe072d..46b98047 100644 --- a/docs/pages/vectors-equality.html +++ b/docs/pages/vectors-equality.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -283,6 +283,6 @@ - + \ No newline at end of file diff --git a/docs/pages/vectors-subtraction.html b/docs/pages/vectors-subtraction.html index 9323d6f5..2bb25692 100644 --- a/docs/pages/vectors-subtraction.html +++ b/docs/pages/vectors-subtraction.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -300,6 +300,6 @@ - + \ No newline at end of file diff --git a/docs/pages/vectors-sum.html b/docs/pages/vectors-sum.html index d341ec82..5e7a7503 100644 --- a/docs/pages/vectors-sum.html +++ b/docs/pages/vectors-sum.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -300,6 +300,6 @@ - + \ No newline at end of file diff --git a/docs/pages/vectors.html b/docs/pages/vectors.html index 53d939e4..02ef61cf 100644 --- a/docs/pages/vectors.html +++ b/docs/pages/vectors.html @@ -16,8 +16,8 @@ - - + + @@ -235,7 +235,7 @@ -
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature Conversion
+
Set Decimal PlacesConvert String To NumberSquare In CircleModuloConvert RangeCheck If Ranges OverlapCheck If Value Is NumberPolar To CartesianTemperature ConversionSeries
@@ -287,6 +287,6 @@ - + \ No newline at end of file diff --git a/docs/sitemap.txt b/docs/sitemap.txt index 44eb1584..2bde69fc 100644 --- a/docs/sitemap.txt +++ b/docs/sitemap.txt @@ -98,3 +98,4 @@ https://math.mzsoft.org/pages/check-if-ranges-overlap.html https://math.mzsoft.org/pages/check-if-value-is-number.html https://math.mzsoft.org/pages/polar-to-cartesian.html https://math.mzsoft.org/pages/temperature-conversion.html +https://math.mzsoft.org/pages/series.html diff --git a/package.json b/package.json index d544af30..4a1cd875 100644 --- a/package.json +++ b/package.json @@ -1,6 +1,6 @@ { "name": "mz-math", - "version": "3.0.24", + "version": "3.0.25", "description": "mzMath - a collection of TypeScript-based math helpers.", "main": "./dist/mz-math.min.js", "module": "./dist/mz-math.esm.js", diff --git a/src/docs/data/pages/1000-other/10-series.md b/src/docs/data/pages/1000-other/10-series.md new file mode 100644 index 00000000..f98a48e1 --- /dev/null +++ b/src/docs/data/pages/1000-other/10-series.md @@ -0,0 +1,15 @@ +# Series + +```js +import { naturalNumbersSum1ToN } from 'mz-math'; + +// 1 + 2 + 3 +const sum = naturalNumbersSum1ToN(3); // 6; +``` + +```js +import { naturalNumbersSumMToN } from 'mz-math'; + +// 5 + 6 + 7 +const sum = naturalNumbersSumMToN(5, 7); // 18 +``` diff --git a/src/index-esm.ts b/src/index-esm.ts index a892ad09..ec2f722d 100644 --- a/src/index-esm.ts +++ b/src/index-esm.ts @@ -18,4 +18,5 @@ export * from './main/animation'; export * from './main/circle-ellipse'; export * from './main/sequence'; export * from './main/statistics'; -export * from './main/ml'; \ No newline at end of file +export * from './main/ml'; +export * from './main/series'; \ No newline at end of file diff --git a/src/index.ts b/src/index.ts index 40d5dc2d..f87037c8 100644 --- a/src/index.ts +++ b/src/index.ts @@ -19,6 +19,7 @@ import * as circleEllipse from './main/circle-ellipse'; import * as sequence from './main/sequence'; import * as statistics from './main/statistics'; import * as ml from './main/ml'; +import * as series from './main/series'; const api = { ...vector, @@ -42,6 +43,7 @@ const api = { ...sequence, ...statistics, ...ml, + ...series, }; declare global { @@ -72,4 +74,5 @@ export * from './main/animation'; export * from './main/circle-ellipse'; export * from './main/sequence'; export * from './main/statistics'; -export * from './main/ml'; \ No newline at end of file +export * from './main/ml'; +export * from './main/series'; \ No newline at end of file diff --git a/src/main/series.ts b/src/main/series.ts new file mode 100644 index 00000000..41729b73 --- /dev/null +++ b/src/main/series.ts @@ -0,0 +1,14 @@ +/** + * Sum of 1 to n numbers: + * (n * (n + 1)) / 2 + */ +export const naturalNumbersSum1ToN = (n: number): number => { + return (n / 2) * (n + 1); +}; + +/** + * Sum of m to n numbers. + */ +export const naturalNumbersSumMToN = (m: number, n: number): number => { + return (n - m + 1) * (m + n) / 2; +}; \ No newline at end of file diff --git a/test/series.test.ts b/test/series.test.ts new file mode 100644 index 00000000..b002f71f --- /dev/null +++ b/test/series.test.ts @@ -0,0 +1,31 @@ +import { + naturalNumbersSum1ToN, + naturalNumbersSumMToN, +} from '../src/main/series'; + +describe('Series', () => { + + describe('naturalNumbersSum1ToN()', () => { + test('1', () => { + expect(naturalNumbersSum1ToN(1)).toStrictEqual(1); + }); + + test('2', () => { + expect(naturalNumbersSum1ToN(2)).toStrictEqual(3); + }); + + test('3', () => { + expect(naturalNumbersSum1ToN(3)).toStrictEqual(6); + }); + }); + + describe('naturalNumbersSumMToN()', () => { + test('1, 1', () => { + expect(naturalNumbersSumMToN(1,1)).toStrictEqual(1); + }); + + test('5, 7', () => { + expect(naturalNumbersSumMToN(5,7)).toStrictEqual(18); + }); + }); +}); \ No newline at end of file