From ee451640b2e98f4b220054089423645e4d1b72a9 Mon Sep 17 00:00:00 2001 From: kjerandp Date: Mon, 18 Sep 2023 14:30:51 +0200 Subject: [PATCH] Added function to CurveInterpolator for returning Frenet-frames + a few fixes --- .vscode/settings.json | 5 + docs/assets/search.js | 2 +- docs/classes/CurveInterpolator.html | 245 ++++++++++++------ docs/classes/LinearCurveMapper.html | 52 ++-- docs/classes/NumericalCurveMapper.html | 62 ++--- docs/classes/Point.html | 30 +-- .../_internal_.AbstractCurveMapper.html | 48 ++-- docs/functions/add.html | 104 ++++++++ docs/functions/binarySearch.html | 7 +- docs/functions/calcKnotSequence.html | 7 +- docs/functions/calculateCoefficients.html | 7 +- docs/functions/clamp.html | 7 +- docs/functions/copyValues.html | 7 +- docs/functions/cross.html | 7 +- docs/functions/derivativeAtT.html | 7 +- docs/functions/distance.html | 7 +- docs/functions/dot.html | 7 +- docs/functions/evaluateForT.html | 7 +- docs/functions/extrapolateControlPoint.html | 7 +- docs/functions/fill.html | 7 +- docs/functions/findRootsOfT.html | 7 +- docs/functions/getControlPoints.html | 7 +- docs/functions/getCubicRoots.html | 7 +- docs/functions/getQuadRoots.html | 7 +- docs/functions/getSegmentIndexAndT.html | 7 +- docs/functions/magnitude.html | 7 +- docs/functions/map.html | 7 +- docs/functions/normalize.html | 7 +- docs/functions/orthogonal.html | 7 +- docs/functions/reduce.html | 7 +- docs/functions/rotate3d.html | 108 ++++++++ docs/functions/secondDerivativeAtT.html | 7 +- docs/functions/simplify2d.html | 7 +- docs/functions/sub.html | 104 ++++++++ docs/functions/sumOfSquares.html | 7 +- docs/functions/valueAtT.html | 7 +- docs/interfaces/_internal_.BBox.html | 6 +- .../_internal_.CurveInterpolatorOptions.html | 16 +- docs/interfaces/_internal_.CurveMapper.html | 22 +- .../_internal_.CurveParameters.html | 6 +- .../_internal_.SplineCurveOptions.html | 8 +- docs/interfaces/_internal_.VectorType.html | 20 +- docs/modules.html | 5 +- docs/types/_internal_.NumArray4.html | 2 +- docs/types/_internal_.SegmentFunction.html | 2 +- docs/types/_internal_.Vector.html | 2 +- docs/variables/EPS.html | 7 +- package.json | 2 +- src/core/interfaces.ts | 2 +- src/core/math.spec.ts | 8 + src/core/math.ts | 67 ++++- src/curve-interpolator.spec.ts | 31 +++ src/curve-interpolator.ts | 103 +++++++- 53 files changed, 958 insertions(+), 293 deletions(-) create mode 100644 .vscode/settings.json create mode 100644 docs/functions/add.html create mode 100644 docs/functions/rotate3d.html create mode 100644 docs/functions/sub.html diff --git a/.vscode/settings.json b/.vscode/settings.json new file mode 100644 index 0000000..e715fdf --- /dev/null +++ b/.vscode/settings.json @@ -0,0 +1,5 @@ +{ + "cSpell.words": [ + "binormals" + ] +} \ No newline at end of file diff --git a/docs/assets/search.js b/docs/assets/search.js index c543457..f38e974 100644 --- a/docs/assets/search.js +++ b/docs/assets/search.js @@ -1 +1 @@ -window.searchData = 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\ No newline at end of file diff --git a/docs/classes/CurveInterpolator.html b/docs/classes/CurveInterpolator.html index cb029cc..b160a93 100644 --- a/docs/classes/CurveInterpolator.html +++ b/docs/classes/CurveInterpolator.html @@ -23,7 +23,7 @@

Hierarchy

  • CurveInterpolator
+
  • Defined in curve-interpolator.ts:38
    • @@ -62,6 +62,7 @@

    Methods

    getCurvatureAt getCurvatureAtTime getDerivativeAt +getFrenetFrames getIntersects getIntersectsAsPositions getIntersectsAsTime @@ -106,24 +107,24 @@
    options:

    Returns CurveInterpolator

    +
  • Defined in curve-interpolator.ts:48

    • Properties

    _cache

    _cache: Map<string, object> = ...
    +
  • Defined in curve-interpolator.ts:41

    • _curveMapper

    _curveMapper: CurveMapper
    +
  • Defined in curve-interpolator.ts:40

    • _lmargin

    _lmargin: number
    +
  • Defined in curve-interpolator.ts:39

    • Accessors

    @@ -133,7 +134,7 @@

    alpha

    Returns number

     +
  • Defined in curve-interpolator.ts:762
  • set alpha(a: number): void
  • @@ -143,7 +144,7 @@

    Parameters

    a: number

    • Returns void

    +
  • Defined in curve-interpolator.ts:764

    • closed

  • set closed(isClosed: boolean): void
  • @@ -161,7 +162,7 @@

    Parameters

    isClosed: boolean

    • Returns void

    +
  • Defined in curve-interpolator.ts:768

    • length

    +
  • Defined in curve-interpolator.ts:770

    • maxX

    +
  • Defined in curve-interpolator.ts:779

    • maxY

    +
  • Defined in curve-interpolator.ts:789

    • maxZ

    +
  • Defined in curve-interpolator.ts:799

    • minX

    +
  • Defined in curve-interpolator.ts:774

    • minY

    +
  • Defined in curve-interpolator.ts:784

    • minZ

    +
  • Defined in curve-interpolator.ts:794

    • points

  • set points(pts: Vector[]): void
  • @@ -235,7 +236,7 @@

    Parameters

    pts: Vector[]

    • Returns void

    +
  • Defined in curve-interpolator.ts:756

    • tension

  • set tension(t: number): void
  • @@ -253,7 +254,7 @@

    Parameters

    t: number

    • Returns void

    +
  • Defined in curve-interpolator.ts:760

    • Methods

    @@ -265,38 +266,63 @@

    Private

    Returns CurveInterpolator

    +
  • Defined in curve-interpolator.ts:742

    • createLookupTable

      - +

    • Create and cache a lookup table of n=samples points, indexed by position (u)

      Returns

      Map of positions -> points

      +
      +

      Type Parameters

      +
        +
      • +

        T

      +
      +

      Parameters

      +
        +
      • +
        func: ((u: number) => T)
        +

        function generating lookup table value

        +
        +
          +
        • +
            +
          • (u: number): T
            • +

          • Parameters

            • +
              u: number
            +

            Returns T

        • +
      • samples: number

        number of samples (segments)

      • -
        from: number = 0
        -

        start at position

        -
        • -
      • -
        to: number = 1
        -

        end at position

        -
      -

      Returns Map<number, Vector>

    +

    Returns Map<number, T>

    +
  • Defined in curve-interpolator.ts:606

    • forEach

  • samples: number | number[]

    number of (evenly spaced) samples OR an array of user specified positions (u)

    @@ -336,7 +367,7 @@
    to: numberReturns void
    • +
  • Defined in curve-interpolator.ts:646

    • getBoundingBox

    +
  • Defined in curve-interpolator.ts:388

    • getCurvatureAt

      @@ -388,7 +419,7 @@
      radius:
      tangent: Vector
    +
  • Defined in curve-interpolator.ts:307

    • getCurvatureAtTime

      @@ -418,7 +449,7 @@
      radius:
      tangent: Vector
    +
  • Defined in curve-interpolator.ts:319

    • getDerivativeAt

      @@ -444,7 +475,7 @@
      target: T

    Returns T

    +
  • Defined in curve-interpolator.ts:361
  • @@ -454,7 +485,36 @@

    Parameters

    position: number

    • Returns Vector

    +
  • Defined in curve-interpolator.ts:362
    • +
    +

    getFrenetFrames

    +
      + +
    • +

      Calculate the Frenet-Serret frames for a 3d curve, using the concept of parallel transport. +The implementation used here is basically a copy of the function used in THREE.js (https://github.com/mrdoob/three.js), +which in turn is based on the the paper "Parallel Transport Approach to Curve Framing" by Hanson and Ma +(https://legacy.cs.indiana.edu/ftp/techreports/TR425.pdf)

      + +

      Returns

      object containing arrays for tangents, normals and binormals

      +
      +
      +

      Parameters

      +
        +
      • +
        segments: number
        +

        number of samples (segments) along the curve (will return segments + 1 frames)

        +
      +

      Returns {
          binormals: Vector[];
          normals: Vector[];
          tangents: Vector[];
      }

      +

    getIntersects

      @@ -487,7 +547,7 @@
      max: numbernumber = ...

    Returns Vector | Vector[]

    +
  • Defined in curve-interpolator.ts:541

    • getIntersectsAsPositions

      @@ -514,7 +574,7 @@
      max: numbernumber = ...

    Returns number[]

    +
  • Defined in curve-interpolator.ts:552

    • getIntersectsAsTime

      @@ -541,7 +601,7 @@
      max: numbernumber = ...

    Returns number[]

    +
  • Defined in curve-interpolator.ts:562

    • getLengthAt

      @@ -561,11 +621,11 @@
      position: numberboolean = false

    Returns number

    +
  • Defined in curve-interpolator.ts:103

    • getNearestPosition

      - +

    • Get the nearest position on the curve from a point. This is an approximation and its accuracy is determined by the threshold value (smaller number requires more passes but is more precise)

      @@ -582,7 +642,9 @@
      point:
      threshold: number = 0.00001

      Precision

      -
    + +
  • +
    Optional samples: number

    • Returns {
        distance: number;
        point:     Vector;
        u: number;
    }

    +
  • Defined in curve-interpolator.ts:480

    • getNormalAt

      @@ -619,7 +681,7 @@
      target: T

    Returns T

    +
  • Defined in curve-interpolator.ts:191
  • @@ -629,7 +691,7 @@

    Parameters

    position: number

    • Returns Vector

    +
  • Defined in curve-interpolator.ts:192

    • getNormalAtTime

      @@ -656,7 +718,7 @@
      target: T

    Returns T

    +
  • Defined in curve-interpolator.ts:204
  • @@ -666,7 +728,7 @@

    Parameters

    t: number

    • Returns Vector

    +
  • Defined in curve-interpolator.ts:205

    • getPointAt

      @@ -692,7 +754,7 @@
      target: T

    Returns T

    +
  • Defined in curve-interpolator.ts:155
  • @@ -702,7 +764,7 @@

    Parameters

    position: number

    • Returns Vector

    +
  • Defined in curve-interpolator.ts:156

    • getPointAtTime

    +
  • Defined in curve-interpolator.ts:140

    • getPoints

      @@ -760,7 +822,7 @@
      returnType: (Returns T

    Returns T[]

    +
  • Defined in curve-interpolator.ts:453
  • @@ -785,7 +847,7 @@

    Returns from: number

    • Returns T[]

    +
  • Defined in curve-interpolator.ts:454
  • @@ -812,12 +874,12 @@
    from: number
    • to: number

    Returns T[]

    +
  • Defined in curve-interpolator.ts:455

  • Returns any

    • +
  • Defined in curve-interpolator.ts:456
  • @@ -827,7 +889,7 @@

    Parameters

    segments: number

    • Returns any

    +
  • Defined in curve-interpolator.ts:457
  • @@ -843,7 +905,7 @@
    from: number
    • to: number

    Returns Vector[]

    +
  • Defined in curve-interpolator.ts:458

    • getPositionAtKnot

      @@ -862,7 +924,7 @@
      index: number

    Returns number

    +
  • Defined in curve-interpolator.ts:127

    • getPositionFromLength

    +
  • Defined in curve-interpolator.ts:93

    • getPositionFromTime

    +
  • Defined in curve-interpolator.ts:83

    • getSecondDerivativeAt

      @@ -932,7 +994,7 @@
      target: T

    Returns T

    +
  • Defined in curve-interpolator.ts:374
  • @@ -942,7 +1004,7 @@

    Parameters

    position: number

    • Returns Vector

    +
  • Defined in curve-interpolator.ts:375

    • getTangentAt

      @@ -968,7 +1030,7 @@
      target: T

    Returns T

    +
  • Defined in curve-interpolator.ts:166
  • @@ -978,7 +1040,7 @@

    Parameters

    position: number

    • Returns Vector

    +
  • Defined in curve-interpolator.ts:167

    • getTangentAtTime

      @@ -1004,7 +1066,7 @@
      target: T

    Returns T

    +
  • Defined in curve-interpolator.ts:178
  • @@ -1014,7 +1076,7 @@

    Parameters

    t: number

    • Returns Vector

    +
  • Defined in curve-interpolator.ts:179

    • getTimeAtKnot

      @@ -1033,7 +1095,7 @@
      index: number

    Returns number

    +
  • Defined in curve-interpolator.ts:112

    • getTimeFromPosition

    +
  • Defined in curve-interpolator.ts:73

    • map

      - +

    • Convenience function for returning multiple values for a set of samples along the curve. The map function takes a user defined mapping function, which will be called for each position @@ -1066,24 +1128,29 @@

      map +

      Type Parameters

      +
        +
      • +

        T

    Parameters

    • -
      func: ((__namedParameters: Object) => unknown)
      +
      func: ((__namedParameters: Object) => T)

      mapping function

        • -
        • (__namedParameters: Object): unknown
          • +
        • (__namedParameters: Object): T

        • Parameters

          • __namedParameters: Object
          -

          Returns unknown

      • +

      Returns T

  • samples: number | number[]

    number of (evenly spaced) samples OR an array of user specified positions (u)

    @@ -1096,13 +1163,13 @@
    from: numbernumber = 1

    to position

    • -

    Returns unknown[]

    reduce

      - +

    • Convenience function for reducing multiple values for a set of samples along the curve. This function takes a user defined reduce function, which will be called for each position @@ -1110,26 +1177,31 @@

      reduce +

      Type Parameters

      +
        +
      • +

        T

    Parameters

    • -
      func: ((__namedParameters: Object) => unknown)
      +
      func: ((__namedParameters: Object) => T)

      reduce function

        • -
        • (__namedParameters: Object): unknown
          • +
        • (__namedParameters: Object): T

        • Parameters

          • __namedParameters: Object
          -

          Returns unknown

      • +

      Returns T

  • -
    initialValue: unknown
    +
    initialValue: T

    initial accumulator value

  • @@ -1144,9 +1216,9 @@
    from: numbernumber = 1

    to position

    • -

    Returns unknown[]

    reset

    +
  • Defined in curve-interpolator.ts:750
    • @@ -1205,6 +1277,7 @@

    getCurvatureAt
  • getCurvatureAtTime
  • getDerivativeAt
    • +
  • getFrenetFrames
  • getIntersects
  • getIntersectsAsPositions
  • getIntersectsAsTime
    • diff --git a/docs/classes/LinearCurveMapper.html b/docs/classes/LinearCurveMapper.html index 131c53d..4c18c86 100644 --- a/docs/classes/LinearCurveMapper.html +++ b/docs/classes/LinearCurveMapper.html @@ -27,7 +27,7 @@

    Hierarchy

    • LinearCurveMapper
    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:12
    • @@ -93,7 +93,7 @@

    Returns voidReturns LinearCurveMapper

    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:21

    • Properties

    @@ -101,19 +101,19 @@

    _alpha_alpha: number = 0.0

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:19

    • _cache

    _cache: object
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:17

    • _closed

    _closed: boolean = false
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:21

    • _onInvalidateCache

    _onInvalidateCache: (() => void) = null
    @@ -127,25 +127,25 @@

    Type declaration

    Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:22

    • _points

    _points: Vector[]
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:18

    • _subDivisions

    _subDivisions: number
    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:14

    • _tension

    _tension: number = 0.5
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:20

    • Accessors

    @@ -158,7 +158,7 @@

    alphaReturns number

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:61
  • set alpha(alpha: number): void
  • @@ -169,7 +169,7 @@
    alpha: number

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:62

    • arcLengths

    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:26

    • closed

  • set closed(closed: boolean): void
  • @@ -199,7 +199,7 @@
    closed: boolean

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:94

    • points

  • set points(points: Vector[]): void
  • @@ -221,7 +221,7 @@
    points: Returns void
    • +
  • Defined in curve-mappers/abstract-curve-mapper.ts:84

    • tension

  • set tension(tension: number): void
  • @@ -243,7 +243,7 @@
    tension: number

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:73

    • Methods

    @@ -256,7 +256,7 @@

    _invalidateCacheReturns void

    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:36

    • computeArcLengths

    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:45

    • evaluateForT

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:112

    • getCoefficients

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:124

    • getT

    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:76

    • getU

    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:103

    • lengthAt

    +
  • Defined in curve-mappers/segmented-curve-mapper.ts:66

    • reset

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:102
    • diff --git a/docs/classes/NumericalCurveMapper.html b/docs/classes/NumericalCurveMapper.html index 4e38b69..dd12852 100644 --- a/docs/classes/NumericalCurveMapper.html +++ b/docs/classes/NumericalCurveMapper.html @@ -29,7 +29,7 @@

    Hierarchy

    • NumericalCurveMapper
    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:24
    • @@ -104,7 +104,7 @@

    Returns voidReturns NumericalCurveMapper

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:34

    • Properties

    @@ -112,29 +112,29 @@

    _alpha_alpha: number = 0.0

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:19

    • _cache

    _cache: object
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:17

    • _closed

    _closed: boolean = false
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:21

    • _gauss

    _gauss: number[][]
    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:26

    • _nSamples

    _nSamples: number = 21
    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:25

    • _onInvalidateCache

    _onInvalidateCache: (() => void) = null
    @@ -148,25 +148,25 @@

    Type declaration

    Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:22

    • _points

    _points: Vector[]
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:18

    • _subDivisions

    _subDivisions: number
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:16

    • _tension

    _tension: number = 0.5
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:20

    • Accessors

    @@ -179,7 +179,7 @@

    alphaReturns number

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:61
  • set alpha(alpha: number): void
  • @@ -190,7 +190,7 @@
    alpha: number

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:62

    • arcLengths

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:49

    • closed

  • set closed(closed: boolean): void
  • @@ -220,7 +220,7 @@
    closed: boolean

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:94

    • points

  • set points(points: Vector[]): void
  • @@ -242,7 +242,7 @@
    points: Returns void
    • +
  • Defined in curve-mappers/abstract-curve-mapper.ts:84

    • tension

  • set tension(tension: number): void
  • @@ -264,7 +264,7 @@
    tension: number

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:73

    • Methods

    @@ -277,7 +277,7 @@

    _invalidateCacheReturns void

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:43

    • computeArcLength

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:117

    • computeArcLengths

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:138

    • evaluateForT

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:112

    • getCoefficients

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:124

    • getSamples

      @@ -384,7 +384,7 @@
      idx: number

    Returns [number[], number[], number[], number[]]

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:62

    • getT

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:201

    • getU

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:222

    • inverse

      @@ -447,7 +447,7 @@
      len: number

    Returns number

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:159

    • lengthAt

    +
  • Defined in curve-mappers/numerical-curve-mapper.ts:192

    • reset

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:102
    • diff --git a/docs/classes/Point.html b/docs/classes/Point.html index 1407f81..604f7ad 100644 --- a/docs/classes/Point.html +++ b/docs/classes/Point.html @@ -29,7 +29,7 @@

    Hierarchy

    • Point
    +
  • Defined in core/point.ts:6
    • @@ -74,29 +74,29 @@
    z: numbernumber = null

    Returns Point

    +
  • Defined in core/point.ts:12

    • Properties

    Optional w

    w?: number
    +
  • Defined in core/point.ts:10

    • x

    x: number
    +
  • Defined in core/point.ts:7

    • y

    y: number
    +
  • Defined in core/point.ts:8

    • Optional z

    z?: number
    +
  • Defined in core/point.ts:9

    • Accessors

    @@ -106,7 +106,7 @@

    0

    Returns number

     +
  • Defined in core/point.ts:19
  • set 0(x: number): void
  • @@ -116,7 +116,7 @@

    Parameters

    x: number

    • Returns void

    +
  • Defined in core/point.ts:23

    • 1

  • set 1(y: number): void
  • @@ -134,7 +134,7 @@

    Parameters

    y: number

    • Returns void

    +
  • Defined in core/point.ts:31

    • 2

  • set 2(z: number): void
  • @@ -152,7 +152,7 @@

    Parameters

    z: number

    • Returns void

    +
  • Defined in core/point.ts:39

    • 3

  • set 3(w: number): void
  • @@ -170,7 +170,7 @@

    Parameters

    w: number

    • Returns void

    +
  • Defined in core/point.ts:47

    • length

    +
  • Defined in core/point.ts:51
    • diff --git a/docs/classes/_internal_.AbstractCurveMapper.html b/docs/classes/_internal_.AbstractCurveMapper.html index 3a846ff..0907ce4 100644 --- a/docs/classes/_internal_.AbstractCurveMapper.html +++ b/docs/classes/_internal_.AbstractCurveMapper.html @@ -37,7 +37,7 @@

    Implements

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:15
    • @@ -98,24 +98,24 @@
    onInvalidateCache: (Returns void

    Returns AbstractCurveMapper

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:28

    • Properties

    _alpha

    _alpha: number = 0.0
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:19

    • _cache

    _cache: object
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:17

    • _closed

    _closed: boolean = false
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:21

    • _onInvalidateCache

    _onInvalidateCache: (() => void) = null
    @@ -128,22 +128,22 @@

    Type declaration

  • Returns void

    • +
  • Defined in curve-mappers/abstract-curve-mapper.ts:22

    • _points

    _points: Vector[]
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:18

    • _subDivisions

    _subDivisions: number
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:16

    • _tension

    _tension: number = 0.5
    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:20

    • Accessors

    @@ -156,7 +156,7 @@

    alphaReturns number

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:61
  • set alpha(alpha: number): void
  • @@ -167,7 +167,7 @@
    alpha: number

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:62

    • closed

  • set closed(closed: boolean): void
  • @@ -189,7 +189,7 @@
    closed: boolean

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:94

    • points

  • set points(points: Vector[]): void
  • @@ -211,7 +211,7 @@
    points: Returns void
    • +
  • Defined in curve-mappers/abstract-curve-mapper.ts:84

    • tension

  • set tension(tension: number): void
  • @@ -233,7 +233,7 @@
    tension: number

    • Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:73

    • Methods

    @@ -247,7 +247,7 @@

    Returns

    void

    Returns void

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:40

    • evaluateForT

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:112

    • getCoefficients

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:124

    • Abstract getT

      @@ -308,7 +308,7 @@
      u: number

    Returns number

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:55

    • Abstract getU

      @@ -322,7 +322,7 @@
      t: number

    Returns number

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:56

    • Abstract lengthAt

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:54

    • reset

    +
  • Defined in curve-mappers/abstract-curve-mapper.ts:102
    • diff --git a/docs/functions/add.html b/docs/functions/add.html new file mode 100644 index 0000000..d215913 --- /dev/null +++ b/docs/functions/add.html @@ -0,0 +1,104 @@ +add | curve-interpolator
    +
    + +
    +
    +
    +
    + +

    Function add

    +
    +
    +
    +
    +
    +

    Settings

     +
    +
    +

    Member Visibility

    +
      +
      • +
      • +
      • +
    +
    +

    Theme

    + +
    +
    +

    Generated using TypeDoc

    +
    \ No newline at end of file diff --git a/docs/functions/binarySearch.html b/docs/functions/binarySearch.html index b322694..c3652ad 100644 --- a/docs/functions/binarySearch.html +++ b/docs/functions/binarySearch.html @@ -35,7 +35,7 @@
    accumulatedValues: number

    Returns number

    +
  • Defined in core/utils.ts:112
    • @@ -65,7 +65,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -87,8 +88,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/calcKnotSequence.html b/docs/functions/calcKnotSequence.html index 29ef92a..4275868 100644 --- a/docs/functions/calcKnotSequence.html +++ b/docs/functions/calcKnotSequence.html @@ -51,7 +51,7 @@
    alpha: numberReturns NumArray4
    +
  • Defined in core/spline-segment.ts:19
    • @@ -81,7 +81,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -103,8 +104,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/calculateCoefficients.html b/docs/functions/calculateCoefficients.html index c0f6185..f3d7f3f 100644 --- a/docs/functions/calculateCoefficients.html +++ b/docs/functions/calculateCoefficients.html @@ -48,7 +48,7 @@
    options: Returns NumArray4[]
    +
  • Defined in core/spline-segment.ts:40
    • @@ -78,7 +78,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -100,8 +101,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/clamp.html b/docs/functions/clamp.html index f0a6ada..f9011ef 100644 --- a/docs/functions/clamp.html +++ b/docs/functions/clamp.html @@ -38,7 +38,7 @@
    max: numberReturns number
    +
  • Defined in core/utils.ts:100
    • @@ -68,7 +68,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -90,8 +91,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/copyValues.html b/docs/functions/copyValues.html index 0371475..8c5a8cc 100644 --- a/docs/functions/copyValues.html +++ b/docs/functions/copyValues.html @@ -36,7 +36,7 @@
    Optional target: Returns Vector
    +
  • Defined in core/utils.ts:46
    • @@ -66,7 +66,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -88,8 +89,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/cross.html b/docs/functions/cross.html index 854ff02..31ab60b 100644 --- a/docs/functions/cross.html +++ b/docs/functions/cross.html @@ -41,7 +41,7 @@
    Optional target: Returns Vector
    +
  • Defined in core/math.ts:103
    • @@ -71,7 +71,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -93,8 +94,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/derivativeAtT.html b/docs/functions/derivativeAtT.html index 42370dd..2ec2c71 100644 --- a/docs/functions/derivativeAtT.html +++ b/docs/functions/derivativeAtT.html @@ -36,7 +36,7 @@
    coefficients: Returns number
    +
  • Defined in core/spline-segment.ts:92
    • @@ -66,7 +66,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -88,8 +89,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/distance.html b/docs/functions/distance.html index 0225295..c1235fe 100644 --- a/docs/functions/distance.html +++ b/docs/functions/distance.html @@ -36,7 +36,7 @@
    p2:

    Returns number

     +
  • Defined in core/math.ts:180
    • @@ -66,7 +66,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -88,8 +89,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/dot.html b/docs/functions/dot.html index 6e17b20..ad4b1de 100644 --- a/docs/functions/dot.html +++ b/docs/functions/dot.html @@ -36,7 +36,7 @@
    v2:

    Returns number

     +
  • Defined in core/math.ts:86
    • @@ -66,7 +66,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -88,8 +89,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/evaluateForT.html b/docs/functions/evaluateForT.html index 30041e1..bd2adaa 100644 --- a/docs/functions/evaluateForT.html +++ b/docs/functions/evaluateForT.html @@ -44,7 +44,7 @@
    target:

    Returns Vector

    +
  • Defined in core/spline-segment.ts:132
    • @@ -74,7 +74,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -96,8 +97,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/extrapolateControlPoint.html b/docs/functions/extrapolateControlPoint.html index a0b7e1e..27c8eef 100644 --- a/docs/functions/extrapolateControlPoint.html +++ b/docs/functions/extrapolateControlPoint.html @@ -36,7 +36,7 @@
    v:

    Returns Vector

    +
  • Defined in core/spline-curve.ts:11
    • @@ -66,7 +66,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -88,8 +89,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/fill.html b/docs/functions/fill.html index 0777c43..298b216 100644 --- a/docs/functions/fill.html +++ b/docs/functions/fill.html @@ -34,7 +34,7 @@
    val: number

    Returns Vector

    +
  • Defined in core/utils.ts:8
    • @@ -64,7 +64,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -86,8 +87,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/findRootsOfT.html b/docs/functions/findRootsOfT.html index 5deb5a5..5064279 100644 --- a/docs/functions/findRootsOfT.html +++ b/docs/functions/findRootsOfT.html @@ -34,7 +34,7 @@
    coefficients: Returns number[]
    +
  • Defined in core/spline-segment.ts:114
    • @@ -64,7 +64,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -86,8 +87,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/getControlPoints.html b/docs/functions/getControlPoints.html index 0ff4921..2c59569 100644 --- a/docs/functions/getControlPoints.html +++ b/docs/functions/getControlPoints.html @@ -40,7 +40,7 @@
    closed: boolean

    Returns Vector[]

    +
  • Defined in core/spline-curve.ts:26
    • @@ -70,7 +70,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -92,8 +93,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/getCubicRoots.html b/docs/functions/getCubicRoots.html index 97ffbb8..5e6612d 100644 --- a/docs/functions/getCubicRoots.html +++ b/docs/functions/getCubicRoots.html @@ -42,7 +42,7 @@
    d: number

    Returns number[]

    +
  • Defined in core/math.ts:43
    • @@ -72,7 +72,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -94,8 +95,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/getQuadRoots.html b/docs/functions/getQuadRoots.html index 6aaf206..474b6c8 100644 --- a/docs/functions/getQuadRoots.html +++ b/docs/functions/getQuadRoots.html @@ -38,7 +38,7 @@
    c: number

    Returns number[]

    +
  • Defined in core/math.ts:23
    • @@ -68,7 +68,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -90,8 +91,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/getSegmentIndexAndT.html b/docs/functions/getSegmentIndexAndT.html index 62da13d..3cabebd 100644 --- a/docs/functions/getSegmentIndexAndT.html +++ b/docs/functions/getSegmentIndexAndT.html @@ -43,7 +43,7 @@
    index:
    weight: number
    +
  • Defined in core/spline-curve.ts:55
    • @@ -73,7 +73,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -95,8 +96,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/magnitude.html b/docs/functions/magnitude.html index 3c0a397..7b5e659 100644 --- a/docs/functions/magnitude.html +++ b/docs/functions/magnitude.html @@ -30,7 +30,7 @@
    v:

    Returns number

     +
  • Defined in core/math.ts:166
    • @@ -60,7 +60,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -82,8 +83,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/map.html b/docs/functions/map.html index d17b448..aa3e12d 100644 --- a/docs/functions/map.html +++ b/docs/functions/map.html @@ -47,7 +47,7 @@
    i: number

    Returns number

    Returns Vector

    +
  • Defined in core/utils.ts:20
    • @@ -77,7 +77,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -99,8 +100,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/normalize.html b/docs/functions/normalize.html index af755ee..6dd3076 100644 --- a/docs/functions/normalize.html +++ b/docs/functions/normalize.html @@ -36,7 +36,7 @@
    Optional target: Returns Vector
    +
  • Defined in core/math.ts:191
    • @@ -66,7 +66,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -88,8 +89,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/orthogonal.html b/docs/functions/orthogonal.html index 3a90bb1..e09ac84 100644 --- a/docs/functions/orthogonal.html +++ b/docs/functions/orthogonal.html @@ -34,7 +34,7 @@
    Optional target: Returns Vector
    +
  • Defined in core/math.ts:205
    • @@ -64,7 +64,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -86,8 +87,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/reduce.html b/docs/functions/reduce.html index b1708a0..01a4ef4 100644 --- a/docs/functions/reduce.html +++ b/docs/functions/reduce.html @@ -53,7 +53,7 @@
    r: numberReturns number
    +
  • Defined in core/utils.ts:33
    • @@ -83,7 +83,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -105,8 +106,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/rotate3d.html b/docs/functions/rotate3d.html new file mode 100644 index 0000000..c726364 --- /dev/null +++ b/docs/functions/rotate3d.html @@ -0,0 +1,108 @@ +rotate3d | curve-interpolator
    +
    + +
    +
    +
    +
    + +

    Function rotate3d

    +
    +
      + +
    • +

      Rotate a point around the given axis and angle

      + +

      Returns

      rotated vector

      +
      +
      +

      Parameters

      +
        +
      • +
        vector: Vector
        +

        vector to rotate

        +
        • +
      • +
        axis: Vector = ...
        +

        vector defining the rotation axis

        +
        • +
      • +
        angle: number = 0
        +

        angle of rotation in radians

        +
        • +
      • +
        Optional target: Vector
        +

        optional target

        +
      +

      Returns Vector

    +
    +
    +
    +

    Settings

     +
    +
    +

    Member Visibility

    +
      +
      • +
      • +
      • +
    +
    +

    Theme

    + +
    +
    +

    Generated using TypeDoc

    +
    \ No newline at end of file diff --git a/docs/functions/secondDerivativeAtT.html b/docs/functions/secondDerivativeAtT.html index 8aa3687..3bd2a97 100644 --- a/docs/functions/secondDerivativeAtT.html +++ b/docs/functions/secondDerivativeAtT.html @@ -36,7 +36,7 @@
    coefficients: Returns number
    +
  • Defined in core/spline-segment.ts:104
    • @@ -66,7 +66,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -88,8 +89,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/simplify2d.html b/docs/functions/simplify2d.html index 3517eec..06a42ff 100644 --- a/docs/functions/simplify2d.html +++ b/docs/functions/simplify2d.html @@ -40,7 +40,7 @@
    maxDistance: numberReturns number[][]
    +
  • Defined in core/utils.ts:62
    • @@ -70,7 +70,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -92,8 +93,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/sub.html b/docs/functions/sub.html new file mode 100644 index 0000000..10bef29 --- /dev/null +++ b/docs/functions/sub.html @@ -0,0 +1,104 @@ +sub | curve-interpolator
    +
    + +
    +
    +
    +
    + +

    Function sub

    +
    +
    +
    +
    +
    +

    Settings

     +
    +
    +

    Member Visibility

    +
      +
      • +
      • +
      • +
    +
    +

    Theme

    + +
    +
    +

    Generated using TypeDoc

    +
    \ No newline at end of file diff --git a/docs/functions/sumOfSquares.html b/docs/functions/sumOfSquares.html index 5c21fee..cc31ad6 100644 --- a/docs/functions/sumOfSquares.html +++ b/docs/functions/sumOfSquares.html @@ -34,7 +34,7 @@
    v2:

    Returns number

     +
  • Defined in core/math.ts:154
    • @@ -64,7 +64,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -86,8 +87,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/functions/valueAtT.html b/docs/functions/valueAtT.html index c0fefd4..8daad98 100644 --- a/docs/functions/valueAtT.html +++ b/docs/functions/valueAtT.html @@ -36,7 +36,7 @@
    coefficients: Returns number
    +
  • Defined in core/spline-segment.ts:79
    • @@ -66,7 +66,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -88,8 +89,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/docs/interfaces/_internal_.BBox.html b/docs/interfaces/_internal_.BBox.html index 0a2d101..b79248a 100644 --- a/docs/interfaces/_internal_.BBox.html +++ b/docs/interfaces/_internal_.BBox.html @@ -24,7 +24,7 @@

    Hierarchy

    • BBox
    +
  • Defined in core/interfaces.ts:87
    • @@ -41,12 +41,12 @@

    Properties

    max

    max: Vector
    +
  • Defined in core/interfaces.ts:89

    • min

    min: Vector
    +
  • Defined in core/interfaces.ts:88
    • diff --git a/docs/interfaces/_internal_.CurveInterpolatorOptions.html b/docs/interfaces/_internal_.CurveInterpolatorOptions.html index 294a614..0f31904 100644 --- a/docs/interfaces/_internal_.CurveInterpolatorOptions.html +++ b/docs/interfaces/_internal_.CurveInterpolatorOptions.html @@ -26,7 +26,7 @@

    Hierarchy

    • CurveInterpolatorOptions
    +
  • Defined in curve-interpolator.ts:28
    • @@ -49,39 +49,39 @@

    Optionalalpha?: number

    +
  • Defined in core/interfaces.ts:46

    • Optional arcDivisions

    arcDivisions?: number
    +
  • Defined in curve-interpolator.ts:29

    • Optional closed

    closed?: boolean
    +
  • Defined in core/interfaces.ts:62

    • Optional lmargin

    lmargin?: number
    +
  • Defined in curve-interpolator.ts:32

    • Optional numericalApproximationOrder

    numericalApproximationOrder?: number
    +
  • Defined in curve-interpolator.ts:30

    • Optional numericalInverseSamples

    numericalInverseSamples?: number
    +
  • Defined in curve-interpolator.ts:31

    • Optional tension

    tension?: number
    +
  • Defined in core/interfaces.ts:44
    • diff --git a/docs/interfaces/_internal_.CurveMapper.html b/docs/interfaces/_internal_.CurveMapper.html index c76340a..90542f4 100644 --- a/docs/interfaces/_internal_.CurveMapper.html +++ b/docs/interfaces/_internal_.CurveMapper.html @@ -25,7 +25,7 @@

    Implemented by

    +
  • Defined in core/interfaces.ts:12
    • @@ -50,12 +50,12 @@

    Properties

    alpha

    alpha: number
    +
  • Defined in core/interfaces.ts:13

    • closed

    closed: boolean
    +
  • Defined in core/interfaces.ts:16

    • evaluateForT

    evaluateForT: ((func: SegmentFunction, t: number, target?: VectorType) => Vector)
    @@ -77,7 +77,7 @@
    t: number
    Optional target: VectorType

    Returns Vector

    +
  • Defined in core/interfaces.ts:18

    • getCoefficients

    getCoefficients: ((idx: number) => NumArray4[])
    @@ -95,7 +95,7 @@

    Parameters

    idx: number

    Returns NumArray4[]

    +
  • Defined in core/interfaces.ts:22

    • getT

    getT: ((u: number) => number)
    @@ -113,7 +113,7 @@

    Parameters

    u: number

    Returns number

    +
  • Defined in core/interfaces.ts:20

    • getU

    getU: ((t: number) => number)
    @@ -131,7 +131,7 @@

    Parameters

    t: number

    Returns number

    +
  • Defined in core/interfaces.ts:21

    • lengthAt

    lengthAt: ((u: number) => number)
    @@ -149,12 +149,12 @@

    Parameters

    u: number

    Returns number

    +
  • Defined in core/interfaces.ts:19

    • points

    points: Vector[]
    +
  • Defined in core/interfaces.ts:15

    • reset

    reset: (() => void)
    @@ -167,12 +167,12 @@

    Type declaration

  • Returns void

    • +
  • Defined in core/interfaces.ts:23

    • tension

    tension: number
    +
  • Defined in core/interfaces.ts:14
    • diff --git a/docs/interfaces/_internal_.CurveParameters.html b/docs/interfaces/_internal_.CurveParameters.html index f6b8609..51953e1 100644 --- a/docs/interfaces/_internal_.CurveParameters.html +++ b/docs/interfaces/_internal_.CurveParameters.html @@ -23,7 +23,7 @@

    Hierarchy

    +
  • Defined in core/interfaces.ts:42
    • @@ -40,12 +40,12 @@

    Properties

    Optional alpha

    alpha?: number
    +
  • Defined in core/interfaces.ts:46

    • Optional tension

    tension?: number
    +
  • Defined in core/interfaces.ts:44
    • diff --git a/docs/interfaces/_internal_.SplineCurveOptions.html b/docs/interfaces/_internal_.SplineCurveOptions.html index afd2fd9..155de5f 100644 --- a/docs/interfaces/_internal_.SplineCurveOptions.html +++ b/docs/interfaces/_internal_.SplineCurveOptions.html @@ -28,7 +28,7 @@

    Hierarchy

    +
  • Defined in core/interfaces.ts:60
    • @@ -47,18 +47,18 @@

    Optionalalpha?: number

    +
  • Defined in core/interfaces.ts:46

    • Optional closed

    closed?: boolean
    +
  • Defined in core/interfaces.ts:62

    • Optional tension

    tension?: number
    +
  • Defined in core/interfaces.ts:44
    • diff --git a/docs/interfaces/_internal_.VectorType.html b/docs/interfaces/_internal_.VectorType.html index 8946ee2..dceb68b 100644 --- a/docs/interfaces/_internal_.VectorType.html +++ b/docs/interfaces/_internal_.VectorType.html @@ -25,7 +25,7 @@

    Hierarchy

    • VectorType
    +
  • Defined in core/interfaces.ts:30
    • @@ -49,47 +49,47 @@

    Properties

    0

    0: number
    +
  • Defined in core/interfaces.ts:31

    • 1

    1: number
    +
  • Defined in core/interfaces.ts:32

    • Optional 2

    2?: number
    +
  • Defined in core/interfaces.ts:33

    • Optional 3

    3?: number
    +
  • Defined in core/interfaces.ts:34

    • length

    length: number
    +
  • Defined in core/interfaces.ts:39

    • Optional w

    w?: number
    +
  • Defined in core/interfaces.ts:38

    • Optional x

    x?: number
    +
  • Defined in core/interfaces.ts:35

    • Optional y

    y?: number
    +
  • Defined in core/interfaces.ts:36

    • Optional z

    z?: number
    +
  • Defined in core/interfaces.ts:37
    • diff --git a/docs/modules.html b/docs/modules.html index 7e87160..abe2527 100644 --- a/docs/modules.html +++ b/docs/modules.html @@ -32,7 +32,8 @@

    Variables

    Functions

    -
    binarySearch +
    add +binarySearch calcKnotSequence calculateCoefficients clamp @@ -54,8 +55,10 @@

    Functions

    normalize orthogonal reduce +rotate3d secondDerivativeAtT simplify2d +sub sumOfSquares valueAtT
    diff --git a/docs/types/_internal_.NumArray4.html b/docs/types/_internal_.NumArray4.html index 1f103e9..5d6d74a 100644 --- a/docs/types/_internal_.NumArray4.html +++ b/docs/types/_internal_.NumArray4.html @@ -20,7 +20,7 @@

    Type alias NumArray4

    Array of four number items

    +
  • Defined in core/interfaces.ts:4
    • diff --git a/docs/types/_internal_.SegmentFunction.html b/docs/types/_internal_.SegmentFunction.html index 3efd3e1..d82afa4 100644 --- a/docs/types/_internal_.SegmentFunction.html +++ b/docs/types/_internal_.SegmentFunction.html @@ -33,7 +33,7 @@
    t: number
    coefficients: NumArray4

    Returns number

    +
  • Defined in core/interfaces.ts:11
    • diff --git a/docs/types/_internal_.Vector.html b/docs/types/_internal_.Vector.html index 149ada0..e430712 100644 --- a/docs/types/_internal_.Vector.html +++ b/docs/types/_internal_.Vector.html @@ -20,7 +20,7 @@

    Type alias Vector

    Either a number array or an object implementing the VectorType interface

    +
  • Defined in core/interfaces.ts:9
    • diff --git a/docs/variables/EPS.html b/docs/variables/EPS.html index d531db3..fd3d970 100644 --- a/docs/variables/EPS.html +++ b/docs/variables/EPS.html @@ -17,7 +17,7 @@

    Variable EPSConst

    EPS: number = ...
    +
  • Defined in core/math.ts:6
    • @@ -47,7 +47,8 @@

    NumericalCurveMapper
  • Point
  • EPS
    • -
  • binarySearch
    • +
  • add
    • +
  • binarySearch
  • calcKnotSequence
  • calculateCoefficients
  • clamp
    • @@ -69,8 +70,10 @@

    normalize
  • orthogonal
  • reduce
    • +
  • rotate3d
  • secondDerivativeAtT
  • simplify2d
    • +
  • sub
  • sumOfSquares
  • valueAtT

    • diff --git a/package.json b/package.json index ada7bb4..d6b29db 100644 --- a/package.json +++ b/package.json @@ -1,7 +1,7 @@ { "private": false, "name": "curve-interpolator", - "version": "3.1.1", + "version": "3.2.0", "description": "Interpolate values on a Cardinal/Catmull-Rom spline curve", "repository": "https://github.com/kjerandp/curve-interpolator", "bugs": { diff --git a/src/core/interfaces.ts b/src/core/interfaces.ts index e8ca21c..9fb9a3d 100644 --- a/src/core/interfaces.ts +++ b/src/core/interfaces.ts @@ -42,7 +42,7 @@ export interface VectorType { export interface CurveParameters { /* curve tension (0 = Catmull-Rom curve, 1 = linear curve) */ tension?: number, - /* curve velocity vector modifier (0 = uniform, 0.5 = centrepetal, 1 = chordal */ + /* curve velocity vector modifier (0 = uniform, 0.5 = centripetal, 1 = chordal */ alpha?: number, } diff --git a/src/core/math.spec.ts b/src/core/math.spec.ts index b2943be..2636e15 100644 --- a/src/core/math.spec.ts +++ b/src/core/math.spec.ts @@ -8,6 +8,7 @@ import { sumOfSquares, magnitude, dot, + rotate3d, } from './math'; import { expect } from 'chai'; import { @@ -131,4 +132,11 @@ describe('math.ts', () => { expect(dot([0, 0], [2, 1])).to.eq(0); expect(dot([-1, 3, 6], [2, 6, -3])).to.eq(-2); }); + + it('should rotate a point at a given angle and rotation axis', () => { + compareNumArrays(rotate3d([1, 0, 0], [0, 1, 0], Math.PI), [-1, 0, 0], EPS); + compareNumArrays(rotate3d([1, 5, 0], [0, 1, 0], Math.PI), [-1, 5, 0], EPS); + compareNumArrays(rotate3d([1, -2, 0], [0, 0, 1], Math.PI / 2), [2, 1, 0], EPS); + compareNumArrays(rotate3d([1, -2, 0], [0, 0, 1], Math.PI / 3), [2.23205080, -0.1339746, 0], EPS); + }); }); diff --git a/src/core/math.ts b/src/core/math.ts index 6bc3ae6..e698a31 100644 --- a/src/core/math.ts +++ b/src/core/math.ts @@ -100,7 +100,7 @@ export function dot(v1:Vector, v2:Vector) : number { * @param target optional target * @returns Vector perpendicular to p1 and p2 */ -export function cross(v1:Vector, v2:Vector, target? : Vector) : Vector { +export function cross(v1:Vector, v2:Vector, target?:Vector) : Vector { if (v1.length > 3) return undefined; target = target || new Array(3); @@ -114,6 +114,38 @@ export function cross(v1:Vector, v2:Vector, target? : Vector) : Vector { return target; } +/** + * Add two vectors + * @param v1 Vector + * @param v2 Vector + * @param target optional target + * @returns Sum of v1 and v2 + */ +export function add(v1:Vector, v2:Vector, target?:Vector) : Vector { + target = target || new Array(v1.length); + + for (let k = 0; k < v1.length; k++) { + target[k] = v1[k] + v2[k]; + } + return target; +} + +/** + * Subtract two vectors + * @param v1 Vector + * @param v2 Vector + * @param target optional target + * @returns Difference of v1 and v2 + */ +export function sub(v1:Vector, v2:Vector, target?:Vector) : Vector { + target = target || new Array(v1.length); + + for (let k = 0; k < v1.length; k++) { + target[k] = v1[k] - v2[k]; + } + return target; +} + /** * Calculate the sum of squares between two points * @param v1 coordinates of point 1 @@ -178,3 +210,36 @@ export function orthogonal(v:Vector, target?: Vector) : Vector { u[0] = x; return u; } + +/** + * Rotate a point around the given axis and angle + * @param vector vector to rotate + * @param axis vector defining the rotation axis + * @param angle angle of rotation in radians + * @param target optional target + * @returns rotated vector + */ +export function rotate3d(vector:Vector, axis:Vector = [0, 1, 0], angle = 0, target?: Vector) : Vector { + const c = Math.cos(angle); + const s = Math.sin(angle); + + const t = 1 - c; + + const vx = vector[0]; + const vy = vector[1]; + const vz = vector[2]; + + const ax = axis[0]; + const ay = axis[1]; + const az = axis[2]; + + const tx = t * ax, ty = t * ay; + + target = target || vector; + + target[0] = (tx * ax + c) * vx + (tx * ay - s * az) * vy + (tx * az + s * ay) * vz; + target[1] = (tx * ay + s * az) * vx + (ty * ay + c) * vy + (ty * az - s * ax) * vz; + target[2] = (tx * az - s * ay) * vx + (ty * az + s * ax) * vy + (t * az * az + c) * vz; + + return target; +} diff --git a/src/curve-interpolator.spec.ts b/src/curve-interpolator.spec.ts index 9cefb5c..889cfd6 100644 --- a/src/curve-interpolator.spec.ts +++ b/src/curve-interpolator.spec.ts @@ -273,5 +273,36 @@ describe('curve-interpolator.ts', () => { const mapped = lerp.reduce(({ acc, i }) => acc + i, 0, 10); expect(mapped).to.deep.eq(45); }); + + it('should return the Frenet-frames in 3d given a number of segments', () => { + const lerp2d = new CurveInterpolator(points, { tension: 0, alpha: 1, arcDivisions: 0 }); + expect(lerp2d.getFrenetFrames(10)).to.be.undefined; + + const lerp3d = new CurveInterpolator(points3d, { tension: 0, alpha: 1, arcDivisions: 0 }); + + const result = lerp3d.getFrenetFrames(10); + + expect(result.tangents.length).to.eq(11); + expect(result.normals.length).to.eq(11); + expect(result.binormals.length).to.eq(11); + + const normals = [ + [-0, -0, -1], + [0.009241715900917333, -0.22355726615559307, -0.9746469819561563], + [0.07519649382870604, -0.8430999136085097, -0.5324734951048672], + [0.10569030233723536, -0.9503013780798257, -0.29284270660449757], + [-0.09322439048956332, -0.8727842582591987, -0.47912091537814344], + [-0.10768487787795038, -0.8718360628865027, -0.47781361065479616], + [-0.03967909137676523, -0.8677655638926591, -0.49538721807245867], + [0.26821056388630016, -0.8510664650835947, -0.4513856061394822], + [0.4323086396065564, -0.849148468493959, -0.30340751239198555], + [0.4192160009210173, -0.8256141926158265, 0.3776495061867643], + [0.4078956847626701, -0.8244649304232898, 0.39227374224400063], + ]; + + result.normals.forEach((actual, i) => { + expect(actual).to.deep.eq(normals[i]); + }); + }); }); diff --git a/src/curve-interpolator.ts b/src/curve-interpolator.ts index d8b9410..bbdd281 100644 --- a/src/curve-interpolator.ts +++ b/src/curve-interpolator.ts @@ -10,6 +10,7 @@ import { getQuadRoots, magnitude, normalize, + rotate3d, } from './core/math'; import { @@ -218,6 +219,84 @@ export default class CurveInterpolator { return normalize(cross(cross(dt, ddt), dt), normal); } + + /** + * Calculate the Frenet-Serret frames for a 3d curve, using the concept of parallel transport. + * The implementation used here is basically a copy of the function used in THREE.js (https://github.com/mrdoob/three.js), + * which in turn is based on the the paper "Parallel Transport Approach to Curve Framing" by Hanson and Ma + * (https://legacy.cs.indiana.edu/ftp/techreports/TR425.pdf) + * @param segments number of samples (segments) along the curve (will return segments + 1 frames) + * @returns object containing arrays for tangents, normals and binormals + */ + getFrenetFrames(segments:number) : { tangents:Vector[], normals:Vector[], binormals:Vector[]} { + if (this.points[0].length !== 3) return undefined; + + const tangents = new Array(segments + 1); + const normals = new Array(segments + 1); + const binormals = new Array(segments + 1); + + for (let i = 0; i <= segments; i++) { + tangents[i] = this.getTangentAt(i / segments); + } + + // select an initial normal vector perpendicular to the first tangent vector, and in the + // direction of the minimum tangent xyz component + let normal: Vector; + + let min = Number.MAX_VALUE; + const tx = Math.abs(tangents[0][0]); + const ty = Math.abs(tangents[0][1]); + const tz = Math.abs(tangents[0][2]); + + if (tx <= min) { + min = tx; + normal = [1, 0, 0]; + } + + if (ty <= min) { + min = ty; + normal = [0, 1, 0]; + } + + if (tz <= min) { + normal = [0, 0, 1]; + } + + let vec = normalize(cross(tangents[0], normal)); + + + normals[0] = cross(tangents[0], vec); + binormals[0] = cross(tangents[0], normals[0]); + + for (let i = 1; i <= segments; i++) { + vec = cross(tangents[i - 1], tangents[i]); + normals[i] = copyValues(normals[i - 1]); + if (magnitude(vec) > EPS) { + normalize(vec); + const theta = Math.acos(clamp(dot(tangents[i - 1], tangents[i]), -1, 1)); // clamp for floating pt errors + rotate3d(normals[i - 1], vec, theta, normals[i]); + } + binormals[i] = cross(tangents[i], normals[i]); + } + + // if the curve is closed, postprocess the vectors so the first and last normal vectors are the same + if (this.closed === true) { + let theta = Math.acos(clamp(dot(normals[0], normals[segments]), -1, 1)) / segments; + + if (dot(tangents[0], cross(normals[0], normals[segments])) > 0) { + theta = -theta; + } + + for (let i = 1; i <= segments; i++) { + // twist a little... + rotate3d(normals[i], tangents[i], theta * i, normals[i]); + binormals[i] = cross(tangents[i], normals[i]); + } + } + + return { tangents, normals, binormals }; + } + /** * Finds the curvature and radius at the specified position (0..1) on the curve. The unsigned curvature * is returned along with radius, tangent vector and, for 2D and 3D curves, a direction vector is included @@ -521,14 +600,15 @@ export default class CurveInterpolator { * Create and cache a lookup table of n=samples points, indexed by position (u) * @param func function generating lookup table value * @param samples number of samples (segments) - * @param options object of { from, to, cacheKey } - if cacheKey is included, the map will be stored in the internal cache + * @param options object of \{ from, to, cacheKey \} - if cacheKey is included, the map will be stored in the internal cache * @returns Map of positions -> points */ - createLookupTable(func: (u:number) => T, samples: number, options?: { from?: number, to?: number, cacheKey?: string }) : Map { + createLookupTable(func: (u:number) => T, samples: number, options?: { from?: number, to?: number, cacheKey?: string, cacheForceUpdate?: boolean }) : Map { if (!samples || samples <= 1) throw Error('Invalid arguments passed to createLookupTable(). You must specify at least 2 samples.') - const { from, to, cacheKey } = { + const { from, to, cacheKey, cacheForceUpdate } = { from: 0, to: 1, + cacheForceUpdate: false, ...options, }; @@ -536,7 +616,7 @@ export default class CurveInterpolator { let lut = null; - if (!cacheKey || !this._cache.has(cacheKey)) { + if (!cacheKey || cacheForceUpdate || !this._cache.has(cacheKey)) { lut = new Map(); for (let d = 0; d < samples; d++) { @@ -566,9 +646,10 @@ export default class CurveInterpolator { forEach(func: ({ u, t, i, prev }) => T, samples: (number | number[]), from = 0, to = 1) : void { let positions = []; if (Number.isFinite(samples)) { - if (samples <= 1) throw Error('Invalid arguments passed to forEach(). You must specify at least 2 samples.') const nSamples = samples as number; - for (let i = 0; i < samples; i++) { + if (nSamples <= 1) throw Error('Invalid arguments passed to forEach(). You must specify at least 2 samples.') + + for (let i = 0; i < nSamples; i++) { const u = from === 0 && to === 1 ? i / (nSamples - 1) : from + ((i / (nSamples - 1)) * (to - from)); positions.push(u); @@ -599,9 +680,10 @@ export default class CurveInterpolator { map(func: ({ u, t, i, prev }) => T, samples: (number | number[]), from = 0, to = 1) : T[] { let positions = []; if (Number.isFinite(samples)) { - if (samples <= 1) throw Error('Invalid arguments passed to map(). You must specify at least 2 samples.') const nSamples = samples as number; - for (let i = 0; i < samples; i++) { + if (nSamples <= 1) throw Error('Invalid arguments passed to map(). You must specify at least 2 samples.') + + for (let i = 0; i < nSamples; i++) { const u = from === 0 && to === 1 ? i / (nSamples - 1) : from + ((i / (nSamples - 1)) * (to - from)); positions.push(u); @@ -634,9 +716,10 @@ export default class CurveInterpolator { reduce(func: ({ acc, u, t, i }) => T, initialValue:T, samples: (number | number[]), from = 0, to = 1) : T { let positions = []; if (Number.isFinite(samples)) { - if (samples <= 1) throw Error('Invalid arguments passed to map(). You must specify at least 2 samples.') const nSamples = samples as number; - for (let i = 0; i < samples; i++) { + if (nSamples <= 1) throw Error('Invalid arguments passed to map(). You must specify at least 2 samples.') + + for (let i = 0; i < nSamples; i++) { const u = from === 0 && to === 1 ? i / (nSamples - 1) : from + ((i / (nSamples - 1)) * (to - from)); positions.push(u);