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mat.h
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mat.h
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/*
October 2021
Requires vec.h: https://gist.github.com/mrbid/77a92019e1ab8b86109bf103166bd04e
Credits:
Aaftab Munshi, Dan Ginsburg, Dave Shreiner, James William Fletcher, Intel, Gabriel Cramer
*/
#ifndef MAT_H
#define MAT_H
#include "vec.h"
typedef struct
{
float m[4][4];
} mat;
void mIdent(mat *m);
void mCopy(mat *restrict r, const mat *restrict v);
void mMul(mat *restrict r, const mat *restrict a, const mat *restrict b);
void mMulP(vec *restrict r, const mat *restrict a, const float x, const float y, const float z);
void mMulV(vec *restrict r, const mat *restrict a, const vec v);
void mScale(mat *r, const float x, const float y, const float z);
void mTranslate(mat *r, const float x, const float y, const float z);
void mRotate(mat *r, const float radians, float x, float y, float z);
void mRotX(mat *r, const float radians);
void mRotY(mat *r, const float radians);
void mRotZ(mat *r, const float radians);
void mFrustum(mat *r, const float left, const float right, const float bottom, const float top, const float nearZ, const float farZ);
void mPerspective(mat *r, const float fovy, const float aspect, const float nearZ, const float farZ);
void mOrtho(mat *r, const float left, const float right, const float bottom, const float top, const float nearZ, const float farZ);
void mLookAt(mat *r, const vec origin, const vec unit_dir);
void mInvert(float *restrict dst, const float *restrict mat);
void mTranspose(mat *restrict r, const mat *restrict m);
void mSetViewDir(mat *r, const vec dir_norm, const vec up_norm);
void mGetViewDir(vec *r, const mat matrix); // returns normal/unit vector
void mGetDirX(vec *r, const mat matrix);
void mGetDirY(vec *r, const mat matrix);
void mGetDirZ(vec *r, const mat matrix);
void mGetPos(vec *r, const mat matrix);
//
void mIdent(mat *m)
{
memset(m, 0x0, sizeof(mat));
m->m[0][0] = 1.0f;
m->m[1][1] = 1.0f;
m->m[2][2] = 1.0f;
m->m[3][3] = 1.0f;
}
void mCopy(mat *restrict r, const mat *restrict v)
{
memcpy(r, v, sizeof(mat));
}
void mMul(mat *restrict r, const mat *restrict a, const mat *restrict b)
{
mat tmp;
for(int i = 0; i < 4; i++)
{
tmp.m[i][0] = (a->m[i][0] * b->m[0][0]) +
(a->m[i][1] * b->m[1][0]) +
(a->m[i][2] * b->m[2][0]) +
(a->m[i][3] * b->m[3][0]) ;
tmp.m[i][1] = (a->m[i][0] * b->m[0][1]) +
(a->m[i][1] * b->m[1][1]) +
(a->m[i][2] * b->m[2][1]) +
(a->m[i][3] * b->m[3][1]) ;
tmp.m[i][2] = (a->m[i][0] * b->m[0][2]) +
(a->m[i][1] * b->m[1][2]) +
(a->m[i][2] * b->m[2][2]) +
(a->m[i][3] * b->m[3][2]) ;
tmp.m[i][3] = (a->m[i][0] * b->m[0][3]) +
(a->m[i][1] * b->m[1][3]) +
(a->m[i][2] * b->m[2][3]) +
(a->m[i][3] * b->m[3][3]) ;
}
memcpy(r, &tmp, sizeof(mat));
}
void mMulP(vec *restrict r, const mat *restrict a, const float x, const float y, const float z)
{
r->x = (a->m[0][0] * x) +
(a->m[0][1] * x) +
(a->m[0][2] * x) +
(a->m[0][3] * x) ;
r->y = (a->m[1][0] * y) +
(a->m[1][1] * y) +
(a->m[1][2] * y) +
(a->m[1][3] * y) ;
r->z = (a->m[2][0] * z) +
(a->m[2][1] * z) +
(a->m[2][2] * z) +
(a->m[2][3] * z) ;
}
void mMulV(vec *restrict r, const mat *restrict a, const vec v)
{
r->x = (a->m[0][0] * v.x) +
(a->m[0][1] * v.x) +
(a->m[0][2] * v.x) +
(a->m[0][3] * v.x) ;
r->y = (a->m[1][0] * v.y) +
(a->m[1][1] * v.y) +
(a->m[1][2] * v.y) +
(a->m[1][3] * v.y) ;
r->z = (a->m[2][0] * v.z) +
(a->m[2][1] * v.z) +
(a->m[2][2] * v.z) +
(a->m[2][3] * v.z) ;
r->w = (a->m[3][0] * v.w) +
(a->m[3][1] * v.w) +
(a->m[3][2] * v.w) +
(a->m[3][3] * v.w) ;
}
void mScale(mat *r, const float x, const float y, const float z)
{
r->m[0][0] *= x;
r->m[0][1] *= x;
r->m[0][2] *= x;
r->m[0][3] *= x;
r->m[1][0] *= y;
r->m[1][1] *= y;
r->m[1][2] *= y;
r->m[1][3] *= y;
r->m[2][0] *= z;
r->m[2][1] *= z;
r->m[2][2] *= z;
r->m[2][3] *= z;
}
void mTranslate(mat *r, const float x, const float y, const float z)
{
r->m[3][0] += (r->m[0][0] * x + r->m[1][0] * y + r->m[2][0] * z);
r->m[3][1] += (r->m[0][1] * x + r->m[1][1] * y + r->m[2][1] * z);
r->m[3][2] += (r->m[0][2] * x + r->m[1][2] * y + r->m[2][2] * z);
r->m[3][3] += (r->m[0][3] * x + r->m[1][3] * y + r->m[2][3] * z);
}
void mRotate(mat *r, const float radians, float x, float y, float z)
{
const float mag = rsqrtss(x * x + y * y + z * z);
const float sinAngle = sinf(radians);
const float cosAngle = cosf(radians);
if(mag > 0.0f)
{
x *= mag;
y *= mag;
z *= mag;
const float xx = x * x;
const float yy = y * y;
const float zz = z * z;
const float xy = x * y;
const float yz = y * z;
const float zx = z * x;
const float xs = x * sinAngle;
const float ys = y * sinAngle;
const float zs = z * sinAngle;
const float oneMinusCos = 1.0f - cosAngle;
mat rotMat;
rotMat.m[0][0] = (oneMinusCos * xx) + cosAngle;
rotMat.m[0][1] = (oneMinusCos * xy) - zs;
rotMat.m[0][2] = (oneMinusCos * zx) + ys;
rotMat.m[0][3] = 0.0F;
rotMat.m[1][0] = (oneMinusCos * xy) + zs;
rotMat.m[1][1] = (oneMinusCos * yy) + cosAngle;
rotMat.m[1][2] = (oneMinusCos * yz) - xs;
rotMat.m[1][3] = 0.0F;
rotMat.m[2][0] = (oneMinusCos * zx) - ys;
rotMat.m[2][1] = (oneMinusCos * yz) + xs;
rotMat.m[2][2] = (oneMinusCos * zz) + cosAngle;
rotMat.m[2][3] = 0.0F;
rotMat.m[3][0] = 0.0F;
rotMat.m[3][1] = 0.0F;
rotMat.m[3][2] = 0.0F;
rotMat.m[3][3] = 1.0F;
mMul(r, &rotMat, r);
}
}
void mRotX(mat *r, const float radians)
{
const float s = sinf(radians);
const float c = cosf(radians);
const mat t = { c, 0.f, s, 0.f,
0.f, 1.f, 0.f, 0.f,
-s, 0.f, c, 0.f,
0.f, 0.f, 0.f, 1.f };
mMul(r, &t, r);
}
void mRotY(mat *r, const float radians)
{
const float s = sinf(radians);
const float c = cosf(radians);
const mat t = { 1.f, 0.f, 0.f, 0.f,
0.f, c, -s, 0.f,
0.f, s, c, 0.f,
0.f, 0.f, 0.f, 1.f };
mMul(r, &t, r);
}
void mRotZ(mat *r, const float radians)
{
const float s = sinf(radians);
const float c = cosf(radians);
const mat t = { c, -s, 0.f, 0.f,
s, c, 0.f, 0.f,
0.f, 0.f, 1.f, 0.f,
0.f, 0.f, 0.f, 1.f };
mMul(r, &t, r);
}
void mFrustum(mat *r, const float left, const float right, const float bottom, const float top, const float nearZ, const float farZ)
{
const float dX = right - left;
const float dY = top - bottom;
const float dZ = farZ - nearZ;
const float rdX = 1.f/dX;
const float rdY = 1.f/dY;
const float rdZ = 1.f/dZ;
mat frust;
if(nearZ <= 0.0f || farZ <= 0.0f || dX <= 0.0f || dY <= 0.0f || dZ <= 0.0f)
return;
frust.m[0][0] = 2.0f * nearZ * rdX;
frust.m[0][1] = frust.m[0][2] = frust.m[0][3] = 0.0f;
frust.m[1][1] = 2.0f * nearZ * rdY;
frust.m[1][0] = frust.m[1][2] = frust.m[1][3] = 0.0f;
frust.m[2][0] = (right + left) * rdX;
frust.m[2][1] = (top + bottom) * rdY;
frust.m[2][2] = -(nearZ + farZ) * rdZ;
frust.m[2][3] = -1.0f;
frust.m[3][2] = -2.0f * nearZ * farZ * rdZ;
frust.m[3][0] = frust.m[3][1] = frust.m[3][3] = 0.0f;
mMul(r, &frust, r);
}
void mPerspective(mat *r, const float fovy, const float aspect, const float nearZ, const float farZ)
{
float frustumW, frustumH;
frustumH = tanf(fovy * 0.002777778078f * PI ) * nearZ; // 0x3b360b62
frustumW = frustumH * aspect;
mFrustum(r, -frustumW, frustumW, -frustumH, frustumH, nearZ, farZ);
}
void mOrtho(mat *r, const float left, const float right, const float bottom, const float top, const float nearZ, const float farZ)
{
const float dX = right - left;
const float dY = top - bottom;
const float dZ = farZ - nearZ;
const float rdX = 1.f/dX;
const float rdY = 1.f/dY;
const float rdZ = 1.f/dZ;
mat ortho;
if(dX == 0.0f || dY == 0.0f || dZ == 0.0f)
return;
mIdent(&ortho);
ortho.m[0][0] = 2.0f * rdX;
ortho.m[3][0] = -(right + left) * rdX;
ortho.m[1][1] = 2.0f * rdY;
ortho.m[3][1] = -(top + bottom) * rdY;
ortho.m[2][2] = -2.0f * rdZ;
ortho.m[3][2] = -(nearZ + farZ) * rdZ;
mMul(r, &ortho, r);
}
void mLookAt(mat *r, const vec origin, const vec unit_dir)
{
vec up;
up.x = 0.f, up.y = 1.f, up.z = 0.f;
vec dirn;
dirn.x = unit_dir.x;
dirn.y = unit_dir.y;
dirn.z = unit_dir.z;
vec c;
vCross(&c, up, dirn);
vNorm(&c);
vec rup;
vCross(&rup, dirn, c);
r->m[0][0] = c.x;
r->m[0][1] = c.y;
r->m[0][2] = c.z;
r->m[1][0] = rup.x;
r->m[1][1] = rup.y;
r->m[1][2] = rup.z;
r->m[2][0] = dirn.x;
r->m[2][1] = dirn.y;
r->m[2][2] = dirn.z;
r->m[3][0] = origin.x;
r->m[3][1] = origin.y;
r->m[3][2] = origin.z;
}
void mInvert(float *restrict dst, const float *restrict mat)
{
// original source: ftp://download.intel.com/design/PentiumIII/sml/24504301.pdf
// mirrored: https://github.com/esAux/esAux-Menger/raw/main/SIMD%20Matrix%20Inverse.pdf
// Cramer Invert
float tmp[12]; /* temp array for pairs */
float src[16]; /* array of transpose source matrix */
float det; /* determinant */
/* transpose matrix */
for(int i = 0; i < 4; i++)
{
src[i] = mat[i*4];
src[i + 4] = mat[i*4 + 1];
src[i + 8] = mat[i*4 + 2];
src[i + 12] = mat[i*4 + 3];
}
/* calculate pairs for first 8 elements (cofactors) */
tmp[0] = src[10] * src[15];
tmp[1] = src[11] * src[14];
tmp[2] = src[9] * src[15];
tmp[3] = src[11] * src[13];
tmp[4] = src[9] * src[14];
tmp[5] = src[10] * src[13];
tmp[6] = src[8] * src[15];
tmp[7] = src[11] * src[12];
tmp[8] = src[8] * src[14];
tmp[9] = src[10] * src[12];
tmp[10] = src[8] * src[13];
tmp[11] = src[9] * src[12];
/* calculate first 8 elements (cofactors) */
dst[0] = tmp[0]*src[5] + tmp[3]*src[6] + tmp[4]*src[7];
dst[0] -= tmp[1]*src[5] + tmp[2]*src[6] + tmp[5]*src[7];
dst[1] = tmp[1]*src[4] + tmp[6]*src[6] + tmp[9]*src[7];
dst[1] -= tmp[0]*src[4] + tmp[7]*src[6] + tmp[8]*src[7];
dst[2] = tmp[2]*src[4] + tmp[7]*src[5] + tmp[10]*src[7];
dst[2] -= tmp[3]*src[4] + tmp[6]*src[5] + tmp[11]*src[7];
dst[3] = tmp[5]*src[4] + tmp[8]*src[5] + tmp[11]*src[6];
dst[3] -= tmp[4]*src[4] + tmp[9]*src[5] + tmp[10]*src[6];
dst[4] = tmp[1]*src[1] + tmp[2]*src[2] + tmp[5]*src[3];
dst[4] -= tmp[0]*src[1] + tmp[3]*src[2] + tmp[4]*src[3];
dst[5] = tmp[0]*src[0] + tmp[7]*src[2] + tmp[8]*src[3];
dst[5] -= tmp[1]*src[0] + tmp[6]*src[2] + tmp[9]*src[3];
dst[6] = tmp[3]*src[0] + tmp[6]*src[1] + tmp[11]*src[3];
dst[6] -= tmp[2]*src[0] + tmp[7]*src[1] + tmp[10]*src[3];
dst[7] = tmp[4]*src[0] + tmp[9]*src[1] + tmp[10]*src[2];
dst[7] -= tmp[5]*src[0] + tmp[8]*src[1] + tmp[11]*src[2];
/* calculate pairs for second 8 elements (cofactors) */
tmp[0] = src[2]*src[7];
tmp[1] = src[3]*src[6];
tmp[2] = src[1]*src[7];
tmp[3] = src[3]*src[5];
tmp[4] = src[1]*src[6];
tmp[5] = src[2]*src[5];
tmp[6] = src[0]*src[7];
tmp[7] = src[3]*src[4];
tmp[8] = src[0]*src[6];
tmp[9] = src[2]*src[4];
tmp[10] = src[0]*src[5];
tmp[11] = src[1]*src[4];
/* calculate second 8 elements (cofactors) */
dst[8] = tmp[0]*src[13] + tmp[3]*src[14] + tmp[4]*src[15];
dst[8] -= tmp[1]*src[13] + tmp[2]*src[14] + tmp[5]*src[15];
dst[9] = tmp[1]*src[12] + tmp[6]*src[14] + tmp[9]*src[15];
dst[9] -= tmp[0]*src[12] + tmp[7]*src[14] + tmp[8]*src[15];
dst[10] = tmp[2]*src[12] + tmp[7]*src[13] + tmp[10]*src[15];
dst[10]-= tmp[3]*src[12] + tmp[6]*src[13] + tmp[11]*src[15];
dst[11] = tmp[5]*src[12] + tmp[8]*src[13] + tmp[11]*src[14];
dst[11]-= tmp[4]*src[12] + tmp[9]*src[13] + tmp[10]*src[14];
dst[12] = tmp[2]*src[10] + tmp[5]*src[11] + tmp[1]*src[9];
dst[12]-= tmp[4]*src[11] + tmp[0]*src[9] + tmp[3]*src[10];
dst[13] = tmp[8]*src[11] + tmp[0]*src[8] + tmp[7]*src[10];
dst[13]-= tmp[6]*src[10] + tmp[9]*src[11] + tmp[1]*src[8];
dst[14] = tmp[6]*src[9] + tmp[11]*src[11] + tmp[3]*src[8];
dst[14]-= tmp[10]*src[11] + tmp[2]*src[8] + tmp[7]*src[9];
dst[15] = tmp[10]*src[10] + tmp[4]*src[8] + tmp[9]*src[9];
dst[15]-= tmp[8]*src[9] + tmp[11]*src[10] + tmp[5]*src[8];
/* calculate determinant */
det = src[0]*dst[0]+src[1]*dst[1]+src[2]*dst[2]+src[3]*dst[3];
/* calculate matrix inverse */
det = 1.0f/det;
for(int j = 0; j < 16; j++){dst[j] *= det;}
}
void mTranspose(mat *r, const mat *restrict m)
{
r->m[1][0] = m->m[0][1];
r->m[2][0] = m->m[0][2];
r->m[3][0] = m->m[0][3];
r->m[0][1] = m->m[1][0];
r->m[1][1] = m->m[1][1];
r->m[2][1] = m->m[1][2];
r->m[3][1] = m->m[1][3];
r->m[0][2] = m->m[2][0];
r->m[1][2] = m->m[2][1];
r->m[2][2] = m->m[2][2];
r->m[3][2] = m->m[2][3];
r->m[0][3] = m->m[3][0];
r->m[1][3] = m->m[3][1];
r->m[2][3] = m->m[3][2];
r->m[3][3] = m->m[3][3];
}
void mSetViewDir(mat *r, const vec dir_norm, const vec up_norm)
{
vec c;
vCross(&c, up_norm, dir_norm);
vNorm(&c);
vec rup;
vCross(&rup, dir_norm, c);
r->m[0][0] = c.x;
r->m[0][1] = c.y;
r->m[0][2] = c.z;
r->m[1][0] = rup.x;
r->m[1][1] = rup.y;
r->m[1][2] = rup.z;
r->m[2][0] = dir_norm.x;
r->m[2][1] = dir_norm.y;
r->m[2][2] = dir_norm.z;
}
void mGetViewDir(vec *r, const mat matrix)
{
r->x = -matrix.m[0][2];
r->y = -matrix.m[1][2];
r->z = -matrix.m[2][2];
}
void mGetDirX(vec *r, const mat matrix)
{
r->x = matrix.m[0][0];
r->y = matrix.m[0][1];
r->z = matrix.m[0][2];
}
void mGetDirY(vec *r, const mat matrix)
{
r->x = matrix.m[1][0];
r->y = matrix.m[1][1];
r->z = matrix.m[1][2];
}
void mGetDirZ(vec *r, const mat matrix)
{
r->x = matrix.m[2][0];
r->y = matrix.m[2][1];
r->z = matrix.m[2][2];
}
void mGetPos(vec *r, const mat matrix)
{
r->x = matrix.m[3][0];
r->y = matrix.m[3][1];
r->z = matrix.m[3][2];
}
#endif