lygia/math/inverse)inverse matrixes
Use:
<float|mat2|mat3|mat4> inverse(in <float|mat2|mat3|mat4> m)
#ifndef FNC_INVERSE
#define FNC_INVERSE
#if (__VERSION__ < 140)
float inverse(float m) { return 1.0 / m; }
mat2 inverse(mat2 m) {
return mat2(m[1][1],-m[0][1],
-m[1][0], m[0][0]) / (m[0][0]*m[1][1] - m[0][1]*m[1][0]);
}
mat3 inverse(mat3 m) {
float a00 = m[0][0], a01 = m[0][1], a02 = m[0][2];
float a10 = m[1][0], a11 = m[1][1], a12 = m[1][2];
float a20 = m[2][0], a21 = m[2][1], a22 = m[2][2];
float b01 = a22 * a11 - a12 * a21;
float b11 = -a22 * a10 + a12 * a20;
float b21 = a21 * a10 - a11 * a20;
float det = a00 * b01 + a01 * b11 + a02 * b21;
return mat3(b01, (-a22 * a01 + a02 * a21), (a12 * a01 - a02 * a11),
b11, (a22 * a00 - a02 * a20), (-a12 * a00 + a02 * a10),
b21, (-a21 * a00 + a01 * a20), (a11 * a00 - a01 * a10)) / det;
}
mat4 inverse(mat4 m) {
float
a00 = m[0][0], a01 = m[0][1], a02 = m[0][2], a03 = m[0][3],
a10 = m[1][0], a11 = m[1][1], a12 = m[1][2], a13 = m[1][3],
a20 = m[2][0], a21 = m[2][1], a22 = m[2][2], a23 = m[2][3],
a30 = m[3][0], a31 = m[3][1], a32 = m[3][2], a33 = m[3][3],
b00 = a00 * a11 - a01 * a10,
b01 = a00 * a12 - a02 * a10,
b02 = a00 * a13 - a03 * a10,
b03 = a01 * a12 - a02 * a11,
b04 = a01 * a13 - a03 * a11,
b05 = a02 * a13 - a03 * a12,
b06 = a20 * a31 - a21 * a30,
b07 = a20 * a32 - a22 * a30,
b08 = a20 * a33 - a23 * a30,
b09 = a21 * a32 - a22 * a31,
b10 = a21 * a33 - a23 * a31,
b11 = a22 * a33 - a23 * a32,
det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
return mat4(
a11 * b11 - a12 * b10 + a13 * b09,
a02 * b10 - a01 * b11 - a03 * b09,
a31 * b05 - a32 * b04 + a33 * b03,
a22 * b04 - a21 * b05 - a23 * b03,
a12 * b08 - a10 * b11 - a13 * b07,
a00 * b11 - a02 * b08 + a03 * b07,
a32 * b02 - a30 * b05 - a33 * b01,
a20 * b05 - a22 * b02 + a23 * b01,
a10 * b10 - a11 * b08 + a13 * b06,
a01 * b08 - a00 * b10 - a03 * b06,
a30 * b04 - a31 * b02 + a33 * b00,
a21 * b02 - a20 * b04 - a23 * b00,
a11 * b07 - a10 * b09 - a12 * b06,
a00 * b09 - a01 * b07 + a02 * b06,
a31 * b01 - a30 * b03 - a32 * b00,
a20 * b03 - a21 * b01 + a22 * b00) / det;
}
#endif
#endif
Use:
<float|matrix<float, 2, 2>|matrix<float, 3, 3>|matrix<float, 4, 4>> inverse(<float|matrix<float, 2, 2>|matrix<float, 3, 3>|matrix<float, 4, 4>> m)
#ifndef FNC_INVERSE
#define FNC_INVERSE
float inverse(float m) { return 1.0 / m; }
matrix<float, 2, 2> inverse(matrix<float, 2, 2> m) {
return matrix<float, 2, 2>(m[1][1],-m[0][1],
-m[1][0], m[0][0]) / (m[0][0]*m[1][1] - m[0][1]*m[1][0]);
}
matrix<float, 3, 3> inverse(matrix<float, 3, 3> m) {
float a00 = m[0][0], a01 = m[0][1], a02 = m[0][2];
float a10 = m[1][0], a11 = m[1][1], a12 = m[1][2];
float a20 = m[2][0], a21 = m[2][1], a22 = m[2][2];
float b01 = a22 * a11 - a12 * a21;
float b11 = -a22 * a10 + a12 * a20;
float b21 = a21 * a10 - a11 * a20;
float det = a00 * b01 + a01 * b11 + a02 * b21;
return matrix<float, 3, 3>(b01, (-a22 * a01 + a02 * a21), (a12 * a01 - a02 * a11),
b11, (a22 * a00 - a02 * a20), (-a12 * a00 + a02 * a10),
b21, (-a21 * a00 + a01 * a20), (a11 * a00 - a01 * a10)) / det;
}
matrix<float, 4, 4> inverse(matrix<float, 4, 4> m) {
float
a00 = m[0][0], a01 = m[0][1], a02 = m[0][2], a03 = m[0][3],
a10 = m[1][0], a11 = m[1][1], a12 = m[1][2], a13 = m[1][3],
a20 = m[2][0], a21 = m[2][1], a22 = m[2][2], a23 = m[2][3],
a30 = m[3][0], a31 = m[3][1], a32 = m[3][2], a33 = m[3][3],
b00 = a00 * a11 - a01 * a10,
b01 = a00 * a12 - a02 * a10,
b02 = a00 * a13 - a03 * a10,
b03 = a01 * a12 - a02 * a11,
b04 = a01 * a13 - a03 * a11,
b05 = a02 * a13 - a03 * a12,
b06 = a20 * a31 - a21 * a30,
b07 = a20 * a32 - a22 * a30,
b08 = a20 * a33 - a23 * a30,
b09 = a21 * a32 - a22 * a31,
b10 = a21 * a33 - a23 * a31,
b11 = a22 * a33 - a23 * a32,
det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;
return matrix<float, 4, 4>(
a11 * b11 - a12 * b10 + a13 * b09,
a02 * b10 - a01 * b11 - a03 * b09,
a31 * b05 - a32 * b04 + a33 * b03,
a22 * b04 - a21 * b05 - a23 * b03,
a12 * b08 - a10 * b11 - a13 * b07,
a00 * b11 - a02 * b08 + a03 * b07,
a32 * b02 - a30 * b05 - a33 * b01,
a20 * b05 - a22 * b02 + a23 * b01,
a10 * b10 - a11 * b08 + a13 * b06,
a01 * b08 - a00 * b10 - a03 * b06,
a30 * b04 - a31 * b02 + a33 * b00,
a21 * b02 - a20 * b04 - a23 * b00,
a11 * b07 - a10 * b09 - a12 * b06,
a00 * b09 - a01 * b07 + a02 * b06,
a31 * b01 - a30 * b03 - a32 * b00,
a20 * b03 - a21 * b01 + a22 * b00) / det;
}
#endif
fn inverse(m: mat3x3<f32>) -> mat3x3<f32> {
let a00 = m[0][0];
let a01 = m[0][1];
let a02 = m[0][2];
let a10 = m[1][0];
let a11 = m[1][1];
let a12 = m[1][2];
let a20 = m[2][0];
let a21 = m[2][1];
let a22 = m[2][2];
let b01 = a22 * a11 - a12 * a21;
let b11 = -a22 * a10 + a12 * a20;
let b21 = a21 * a10 - a11 * a20;
let det = a00 * b01 + a01 * b11 + a02 * b21;
let A = vec3f(b01, (-a22 * a01 + a02 * a21), ( a12 * a01 - a02 * a11)) / det;
let B = vec3f(b11, ( a22 * a00 - a02 * a20), (-a12 * a00 + a02 * a10)) / det;
let C = vec3f(b21, (-a21 * a00 + a01 * a20), ( a11 * a00 - a01 * a10)) / det;
return mat3x3<f32>(A, B, C);
}
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