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571 lines
12 KiB
571 lines
12 KiB
#ifndef LINMATH_H |
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#define LINMATH_H |
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#include <math.h> |
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#ifdef _MSC_VER |
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#define inline __inline |
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#endif |
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#define LINMATH_H_DEFINE_VEC(n) \ |
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typedef float vec##n[n]; \ |
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static inline void vec##n##_add(vec##n r, vec##n const a, vec##n const b) \ |
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{ \ |
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int i; \ |
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for(i=0; i<n; ++i) \ |
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r[i] = a[i] + b[i]; \ |
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} \ |
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static inline void vec##n##_sub(vec##n r, vec##n const a, vec##n const b) \ |
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{ \ |
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int i; \ |
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for(i=0; i<n; ++i) \ |
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r[i] = a[i] - b[i]; \ |
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} \ |
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static inline void vec##n##_scale(vec##n r, vec##n const v, float const s) \ |
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{ \ |
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int i; \ |
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for(i=0; i<n; ++i) \ |
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r[i] = v[i] * s; \ |
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} \ |
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static inline float vec##n##_mul_inner(vec##n const a, vec##n const b) \ |
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{ \ |
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float p = 0.; \ |
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int i; \ |
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for(i=0; i<n; ++i) \ |
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p += b[i]*a[i]; \ |
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return p; \ |
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} \ |
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static inline float vec##n##_len(vec##n const v) \ |
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{ \ |
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return (float) sqrt(vec##n##_mul_inner(v,v)); \ |
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} \ |
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static inline void vec##n##_norm(vec##n r, vec##n const v) \ |
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{ \ |
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float k = 1.f / vec##n##_len(v); \ |
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vec##n##_scale(r, v, k); \ |
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} |
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LINMATH_H_DEFINE_VEC(2) |
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LINMATH_H_DEFINE_VEC(3) |
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LINMATH_H_DEFINE_VEC(4) |
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static inline void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b) |
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{ |
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r[0] = a[1]*b[2] - a[2]*b[1]; |
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r[1] = a[2]*b[0] - a[0]*b[2]; |
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r[2] = a[0]*b[1] - a[1]*b[0]; |
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} |
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static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const n) |
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{ |
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float p = 2.f*vec3_mul_inner(v, n); |
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int i; |
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for(i=0;i<3;++i) |
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r[i] = v[i] - p*n[i]; |
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} |
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static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b) |
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{ |
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r[0] = a[1]*b[2] - a[2]*b[1]; |
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r[1] = a[2]*b[0] - a[0]*b[2]; |
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r[2] = a[0]*b[1] - a[1]*b[0]; |
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r[3] = 1.f; |
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} |
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static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) |
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{ |
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float p = 2.f*vec4_mul_inner(v, n); |
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int i; |
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for(i=0;i<4;++i) |
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r[i] = v[i] - p*n[i]; |
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} |
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typedef vec4 mat4x4[4]; |
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static inline void mat4x4_identity(mat4x4 M) |
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{ |
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int i, j; |
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for(i=0; i<4; ++i) |
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for(j=0; j<4; ++j) |
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M[i][j] = i==j ? 1.f : 0.f; |
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} |
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static inline void mat4x4_dup(mat4x4 M, mat4x4 N) |
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{ |
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int i, j; |
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for(i=0; i<4; ++i) |
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for(j=0; j<4; ++j) |
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M[i][j] = N[i][j]; |
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} |
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static inline void mat4x4_row(vec4 r, mat4x4 M, int i) |
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{ |
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int k; |
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for(k=0; k<4; ++k) |
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r[k] = M[k][i]; |
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} |
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static inline void mat4x4_col(vec4 r, mat4x4 M, int i) |
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{ |
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int k; |
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for(k=0; k<4; ++k) |
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r[k] = M[i][k]; |
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} |
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static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) |
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{ |
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int i, j; |
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for(j=0; j<4; ++j) |
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for(i=0; i<4; ++i) |
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M[i][j] = N[j][i]; |
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} |
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static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) |
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{ |
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int i; |
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for(i=0; i<4; ++i) |
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vec4_add(M[i], a[i], b[i]); |
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} |
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static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) |
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{ |
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int i; |
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for(i=0; i<4; ++i) |
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vec4_sub(M[i], a[i], b[i]); |
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} |
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static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k) |
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{ |
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int i; |
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for(i=0; i<4; ++i) |
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vec4_scale(M[i], a[i], k); |
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} |
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static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, float z) |
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{ |
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int i; |
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vec4_scale(M[0], a[0], x); |
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vec4_scale(M[1], a[1], y); |
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vec4_scale(M[2], a[2], z); |
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for(i = 0; i < 4; ++i) { |
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M[3][i] = a[3][i]; |
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} |
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} |
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static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) |
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{ |
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mat4x4 temp; |
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int k, r, c; |
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for(c=0; c<4; ++c) for(r=0; r<4; ++r) { |
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temp[c][r] = 0.f; |
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for(k=0; k<4; ++k) |
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temp[c][r] += a[k][r] * b[c][k]; |
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} |
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mat4x4_dup(M, temp); |
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} |
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static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) |
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{ |
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int i, j; |
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for(j=0; j<4; ++j) { |
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r[j] = 0.f; |
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for(i=0; i<4; ++i) |
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r[j] += M[i][j] * v[i]; |
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} |
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} |
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static inline void mat4x4_translate(mat4x4 T, float x, float y, float z) |
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{ |
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mat4x4_identity(T); |
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T[3][0] = x; |
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T[3][1] = y; |
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T[3][2] = z; |
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} |
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static inline void mat4x4_translate_in_place(mat4x4 M, float x, float y, float z) |
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{ |
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vec4 t = {x, y, z, 0}; |
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vec4 r; |
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int i; |
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for (i = 0; i < 4; ++i) { |
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mat4x4_row(r, M, i); |
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M[3][i] += vec4_mul_inner(r, t); |
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} |
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} |
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static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) |
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{ |
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int i, j; |
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for(i=0; i<4; ++i) for(j=0; j<4; ++j) |
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M[i][j] = i<3 && j<3 ? a[i] * b[j] : 0.f; |
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} |
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static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle) |
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{ |
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float s = sinf(angle); |
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float c = cosf(angle); |
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vec3 u = {x, y, z}; |
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if(vec3_len(u) > 1e-4) { |
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vec3_norm(u, u); |
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mat4x4 T; |
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mat4x4_from_vec3_mul_outer(T, u, u); |
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mat4x4 S = { |
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{ 0, u[2], -u[1], 0}, |
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{-u[2], 0, u[0], 0}, |
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{ u[1], -u[0], 0, 0}, |
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{ 0, 0, 0, 0} |
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}; |
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mat4x4_scale(S, S, s); |
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mat4x4 C; |
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mat4x4_identity(C); |
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mat4x4_sub(C, C, T); |
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mat4x4_scale(C, C, c); |
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mat4x4_add(T, T, C); |
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mat4x4_add(T, T, S); |
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T[3][3] = 1.; |
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mat4x4_mul(R, M, T); |
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} else { |
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mat4x4_dup(R, M); |
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} |
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} |
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static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) |
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{ |
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float s = sinf(angle); |
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float c = cosf(angle); |
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mat4x4 R = { |
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{1.f, 0.f, 0.f, 0.f}, |
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{0.f, c, s, 0.f}, |
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{0.f, -s, c, 0.f}, |
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{0.f, 0.f, 0.f, 1.f} |
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}; |
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mat4x4_mul(Q, M, R); |
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} |
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static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) |
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{ |
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float s = sinf(angle); |
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float c = cosf(angle); |
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mat4x4 R = { |
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{ c, 0.f, s, 0.f}, |
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{ 0.f, 1.f, 0.f, 0.f}, |
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{ -s, 0.f, c, 0.f}, |
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{ 0.f, 0.f, 0.f, 1.f} |
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}; |
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mat4x4_mul(Q, M, R); |
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} |
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static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) |
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{ |
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float s = sinf(angle); |
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float c = cosf(angle); |
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mat4x4 R = { |
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{ c, s, 0.f, 0.f}, |
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{ -s, c, 0.f, 0.f}, |
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{ 0.f, 0.f, 1.f, 0.f}, |
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{ 0.f, 0.f, 0.f, 1.f} |
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}; |
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mat4x4_mul(Q, M, R); |
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} |
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static inline void mat4x4_invert(mat4x4 T, mat4x4 M) |
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{ |
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float s[6]; |
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float c[6]; |
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s[0] = M[0][0]*M[1][1] - M[1][0]*M[0][1]; |
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s[1] = M[0][0]*M[1][2] - M[1][0]*M[0][2]; |
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s[2] = M[0][0]*M[1][3] - M[1][0]*M[0][3]; |
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s[3] = M[0][1]*M[1][2] - M[1][1]*M[0][2]; |
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s[4] = M[0][1]*M[1][3] - M[1][1]*M[0][3]; |
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s[5] = M[0][2]*M[1][3] - M[1][2]*M[0][3]; |
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c[0] = M[2][0]*M[3][1] - M[3][0]*M[2][1]; |
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c[1] = M[2][0]*M[3][2] - M[3][0]*M[2][2]; |
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c[2] = M[2][0]*M[3][3] - M[3][0]*M[2][3]; |
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c[3] = M[2][1]*M[3][2] - M[3][1]*M[2][2]; |
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c[4] = M[2][1]*M[3][3] - M[3][1]*M[2][3]; |
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c[5] = M[2][2]*M[3][3] - M[3][2]*M[2][3]; |
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/* Assumes it is invertible */ |
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float idet = 1.0f/( s[0]*c[5]-s[1]*c[4]+s[2]*c[3]+s[3]*c[2]-s[4]*c[1]+s[5]*c[0] ); |
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T[0][0] = ( M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet; |
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T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet; |
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T[0][2] = ( M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet; |
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T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet; |
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T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet; |
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T[1][1] = ( M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet; |
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T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet; |
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T[1][3] = ( M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet; |
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T[2][0] = ( M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet; |
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T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet; |
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T[2][2] = ( M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet; |
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T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet; |
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T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet; |
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T[3][1] = ( M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet; |
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T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet; |
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T[3][3] = ( M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet; |
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} |
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static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) |
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{ |
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mat4x4_dup(R, M); |
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float s = 1.; |
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vec3 h; |
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vec3_norm(R[2], R[2]); |
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s = vec3_mul_inner(R[1], R[2]); |
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vec3_scale(h, R[2], s); |
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vec3_sub(R[1], R[1], h); |
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vec3_norm(R[2], R[2]); |
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s = vec3_mul_inner(R[1], R[2]); |
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vec3_scale(h, R[2], s); |
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vec3_sub(R[1], R[1], h); |
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vec3_norm(R[1], R[1]); |
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s = vec3_mul_inner(R[0], R[1]); |
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vec3_scale(h, R[1], s); |
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vec3_sub(R[0], R[0], h); |
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vec3_norm(R[0], R[0]); |
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} |
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static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, float n, float f) |
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{ |
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M[0][0] = 2.f*n/(r-l); |
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M[0][1] = M[0][2] = M[0][3] = 0.f; |
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M[1][1] = 2.f*n/(t-b); |
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M[1][0] = M[1][2] = M[1][3] = 0.f; |
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M[2][0] = (r+l)/(r-l); |
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M[2][1] = (t+b)/(t-b); |
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M[2][2] = -(f+n)/(f-n); |
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M[2][3] = -1.f; |
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M[3][2] = -2.f*(f*n)/(f-n); |
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M[3][0] = M[3][1] = M[3][3] = 0.f; |
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} |
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static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, float n, float f) |
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{ |
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M[0][0] = 2.f/(r-l); |
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M[0][1] = M[0][2] = M[0][3] = 0.f; |
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M[1][1] = 2.f/(t-b); |
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M[1][0] = M[1][2] = M[1][3] = 0.f; |
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M[2][2] = -2.f/(f-n); |
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M[2][0] = M[2][1] = M[2][3] = 0.f; |
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M[3][0] = -(r+l)/(r-l); |
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M[3][1] = -(t+b)/(t-b); |
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M[3][2] = -(f+n)/(f-n); |
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M[3][3] = 1.f; |
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} |
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static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect, float n, float f) |
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{ |
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/* NOTE: Degrees are an unhandy unit to work with. |
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* linmath.h uses radians for everything! */ |
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float const a = 1.f / (float) tan(y_fov / 2.f); |
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m[0][0] = a / aspect; |
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m[0][1] = 0.f; |
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m[0][2] = 0.f; |
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m[0][3] = 0.f; |
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m[1][0] = 0.f; |
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m[1][1] = a; |
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m[1][2] = 0.f; |
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m[1][3] = 0.f; |
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m[2][0] = 0.f; |
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m[2][1] = 0.f; |
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m[2][2] = -((f + n) / (f - n)); |
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m[2][3] = -1.f; |
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m[3][0] = 0.f; |
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m[3][1] = 0.f; |
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m[3][2] = -((2.f * f * n) / (f - n)); |
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m[3][3] = 0.f; |
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} |
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static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up) |
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{ |
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/* Adapted from Android's OpenGL Matrix.java. */ |
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/* See the OpenGL GLUT documentation for gluLookAt for a description */ |
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/* of the algorithm. We implement it in a straightforward way: */ |
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/* TODO: The negation of of can be spared by swapping the order of |
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* operands in the following cross products in the right way. */ |
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vec3 f; |
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vec3_sub(f, center, eye); |
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vec3_norm(f, f); |
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vec3 s; |
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vec3_mul_cross(s, f, up); |
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vec3_norm(s, s); |
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vec3 t; |
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vec3_mul_cross(t, s, f); |
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m[0][0] = s[0]; |
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m[0][1] = t[0]; |
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m[0][2] = -f[0]; |
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m[0][3] = 0.f; |
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m[1][0] = s[1]; |
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m[1][1] = t[1]; |
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m[1][2] = -f[1]; |
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m[1][3] = 0.f; |
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m[2][0] = s[2]; |
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m[2][1] = t[2]; |
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m[2][2] = -f[2]; |
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m[2][3] = 0.f; |
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m[3][0] = 0.f; |
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m[3][1] = 0.f; |
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m[3][2] = 0.f; |
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m[3][3] = 1.f; |
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mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]); |
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} |
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typedef float quat[4]; |
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static inline void quat_identity(quat q) |
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{ |
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q[0] = q[1] = q[2] = 0.f; |
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q[3] = 1.f; |
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} |
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static inline void quat_add(quat r, quat a, quat b) |
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{ |
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int i; |
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for(i=0; i<4; ++i) |
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r[i] = a[i] + b[i]; |
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} |
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static inline void quat_sub(quat r, quat a, quat b) |
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{ |
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int i; |
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for(i=0; i<4; ++i) |
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r[i] = a[i] - b[i]; |
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} |
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static inline void quat_mul(quat r, quat p, quat q) |
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{ |
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vec3 w; |
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vec3_mul_cross(r, p, q); |
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vec3_scale(w, p, q[3]); |
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vec3_add(r, r, w); |
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vec3_scale(w, q, p[3]); |
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vec3_add(r, r, w); |
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r[3] = p[3]*q[3] - vec3_mul_inner(p, q); |
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} |
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static inline void quat_scale(quat r, quat v, float s) |
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{ |
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int i; |
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for(i=0; i<4; ++i) |
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r[i] = v[i] * s; |
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} |
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static inline float quat_inner_product(quat a, quat b) |
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{ |
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float p = 0.f; |
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int i; |
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for(i=0; i<4; ++i) |
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p += b[i]*a[i]; |
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return p; |
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} |
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static inline void quat_conj(quat r, quat q) |
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{ |
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int i; |
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for(i=0; i<3; ++i) |
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r[i] = -q[i]; |
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r[3] = q[3]; |
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} |
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static inline void quat_rotate(quat r, float angle, vec3 axis) { |
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vec3 v; |
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vec3_scale(v, axis, sinf(angle / 2)); |
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int i; |
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for(i=0; i<3; ++i) |
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r[i] = v[i]; |
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r[3] = cosf(angle / 2); |
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} |
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#define quat_norm vec4_norm |
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static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) |
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{ |
|
/* |
|
* Method by Fabian 'ryg' Giessen (of Farbrausch) |
|
t = 2 * cross(q.xyz, v) |
|
v' = v + q.w * t + cross(q.xyz, t) |
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*/ |
|
vec3 t = {q[0], q[1], q[2]}; |
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vec3 u = {q[0], q[1], q[2]}; |
|
|
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vec3_mul_cross(t, t, v); |
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vec3_scale(t, t, 2); |
|
|
|
vec3_mul_cross(u, u, t); |
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vec3_scale(t, t, q[3]); |
|
|
|
vec3_add(r, v, t); |
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vec3_add(r, r, u); |
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} |
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static inline void mat4x4_from_quat(mat4x4 M, quat q) |
|
{ |
|
float a = q[3]; |
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float b = q[0]; |
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float c = q[1]; |
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float d = q[2]; |
|
float a2 = a*a; |
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float b2 = b*b; |
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float c2 = c*c; |
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float d2 = d*d; |
|
|
|
M[0][0] = a2 + b2 - c2 - d2; |
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M[0][1] = 2.f*(b*c + a*d); |
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M[0][2] = 2.f*(b*d - a*c); |
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M[0][3] = 0.f; |
|
|
|
M[1][0] = 2*(b*c - a*d); |
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M[1][1] = a2 - b2 + c2 - d2; |
|
M[1][2] = 2.f*(c*d + a*b); |
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M[1][3] = 0.f; |
|
|
|
M[2][0] = 2.f*(b*d + a*c); |
|
M[2][1] = 2.f*(c*d - a*b); |
|
M[2][2] = a2 - b2 - c2 + d2; |
|
M[2][3] = 0.f; |
|
|
|
M[3][0] = M[3][1] = M[3][2] = 0.f; |
|
M[3][3] = 1.f; |
|
} |
|
|
|
static inline void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q) |
|
{ |
|
/* XXX: The way this is written only works for othogonal matrices. */ |
|
/* TODO: Take care of non-orthogonal case. */ |
|
quat_mul_vec3(R[0], q, M[0]); |
|
quat_mul_vec3(R[1], q, M[1]); |
|
quat_mul_vec3(R[2], q, M[2]); |
|
|
|
R[3][0] = R[3][1] = R[3][2] = 0.f; |
|
R[3][3] = 1.f; |
|
} |
|
static inline void quat_from_mat4x4(quat q, mat4x4 M) |
|
{ |
|
float r=0.f; |
|
int i; |
|
|
|
int perm[] = { 0, 1, 2, 0, 1 }; |
|
int *p = perm; |
|
|
|
for(i = 0; i<3; i++) { |
|
float m = M[i][i]; |
|
if( m < r ) |
|
continue; |
|
m = r; |
|
p = &perm[i]; |
|
} |
|
|
|
r = (float) sqrt(1.f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]] ); |
|
|
|
if(r < 1e-6) { |
|
q[0] = 1.f; |
|
q[1] = q[2] = q[3] = 0.f; |
|
return; |
|
} |
|
|
|
q[0] = r/2.f; |
|
q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]])/(2.f*r); |
|
q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]])/(2.f*r); |
|
q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]])/(2.f*r); |
|
} |
|
|
|
#endif
|
|
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