568 lines
12 KiB
C
568 lines
12 KiB
C
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#ifndef LINMATH_H
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#define LINMATH_H
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#include <math.h>
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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 sqrtf(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);
|
||
|
|
vec3_norm(R[1], R[1]);
|
||
|
|
|
||
|
|
s = vec3_mul_inner(R[0], R[1]);
|
||
|
|
vec3_scale(h, R[1], s);
|
||
|
|
vec3_sub(R[0], R[0], h);
|
||
|
|
vec3_norm(R[0], R[0]);
|
||
|
|
}
|
||
|
|
|
||
|
|
static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, float n, float f)
|
||
|
|
{
|
||
|
|
M[0][0] = 2.f*n/(r-l);
|
||
|
|
M[0][1] = M[0][2] = M[0][3] = 0.f;
|
||
|
|
|
||
|
|
M[1][1] = 2.f*n/(t-b);
|
||
|
|
M[1][0] = M[1][2] = M[1][3] = 0.f;
|
||
|
|
|
||
|
|
M[2][0] = (r+l)/(r-l);
|
||
|
|
M[2][1] = (t+b)/(t-b);
|
||
|
|
M[2][2] = -(f+n)/(f-n);
|
||
|
|
M[2][3] = -1.f;
|
||
|
|
|
||
|
|
M[3][2] = -2.f*(f*n)/(f-n);
|
||
|
|
M[3][0] = M[3][1] = M[3][3] = 0.f;
|
||
|
|
}
|
||
|
|
static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, float n, float f)
|
||
|
|
{
|
||
|
|
M[0][0] = 2.f/(r-l);
|
||
|
|
M[0][1] = M[0][2] = M[0][3] = 0.f;
|
||
|
|
|
||
|
|
M[1][1] = 2.f/(t-b);
|
||
|
|
M[1][0] = M[1][2] = M[1][3] = 0.f;
|
||
|
|
|
||
|
|
M[2][2] = -2.f/(f-n);
|
||
|
|
M[2][0] = M[2][1] = M[2][3] = 0.f;
|
||
|
|
|
||
|
|
M[3][0] = -(r+l)/(r-l);
|
||
|
|
M[3][1] = -(t+b)/(t-b);
|
||
|
|
M[3][2] = -(f+n)/(f-n);
|
||
|
|
M[3][3] = 1.f;
|
||
|
|
}
|
||
|
|
static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect, float n, float f)
|
||
|
|
{
|
||
|
|
/* NOTE: Degrees are an unhandy unit to work with.
|
||
|
|
* linmath.h uses radians for everything! */
|
||
|
|
float const a = 1.f / (float) tan(y_fov / 2.f);
|
||
|
|
|
||
|
|
m[0][0] = a / aspect;
|
||
|
|
m[0][1] = 0.f;
|
||
|
|
m[0][2] = 0.f;
|
||
|
|
m[0][3] = 0.f;
|
||
|
|
|
||
|
|
m[1][0] = 0.f;
|
||
|
|
m[1][1] = a;
|
||
|
|
m[1][2] = 0.f;
|
||
|
|
m[1][3] = 0.f;
|
||
|
|
|
||
|
|
m[2][0] = 0.f;
|
||
|
|
m[2][1] = 0.f;
|
||
|
|
m[2][2] = -((f + n) / (f - n));
|
||
|
|
m[2][3] = -1.f;
|
||
|
|
|
||
|
|
m[3][0] = 0.f;
|
||
|
|
m[3][1] = 0.f;
|
||
|
|
m[3][2] = -((2.f * f * n) / (f - n));
|
||
|
|
m[3][3] = 0.f;
|
||
|
|
}
|
||
|
|
static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up)
|
||
|
|
{
|
||
|
|
/* Adapted from Android's OpenGL Matrix.java. */
|
||
|
|
/* See the OpenGL GLUT documentation for gluLookAt for a description */
|
||
|
|
/* of the algorithm. We implement it in a straightforward way: */
|
||
|
|
|
||
|
|
/* TODO: The negation of of can be spared by swapping the order of
|
||
|
|
* operands in the following cross products in the right way. */
|
||
|
|
vec3 f;
|
||
|
|
vec3_sub(f, center, eye);
|
||
|
|
vec3_norm(f, f);
|
||
|
|
|
||
|
|
vec3 s;
|
||
|
|
vec3_mul_cross(s, f, up);
|
||
|
|
vec3_norm(s, s);
|
||
|
|
|
||
|
|
vec3 t;
|
||
|
|
vec3_mul_cross(t, s, f);
|
||
|
|
|
||
|
|
m[0][0] = s[0];
|
||
|
|
m[0][1] = t[0];
|
||
|
|
m[0][2] = -f[0];
|
||
|
|
m[0][3] = 0.f;
|
||
|
|
|
||
|
|
m[1][0] = s[1];
|
||
|
|
m[1][1] = t[1];
|
||
|
|
m[1][2] = -f[1];
|
||
|
|
m[1][3] = 0.f;
|
||
|
|
|
||
|
|
m[2][0] = s[2];
|
||
|
|
m[2][1] = t[2];
|
||
|
|
m[2][2] = -f[2];
|
||
|
|
m[2][3] = 0.f;
|
||
|
|
|
||
|
|
m[3][0] = 0.f;
|
||
|
|
m[3][1] = 0.f;
|
||
|
|
m[3][2] = 0.f;
|
||
|
|
m[3][3] = 1.f;
|
||
|
|
|
||
|
|
mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]);
|
||
|
|
}
|
||
|
|
|
||
|
|
typedef float quat[4];
|
||
|
|
static inline void quat_identity(quat q)
|
||
|
|
{
|
||
|
|
q[0] = q[1] = q[2] = 0.f;
|
||
|
|
q[3] = 1.f;
|
||
|
|
}
|
||
|
|
static inline void quat_add(quat r, quat a, quat b)
|
||
|
|
{
|
||
|
|
int i;
|
||
|
|
for(i=0; i<4; ++i)
|
||
|
|
r[i] = a[i] + b[i];
|
||
|
|
}
|
||
|
|
static inline void quat_sub(quat r, quat a, quat b)
|
||
|
|
{
|
||
|
|
int i;
|
||
|
|
for(i=0; i<4; ++i)
|
||
|
|
r[i] = a[i] - b[i];
|
||
|
|
}
|
||
|
|
static inline void quat_mul(quat r, quat p, quat q)
|
||
|
|
{
|
||
|
|
vec3 w;
|
||
|
|
vec3_mul_cross(r, p, q);
|
||
|
|
vec3_scale(w, p, q[3]);
|
||
|
|
vec3_add(r, r, w);
|
||
|
|
vec3_scale(w, q, p[3]);
|
||
|
|
vec3_add(r, r, w);
|
||
|
|
r[3] = p[3]*q[3] - vec3_mul_inner(p, q);
|
||
|
|
}
|
||
|
|
static inline void quat_scale(quat r, quat v, float s)
|
||
|
|
{
|
||
|
|
int i;
|
||
|
|
for(i=0; i<4; ++i)
|
||
|
|
r[i] = v[i] * s;
|
||
|
|
}
|
||
|
|
static inline float quat_inner_product(quat a, quat b)
|
||
|
|
{
|
||
|
|
float p = 0.f;
|
||
|
|
int i;
|
||
|
|
for(i=0; i<4; ++i)
|
||
|
|
p += b[i]*a[i];
|
||
|
|
return p;
|
||
|
|
}
|
||
|
|
static inline void quat_conj(quat r, quat q)
|
||
|
|
{
|
||
|
|
int i;
|
||
|
|
for(i=0; i<3; ++i)
|
||
|
|
r[i] = -q[i];
|
||
|
|
r[3] = q[3];
|
||
|
|
}
|
||
|
|
static inline void quat_rotate(quat r, float angle, vec3 axis) {
|
||
|
|
vec3 v;
|
||
|
|
vec3_scale(v, axis, sinf(angle / 2));
|
||
|
|
int i;
|
||
|
|
for(i=0; i<3; ++i)
|
||
|
|
r[i] = v[i];
|
||
|
|
r[3] = cosf(angle / 2);
|
||
|
|
}
|
||
|
|
#define quat_norm vec4_norm
|
||
|
|
static inline void quat_mul_vec3(vec3 r, quat q, vec3 v)
|
||
|
|
{
|
||
|
|
/*
|
||
|
|
* Method by Fabian 'ryg' Giessen (of Farbrausch)
|
||
|
|
t = 2 * cross(q.xyz, v)
|
||
|
|
v' = v + q.w * t + cross(q.xyz, t)
|
||
|
|
*/
|
||
|
|
vec3 t = {q[0], q[1], q[2]};
|
||
|
|
vec3 u = {q[0], q[1], q[2]};
|
||
|
|
|
||
|
|
vec3_mul_cross(t, t, v);
|
||
|
|
vec3_scale(t, t, 2);
|
||
|
|
|
||
|
|
vec3_mul_cross(u, u, t);
|
||
|
|
vec3_scale(t, t, q[3]);
|
||
|
|
|
||
|
|
vec3_add(r, v, t);
|
||
|
|
vec3_add(r, r, u);
|
||
|
|
}
|
||
|
|
static inline void mat4x4_from_quat(mat4x4 M, quat q)
|
||
|
|
{
|
||
|
|
float a = q[3];
|
||
|
|
float b = q[0];
|
||
|
|
float c = q[1];
|
||
|
|
float d = q[2];
|
||
|
|
float a2 = a*a;
|
||
|
|
float b2 = b*b;
|
||
|
|
float c2 = c*c;
|
||
|
|
float d2 = d*d;
|
||
|
|
|
||
|
|
M[0][0] = a2 + b2 - c2 - d2;
|
||
|
|
M[0][1] = 2.f*(b*c + a*d);
|
||
|
|
M[0][2] = 2.f*(b*d - a*c);
|
||
|
|
M[0][3] = 0.f;
|
||
|
|
|
||
|
|
M[1][0] = 2*(b*c - a*d);
|
||
|
|
M[1][1] = a2 - b2 + c2 - d2;
|
||
|
|
M[1][2] = 2.f*(c*d + a*b);
|
||
|
|
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 = sqrtf(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
|
