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author | Wolfgang Draxinger <dw@optores.de> | 2019-10-30 16:06:31 +0100 |
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committer | Wolfgang Draxinger <dw@optores.de> | 2019-10-30 16:06:31 +0100 |
commit | 6eb6a0bafa4c8ee985d46fe7b6737cf01906b348 (patch) | |
tree | 74059137605c056481e3cad9822d81b8de3e05ef | |
parent | 50ed4019c084ff1496b8d1b0407e715e9586e7aa (diff) | |
parent | a9b5d0a55e369ccce74a8804c543a2d98827ac31 (diff) | |
download | linmath.h-6eb6a0bafa4c8ee985d46fe7b6737cf01906b348.tar.gz linmath.h-6eb6a0bafa4c8ee985d46fe7b6737cf01906b348.tar.bz2 |
transplanted arcball function
-rw-r--r-- | linmath.h | 518 |
1 files changed, 323 insertions, 195 deletions
@@ -1,42 +1,35 @@ #ifndef LINMATH_H #define LINMATH_H -#if __STDC_VERSION__ < 199901L -# ifndef inline -# if defined(_MSC_VER) -# define inline __inline -# elif defined(__GNUC__) -# define inline __inline__ -# else -# define inline -# endif -# endif -#endif - #include <math.h> -#include <string.h> + +#ifdef LINMATH_NO_INLINE +#define LINMATH_H_FUNC static +#else +#define LINMATH_H_FUNC static inline +#endif #define LINMATH_H_DEFINE_VEC(n) \ typedef float vec##n[n]; \ -static inline void vec##n##_add(vec##n r, vec##n a, vec##n b) \ +LINMATH_H_FUNC void vec##n##_add(vec##n r, vec##n const a, vec##n const b) \ { \ int i; \ for(i=0; i<n; ++i) \ r[i] = a[i] + b[i]; \ } \ -static inline void vec##n##_sub(vec##n r, vec##n a, vec##n b) \ +LINMATH_H_FUNC void vec##n##_sub(vec##n r, vec##n const a, vec##n const b) \ { \ int i; \ for(i=0; i<n; ++i) \ r[i] = a[i] - b[i]; \ } \ -static inline void vec##n##_scale(vec##n r, vec##n v, float s) \ +LINMATH_H_FUNC void vec##n##_scale(vec##n r, vec##n const v, float const s) \ { \ int i; \ for(i=0; i<n; ++i) \ r[i] = v[i] * s; \ } \ -static inline float vec##n##_mul_inner(vec##n a, vec##n b) \ +LINMATH_H_FUNC float vec##n##_mul_inner(vec##n const a, vec##n const b) \ { \ float p = 0.; \ int i; \ @@ -44,119 +37,169 @@ static inline float vec##n##_mul_inner(vec##n a, vec##n b) \ p += b[i]*a[i]; \ return p; \ } \ -static inline float vec##n##_len(vec##n v) \ +LINMATH_H_FUNC float vec##n##_len(vec##n const v) \ { \ return sqrtf(vec##n##_mul_inner(v,v)); \ } \ -static inline void vec##n##_norm(vec##n r, vec##n v) \ +LINMATH_H_FUNC void vec##n##_norm(vec##n r, vec##n const v) \ { \ float k = 1.0 / vec##n##_len(v); \ vec##n##_scale(r, v, k); \ +} \ +LINMATH_H_FUNC void vec##n##_min(vec##n r, vec##n const a, vec##n const b) \ +{ \ + int i; \ + for(i=0; i<n; ++i) \ + r[i] = a[i]<b[i] ? a[i] : b[i]; \ +} \ +LINMATH_H_FUNC void vec##n##_max(vec##n r, vec##n const a, vec##n const b) \ +{ \ + int i; \ + for(i=0; i<n; ++i) \ + r[i] = a[i]>b[i] ? a[i] : b[i]; \ } -LINMATH_H_DEFINE_VEC(2); -LINMATH_H_DEFINE_VEC(3); -LINMATH_H_DEFINE_VEC(4); +LINMATH_H_DEFINE_VEC(2) +LINMATH_H_DEFINE_VEC(3) +LINMATH_H_DEFINE_VEC(4) + +LINMATH_H_FUNC void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b) +{ + r[0] = a[1]*b[2] - a[2]*b[1]; + r[1] = a[2]*b[0] - a[0]*b[2]; + r[2] = a[0]*b[1] - a[1]*b[0]; +} -static inline void vec3_mul_cross(vec3 r, vec3 a, vec3 b) +LINMATH_H_FUNC void vec3_reflect(vec3 r, vec3 const v, vec3 const n) { - vec3 c; - c[0] = a[1]*b[2] - a[2]*b[1]; - c[1] = a[2]*b[0] - a[0]*b[2]; - c[2] = a[0]*b[1] - a[1]*b[0]; - memcpy(r, c, sizeof(c)); + float p = 2.f*vec3_mul_inner(v, n); + int i; + for(i=0;i<3;++i) + r[i] = v[i] - p*n[i]; } -static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b) +LINMATH_H_FUNC void vec4_mul_cross(vec4 r, vec4 a, vec4 b) { - vec4 c; - c[0] = a[1]*b[2] - a[2]*b[1]; - c[1] = a[2]*b[0] - a[0]*b[2]; - c[2] = a[0]*b[1] - a[1]*b[0]; - c[3] = 1.; - memcpy(r, c, sizeof(c)); + r[0] = a[1]*b[2] - a[2]*b[1]; + r[1] = a[2]*b[0] - a[0]*b[2]; + r[2] = a[0]*b[1] - a[1]*b[0]; + r[3] = 1.f; +} + +LINMATH_H_FUNC void vec4_reflect(vec4 r, vec4 v, vec4 n) +{ + float p = 2.f*vec4_mul_inner(v, n); + int i; + for(i=0;i<4;++i) + r[i] = v[i] - p*n[i]; } typedef vec4 mat4x4[4]; -static inline void mat4x4_identity(mat4x4 M) +LINMATH_H_FUNC void mat4x4_identity(mat4x4 M) { int i, j; - for(j=0; j<4; ++j) for(i=0; i<4; ++i) { - M[i][j] = i==j ? 1 : 0; - } + for(i=0; i<4; ++i) + for(j=0; j<4; ++j) + M[i][j] = i==j ? 1.f : 0.f; } -static inline void mat4x4_dup(mat4x4 M, mat4x4 N) +LINMATH_H_FUNC void mat4x4_dup(mat4x4 M, mat4x4 N) { int i, j; - for(j=0; j<4; ++j) { - for(i=0; i<4; ++i) { + for(i=0; i<4; ++i) + for(j=0; j<4; ++j) M[i][j] = N[i][j]; - } - } } -static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) +LINMATH_H_FUNC void mat4x4_row(vec4 r, mat4x4 M, int i) +{ + int k; + for(k=0; k<4; ++k) + r[k] = M[k][i]; +} +LINMATH_H_FUNC void mat4x4_col(vec4 r, mat4x4 M, int i) +{ + int k; + for(k=0; k<4; ++k) + r[k] = M[i][k]; +} +LINMATH_H_FUNC void mat4x4_transpose(mat4x4 M, mat4x4 N) +{ + int i, j; + for(j=0; j<4; ++j) + for(i=0; i<4; ++i) + M[i][j] = N[j][i]; +} +LINMATH_H_FUNC void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) { int i; for(i=0; i<4; ++i) vec4_add(M[i], a[i], b[i]); } -static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) +LINMATH_H_FUNC void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) { int i; for(i=0; i<4; ++i) vec4_sub(M[i], a[i], b[i]); } -static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k) +LINMATH_H_FUNC void mat4x4_scale(mat4x4 M, mat4x4 a, float k) { int i; for(i=0; i<4; ++i) vec4_scale(M[i], a[i], k); } -static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, float z) +LINMATH_H_FUNC void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, float z) { + int i; vec4_scale(M[0], a[0], x); vec4_scale(M[1], a[1], y); vec4_scale(M[2], a[2], z); + for(i = 0; i < 4; ++i) { + M[3][i] = a[3][i]; + } } -static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) +LINMATH_H_FUNC void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) { + mat4x4 temp; int k, r, c; - mat4x4 R; - for(r=0; r<4; ++r) for(c=0; c<4; ++c) { - R[c][r] = 0; - for(k=0; k<4; ++k) { - R[c][r] += a[k][r] * b[c][k]; - } + for(c=0; c<4; ++c) for(r=0; r<4; ++r) { + temp[c][r] = 0.f; + for(k=0; k<4; ++k) + temp[c][r] += a[k][r] * b[c][k]; } - memcpy(M, R, sizeof(R)); + mat4x4_dup(M, temp); } -static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) +LINMATH_H_FUNC void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) { - vec4 r_; int i, j; for(j=0; j<4; ++j) { - r_[j] = 0.; - for(i=0; i<4; ++i) { - r_[j] += M[i][j] * v[i]; - } + r[j] = 0.f; + for(i=0; i<4; ++i) + r[j] += M[i][j] * v[i]; } - memcpy(r, r_, sizeof(r_)); } -static inline void mat4x4_translate(mat4x4 T, float x, float y, float z) +LINMATH_H_FUNC void mat4x4_translate(mat4x4 T, float x, float y, float z) { mat4x4_identity(T); T[3][0] = x; T[3][1] = y; T[3][2] = z; } -static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) +LINMATH_H_FUNC void mat4x4_translate_in_place(mat4x4 M, float x, float y, float z) { - int i, j; - for(i=0; i<4; ++i) for(j=0; j<4; ++j) { - M[i][j] = i<3 && j<3 ? a[i] * b[j] : 0.; + vec4 t = {x, y, z, 0}; + vec4 r; + int i; + for (i = 0; i < 4; ++i) { + mat4x4_row(r, M, i); + M[3][i] += vec4_mul_inner(r, t); } } -static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle) +LINMATH_H_FUNC void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) +{ + int i, j; + for(i=0; i<4; ++i) for(j=0; j<4; ++j) + M[i][j] = i<3 && j<3 ? a[i] * b[j] : 0.f; +} +LINMATH_H_FUNC void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle) { float s = sinf(angle); float c = cosf(angle); @@ -190,90 +233,84 @@ static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, mat4x4_dup(R, M); } } -static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) +LINMATH_H_FUNC void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) { float s = sinf(angle); float c = cosf(angle); mat4x4 R = { - {1, 0, 0, 0}, - {0, c, s, 0}, - {0,-s, c, 0}, - {0, 0, 0, 1} + {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} }; mat4x4_mul(Q, M, R); } -static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) +LINMATH_H_FUNC void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) { float s = sinf(angle); float c = cosf(angle); mat4x4 R = { - { c, 0, s, 0}, - { 0, 1, 0, 0}, - {-s, 0, c, 0}, - { 0, 0, 0, 1} + { 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} }; mat4x4_mul(Q, M, R); } -static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) +LINMATH_H_FUNC void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) { float s = sinf(angle); float c = cosf(angle); mat4x4 R = { - { c, s, 0, 0}, - {-s, c, 0, 0}, - { 0, 0, 1, 0}, - { 0, 0, 0, 1} + { 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} }; mat4x4_mul(Q, M, R); } -static inline void mat4x4_row(vec4 r, mat4x4 M, int i) -{ - int k; - for(k=0; k<4; ++k) - r[k] = M[k][i]; -} -static inline void mat4x4_col(vec4 r, mat4x4 M, int i) -{ - int k; - for(k=0; k<4; ++k) - r[k] = M[i][k]; -} -static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) -{ - int i, j; - mat4x4 R; - for(j=0; j<4; ++j) { - for(i=0; i<4; ++i) { - R[i][j] = N[j][i]; - } - } - memcpy(M, R, sizeof(R)); -} -static inline void mat4x4_invert(mat4x4 T, mat4x4 M) -{ - mat4x4 R; - R[0][0] = M[1][1]*(M[2][2]*M[3][3] - M[2][3]*M[3][2]) - M[2][1]*(M[1][2]*M[3][3] - M[1][3]*M[3][2]) - M[3][1]*(M[1][3]*M[2][2] - M[1][2]*M[2][3]); - R[0][1] = M[0][1]*(M[2][3]*M[3][2] - M[2][2]*M[3][3]) - M[2][1]*(M[0][3]*M[3][2] - M[0][2]*M[3][3]) - M[3][1]*(M[0][2]*M[2][3] - M[0][3]*M[2][2]); - R[0][2] = M[0][1]*(M[1][2]*M[3][3] - M[1][3]*M[3][2]) - M[1][1]*(M[0][2]*M[3][3] - M[0][3]*M[3][2]) - M[3][1]*(M[0][3]*M[1][2] - M[0][2]*M[1][3]); - R[0][3] = M[0][1]*(M[1][3]*M[2][2] - M[1][2]*M[2][3]) - M[1][1]*(M[0][3]*M[2][2] - M[0][2]*M[2][3]) - M[2][1]*(M[0][2]*M[1][3] - M[0][3]*M[1][2]); +LINMATH_H_FUNC void mat4x4_invert(mat4x4 T, mat4x4 M) +{ + float s[6]; + float c[6]; + s[0] = M[0][0]*M[1][1] - M[1][0]*M[0][1]; + s[1] = M[0][0]*M[1][2] - M[1][0]*M[0][2]; + s[2] = M[0][0]*M[1][3] - M[1][0]*M[0][3]; + s[3] = M[0][1]*M[1][2] - M[1][1]*M[0][2]; + s[4] = M[0][1]*M[1][3] - M[1][1]*M[0][3]; + s[5] = M[0][2]*M[1][3] - M[1][2]*M[0][3]; + + c[0] = M[2][0]*M[3][1] - M[3][0]*M[2][1]; + c[1] = M[2][0]*M[3][2] - M[3][0]*M[2][2]; + c[2] = M[2][0]*M[3][3] - M[3][0]*M[2][3]; + c[3] = M[2][1]*M[3][2] - M[3][1]*M[2][2]; + c[4] = M[2][1]*M[3][3] - M[3][1]*M[2][3]; + c[5] = M[2][2]*M[3][3] - M[3][2]*M[2][3]; + + /* Assumes it is invertible */ + 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] ); + + T[0][0] = ( M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet; + T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet; + T[0][2] = ( M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet; + T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet; - R[1][0] = M[1][0]*(M[2][3]*M[3][2] - M[2][2]*M[3][3]) - M[2][0]*(M[1][3]*M[3][2] - M[1][2]*M[3][3]) - M[3][0]*(M[1][2]*M[2][3] - M[1][3]*M[2][2]); - R[1][1] = M[0][0]*(M[2][2]*M[3][3] - M[2][3]*M[3][2]) - M[2][0]*(M[0][2]*M[3][3] - M[0][3]*M[3][2]) - M[3][0]*(M[0][3]*M[2][2] - M[0][2]*M[2][3]); - R[1][2] = M[0][0]*(M[1][3]*M[3][2] - M[1][2]*M[3][3]) - M[1][0]*(M[0][3]*M[3][2] - M[0][2]*M[3][3]) - M[3][0]*(M[0][2]*M[1][3] - M[0][3]*M[1][2]); - R[1][3] = M[0][0]*(M[1][2]*M[2][3] - M[1][3]*M[2][2]) - M[1][0]*(M[0][2]*M[2][3] - M[0][3]*M[2][2]) - M[2][0]*(M[0][3]*M[1][2] - M[0][2]*M[1][3]); + T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet; + T[1][1] = ( M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet; + T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet; + T[1][3] = ( M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet; - R[2][0] = M[1][0]*(M[2][1]*M[3][3] - M[2][3]*M[3][1]) - M[2][0]*(M[1][1]*M[3][3] - M[1][3]*M[3][1]) - M[3][0]*(M[1][3]*M[2][1] - M[1][1]*M[2][3]); - R[2][1] = M[0][0]*(M[2][3]*M[3][1] - M[2][1]*M[3][3]) - M[2][0]*(M[0][3]*M[3][1] - M[0][1]*M[3][3]) - M[3][0]*(M[0][1]*M[2][3] - M[0][3]*M[2][1]); - R[2][2] = M[0][0]*(M[1][1]*M[3][3] - M[1][3]*M[3][1]) - M[1][0]*(M[0][1]*M[3][3] - M[0][3]*M[3][1]) - M[3][0]*(M[0][3]*M[1][1] - M[0][1]*M[1][3]); - R[2][3] = M[0][0]*(M[1][3]*M[2][1] - M[1][1]*M[2][3]) - M[1][0]*(M[0][3]*M[2][1] - M[0][1]*M[2][3]) - M[2][0]*(M[0][1]*M[1][3] - M[0][3]*M[1][1]); + T[2][0] = ( M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet; + T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet; + T[2][2] = ( M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet; + T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet; - R[3][0] = M[1][0]*(M[2][2]*M[3][1] - M[2][1]*M[3][2]) - M[2][0]*(M[1][2]*M[3][1] - M[1][1]*M[3][2]) - M[3][0]*(M[1][1]*M[2][2] - M[1][2]*M[2][1]); - R[3][1] = M[0][0]*(M[2][1]*M[3][2] - M[2][2]*M[3][1]) - M[2][0]*(M[0][1]*M[3][2] - M[0][2]*M[3][1]) - M[3][0]*(M[0][2]*M[2][1] - M[0][1]*M[2][2]); - R[3][2] = M[0][0]*(M[1][2]*M[3][1] - M[1][1]*M[3][2]) - M[1][0]*(M[0][2]*M[3][1] - M[0][1]*M[3][2]) - M[3][0]*(M[0][1]*M[1][2] - M[0][2]*M[1][1]); - R[3][3] = M[0][0]*(M[1][1]*M[2][2] - M[1][2]*M[2][1]) - M[1][0]*(M[0][1]*M[2][2] - M[0][2]*M[2][1]) - M[2][0]*(M[0][2]*M[1][1] - M[0][1]*M[1][2]); - memcpy(T, R, 16*sizeof(float)); + T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet; + T[3][1] = ( M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet; + T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet; + T[3][3] = ( M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet; } -static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) +LINMATH_H_FUNC void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) { mat4x4_dup(R, M); float s = 1.; @@ -284,12 +321,11 @@ static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) s = vec3_mul_inner(R[1], R[2]); vec3_scale(h, R[2], s); vec3_sub(R[1], R[1], h); - vec3_norm(R[2], R[2]); + vec3_norm(R[1], R[1]); - s = vec3_mul_inner(R[1], R[2]); + s = vec3_mul_inner(R[0], R[2]); vec3_scale(h, R[2], s); - vec3_sub(R[1], R[1], h); - vec3_norm(R[1], R[1]); + vec3_sub(R[0], R[0], h); s = vec3_mul_inner(R[0], R[1]); vec3_scale(h, R[1], s); @@ -297,58 +333,125 @@ static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) 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) +LINMATH_H_FUNC void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, float n, float f) { - M[0][0] = 2.*n/(r-l); - M[0][1] = M[0][2] = M[0][3] = 0.; + M[0][0] = 2.f*n/(r-l); + M[0][1] = M[0][2] = M[0][3] = 0.f; M[1][1] = 2.*n/(t-b); - M[1][0] = M[1][2] = M[1][3] = 0.; + 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; + M[2][3] = -1.f; - M[3][2] = -2.*(f*n)/(f-n); - M[3][0] = M[3][1] = M[3][3] = 0.; + 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) +LINMATH_H_FUNC void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, float n, float f) { - M[0][0] = 2./(r-l); - M[0][1] = M[0][2] = M[0][3] = 0.; + M[0][0] = 2.f/(r-l); + M[0][1] = M[0][2] = M[0][3] = 0.f; - M[1][1] = 2./(t-b); - M[1][0] = M[1][2] = M[1][3] = 0.; + M[1][1] = 2.f/(t-b); + M[1][0] = M[1][2] = M[1][3] = 0.f; - M[2][2] = -2./(f-n); - M[2][0] = M[2][1] = M[2][3] = 0.; + 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; +} +LINMATH_H_FUNC 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 / 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; +} +LINMATH_H_FUNC 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); - 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.; + 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) +LINMATH_H_FUNC void quat_identity(quat q) { - q[0] = q[1] = q[2] = 0.; - q[3] = 1.; + q[0] = q[1] = q[2] = 0.f; + q[3] = 1.f; } -static inline void quat_add(quat r, quat a, quat b) +LINMATH_H_FUNC 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) +LINMATH_H_FUNC 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) +LINMATH_H_FUNC void quat_mul(quat r, quat p, quat q) { vec3 w; vec3_mul_cross(r, p, q); @@ -358,40 +461,57 @@ static inline void quat_mul(quat r, quat p, quat q) 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) +LINMATH_H_FUNC 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) +LINMATH_H_FUNC float quat_inner_product(quat a, quat b) { - float p = 0.; + 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) +LINMATH_H_FUNC 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_norm(quat r, quat v) { vec4_norm(r, v); } -static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) +LINMATH_H_FUNC 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 +LINMATH_H_FUNC void quat_mul_vec3(vec3 r, quat q, vec3 v) { - quat q_; - quat v_ = {v[0], v[1], v[2], 0.}; +/* + * Method by Fabian 'ryg' Giessen (of Farbrausch) +t = 2 * cross(q.xyz, v) +v' = v + q.w * t + cross(q.xyz, t) + */ + vec3 t; + vec3 q_xyz = {q[0], q[1], q[2]}; + vec3 u = {q[0], q[1], q[2]}; + + vec3_mul_cross(t, q_xyz, v); + vec3_scale(t, t, 2); - quat_conj(q_, q); - quat_norm(q_, q_); - quat_mul(q_, v_, q_); - quat_mul(q_, q, q_); - memcpy(r, q_, 3*sizeof(float)); + vec3_mul_cross(u, q_xyz, 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) +LINMATH_H_FUNC void mat4x4_from_quat(mat4x4 M, quat q) { float a = q[3]; float b = q[0]; @@ -403,35 +523,38 @@ static inline void mat4x4_from_quat(mat4x4 M, quat q) float d2 = d*d; M[0][0] = a2 + b2 - c2 - d2; - M[0][1] = 2*(b*c + a*d); - M[0][2] = 2*(b*d - a*c); - M[0][3] = 0.; + 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*(c*d + a*b); - M[1][3] = 0.; + M[1][2] = 2.f*(c*d + a*b); + M[1][3] = 0.f; - M[2][0] = 2*(b*d + a*c); - M[2][1] = 2*(c*d - a*b); + 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.; + M[2][3] = 0.f; - M[3][0] = M[3][1] = M[3][2] = 0.; - M[3][3] = 1.; + M[3][0] = M[3][1] = M[3][2] = 0.f; + M[3][3] = 1.f; } -static inline void mat4x4_mul_quat(mat4x4 R, mat4x4 M, quat q) + +LINMATH_H_FUNC void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q) { - quat_mul_vec3(R[0], M[0], q); - quat_mul_vec3(R[1], M[1], q); - quat_mul_vec3(R[2], M[2], 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.; - R[3][3] = 1.; + 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) +LINMATH_H_FUNC void quat_from_mat4x4(quat q, mat4x4 M) { - float r=0.; + float r=0.f; int i; int perm[] = { 0, 1, 2, 0, 1 }; @@ -445,15 +568,21 @@ static inline void quat_from_mat4x4(quat q, mat4x4 M) p = &perm[i]; } - r = sqrtf(1. + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]] ); + r = sqrtf(1.f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]] ); - q[0] = r/2.; - q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]])/(2.*r); - q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]])/(2.*r); - q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]])/(2.*r); + 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); } -static inline void mat4x4_arcball(mat4x4 R, mat4x4 M, vec2 _a, vec2 _b, float s) +LINMATH_H_FUNC mat4x4_arcball(mat4x4 R, mat4x4 M, vec2 _a, vec2 _b, float s) { vec2 a; memcpy(a, _a, sizeof(a)); vec2 b; memcpy(b, _b, sizeof(b)); @@ -482,5 +611,4 @@ static inline void mat4x4_arcball(mat4x4 R, mat4x4 M, vec2 _a, vec2 _b, float s) float const angle = acos(vec3_mul_inner(a_, b_)) * s; mat4x4_rotate(R, M, c_[0], c_[1], c_[2], angle); } - #endif |