diff options
-rw-r--r-- | README | 2 | ||||
-rw-r--r-- | linmath.h | 332 |
2 files changed, 203 insertions, 131 deletions
@@ -1,6 +1,6 @@ # linmath.h -- A small library for linear math as required for computer graphics -linmath.h provides the most used types required programming computer graphice: +linmath.h provides the most used types required for programming computer graphics: vec3 -- 3 element vector of floats vec4 -- 4 element vector of floats (4th component used for homogenous computations) @@ -3,100 +3,90 @@ #include <math.h> -typedef float vec3[3]; -static inline void vec3_add(vec3 r, vec3 a, vec3 b) -{ - int i; - for(i=0; i<3; ++i) - r[i] = a[i] + b[i]; -} -static inline void vec3_sub(vec3 r, vec3 a, vec3 b) -{ - int i; - for(i=0; i<3; ++i) - r[i] = a[i] - b[i]; -} -static inline void vec3_scale(vec3 r, vec3 v, float s) -{ - int i; - for(i=0; i<3; ++i) - r[i] = v[i] * s; -} -static inline float vec3_mul_inner(vec3 a, vec3 b) -{ - float p = 0.f; - int i; - for(i=0; i<3; ++i) - p += b[i]*a[i]; - return p; -} -static inline void vec3_mul_cross(vec3 r, vec3 a, vec3 b) +#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]; \ +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]; \ +} \ +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]; \ +} \ +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; \ +} \ +LINMATH_H_FUNC float vec##n##_mul_inner(vec##n const a, vec##n const b) \ +{ \ + float p = 0.f; \ + int i; \ + for(i=0; i<n; ++i) \ + p += b[i]*a[i]; \ + return p; \ +} \ +LINMATH_H_FUNC float vec##n##_len(vec##n const v) \ +{ \ + return sqrtf(vec##n##_mul_inner(v,v)); \ +} \ +LINMATH_H_FUNC void vec##n##_norm(vec##n r, vec##n const v) \ +{ \ + float k = 1.f / 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_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 float vec3_len(vec3 v) -{ - return sqrtf(vec3_mul_inner(v, v)); -} -static inline void vec3_norm(vec3 r, vec3 v) -{ - float k = 1.f / vec3_len(v); - vec3_scale(r, v, k); -} -static inline void vec3_reflect(vec3 r, vec3 v, vec3 n) + +LINMATH_H_FUNC void vec3_reflect(vec3 r, vec3 const v, vec3 const n) { - float p = 2.f*vec3_mul_inner(v, n); + float p = 2.f * vec3_mul_inner(v, n); int i; for(i=0;i<3;++i) r[i] = v[i] - p*n[i]; } -typedef float vec4[4]; -static inline void vec4_add(vec4 r, vec4 a, vec4 b) -{ - int i; - for(i=0; i<4; ++i) - r[i] = a[i] + b[i]; -} -static inline void vec4_sub(vec4 r, vec4 a, vec4 b) -{ - int i; - for(i=0; i<4; ++i) - r[i] = a[i] - b[i]; -} -static inline void vec4_scale(vec4 r, vec4 v, float s) -{ - int i; - for(i=0; i<4; ++i) - r[i] = v[i] * s; -} -static inline float vec4_mul_inner(vec4 a, vec4 b) -{ - float p = 0.f; - int i; - for(i=0; i<4; ++i) - p += b[i]*a[i]; - return p; -} -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) { 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; } -static inline float vec4_len(vec4 v) -{ - return sqrtf(vec4_mul_inner(v, v)); -} -static inline void vec4_norm(vec4 r, vec4 v) -{ - float k = 1.f / vec4_len(v); - vec4_scale(r, v, k); -} -static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) + +LINMATH_H_FUNC void vec4_reflect(vec4 r, vec4 v, vec4 n) { float p = 2.f*vec4_mul_inner(v, n); int i; @@ -105,73 +95,79 @@ static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) } typedef vec4 mat4x4[4]; -static inline void mat4x4_identity(mat4x4 M) +LINMATH_H_FUNC void mat4x4_identity(mat4x4 M) { int i, j; 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(i=0; i<4; ++i) for(j=0; j<4; ++j) M[i][j] = N[i][j]; } -static inline void mat4x4_row(vec4 r, mat4x4 M, int i) +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]; } -static inline void mat4x4_col(vec4 r, mat4x4 M, int 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]; } -static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) +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]; } -static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) +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; for(c=0; c<4; ++c) for(r=0; r<4; ++r) { - M[c][r] = 0.f; + temp[c][r] = 0.f; for(k=0; k<4; ++k) - M[c][r] += a[k][r] * b[c][k]; + temp[c][r] += a[k][r] * b[c][k]; } + 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) { int i, j; for(j=0; j<4; ++j) { @@ -180,14 +176,14 @@ static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) r[j] += M[i][j] * v[i]; } } -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_translate_in_place(mat4x4 M, float x, float y, float z) +LINMATH_H_FUNC void mat4x4_translate_in_place(mat4x4 M, float x, float y, float z) { vec4 t = {x, y, z, 0}; vec4 r; @@ -197,28 +193,28 @@ static inline void mat4x4_translate_in_place(mat4x4 M, float x, float y, float z M[3][i] += vec4_mul_inner(r, t); } } -static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) +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; } -static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, float angle) +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); vec3 u = {x, y, z}; - vec3_norm(u, u); - { + if(vec3_len(u) > 1e-4) { + vec3_norm(u, u); mat4x4 T; mat4x4_from_vec3_mul_outer(T, u, u); mat4x4 S = { - { 0.f, u[2], -u[1], 0.f}, - {-u[2], 0.f, u[0], 0.f}, - { u[1], -u[0], 0.f, 0.f}, - { 0.f, 0.f, 0.f, 0.f} + { 0, u[2], -u[1], 0}, + {-u[2], 0, u[0], 0}, + { u[1], -u[0], 0, 0}, + { 0, 0, 0, 0} }; mat4x4_scale(S, S, s); @@ -231,11 +227,13 @@ static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, mat4x4_add(T, T, C); mat4x4_add(T, T, S); - T[3][3] = 1.f; + T[3][3] = 1.; mat4x4_mul(R, M, T); + } else { + 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); @@ -247,19 +245,19 @@ static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) }; 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.f, s, 0.f}, + { c, 0.f, -s, 0.f}, { 0.f, 1.f, 0.f, 0.f}, - { -s, 0.f, c, 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); @@ -271,7 +269,7 @@ static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) }; mat4x4_mul(Q, M, R); } -static inline void mat4x4_invert(mat4x4 T, mat4x4 M) +LINMATH_H_FUNC void mat4x4_invert(mat4x4 T, mat4x4 M) { float s[6]; float c[6]; @@ -312,7 +310,30 @@ static inline void mat4x4_invert(mat4x4 T, mat4x4 M) 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_frustum(mat4x4 M, float l, float r, float b, float t, float n, float f) +LINMATH_H_FUNC void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) +{ + mat4x4_dup(R, M); + float s = 1.; + vec3 h; + + vec3_norm(R[2], R[2]); + + s = vec3_mul_inner(R[1], R[2]); + vec3_scale(h, R[2], s); + vec3_sub(R[1], R[1], h); + vec3_norm(R[1], R[1]); + + s = vec3_mul_inner(R[0], R[2]); + vec3_scale(h, R[2], s); + vec3_sub(R[0], R[0], h); + + 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]); +} + +LINMATH_H_FUNC 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; @@ -328,7 +349,7 @@ static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, 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.f/(r-l); M[0][1] = M[0][2] = M[0][3] = 0.f; @@ -344,7 +365,7 @@ static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, fl 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) +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! */ @@ -370,7 +391,7 @@ static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect, float 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) +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 */ @@ -413,24 +434,24 @@ static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up) } 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.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); @@ -440,13 +461,13 @@ 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.f; int i; @@ -454,24 +475,43 @@ static inline float quat_inner_product(quat a, quat b) 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]; } +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 -static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) +LINMATH_H_FUNC void quat_mul_vec3(vec3 r, quat q, vec3 v) { - quat v_ = {v[0], v[1], v[2], 0.f}; +/* + * 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(r, q); - quat_norm(r, r); - quat_mul(r, v_, r); - quat_mul(r, q, r); + 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]; @@ -500,16 +540,19 @@ static inline void mat4x4_from_quat(mat4x4 M, quat q) 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.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.f; int i; @@ -539,4 +582,33 @@ static inline void quat_from_mat4x4(quat q, mat4x4 M) q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]])/(2.f*r); } +LINMATH_H_FUNC void 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)); + + float z_a = 0.; + float z_b = 0.; + + if(vec2_len(a) < 1.) { + z_a = sqrtf(1. - vec2_mul_inner(a, a)); + } else { + vec2_norm(a, a); + } + + if(vec2_len(b) < 1.) { + z_b = sqrtf(1. - vec2_mul_inner(b, b)); + } else { + vec2_norm(b, b); + } + + vec3 a_ = {a[0], a[1], z_a}; + vec3 b_ = {b[0], b[1], z_b}; + + vec3 c_; + vec3_mul_cross(c_, a_, b_); + + float const angle = acos(vec3_mul_inner(a_, b_)) * s; + mat4x4_rotate(R, M, c_[0], c_[1], c_[2], angle); +} #endif |