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Diffstat (limited to 'linmath.h')
| -rw-r--r-- | linmath.h | 562 |
1 files changed, 562 insertions, 0 deletions
diff --git a/linmath.h b/linmath.h new file mode 100644 index 0000000..8d9ff8c --- /dev/null +++ b/linmath.h @@ -0,0 +1,562 @@ +/* + * Copyright (C) 2013 Wolfgang 'datenwolf' Draxinger <code@datenwolf.net> + * Copyright (C) 2018 Tomasz Kramkowski <tk@the-tk.com> + * SPDX-License-Identifier: WTFPL + */ +#ifndef LINMATH_H +#define LINMATH_H + +#include <math.h> + +typedef float lm_elem; +#define LINMATH_H_DEFINE_VEC(n) \ +typedef lm_elem vec##n[n]; \ +static inline void vec##n##_add(vec##n r, vec##n const a, vec##n const b) \ +{ \ + for (int i = 0; i < n; ++i) \ + r[i] = a[i] + b[i]; \ +} \ +static inline void vec##n##_sub(vec##n r, vec##n const a, vec##n const b) \ +{ \ + for (int i = 0; i < n; ++i) \ + r[i] = a[i] - b[i]; \ +} \ +static inline void vec##n##_scale(vec##n r, vec##n const v, lm_elem const s) \ +{ \ + for (int i = 0; i < n; ++i) \ + r[i] = v[i] * s; \ +} \ +static inline lm_elem vec##n##_mul_inner(vec##n const a, vec##n const b) \ +{ \ + lm_elem p = 0.0; \ + for (int i = 0; i < n; ++i) \ + p += b[i] * a[i]; \ + return p; \ +} \ +static inline lm_elem 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 const v) \ +{ \ + lm_elem k = 1.0 / vec##n##_len(v); \ + vec##n##_scale(r, v, k); \ +} \ +static inline void vec##n##_min(vec##n r, vec##n a, vec##n b) \ +{ \ + for (int i = 0; i < n; ++i) \ + r[i] = a[i] < b[i] ? a[i] : b[i]; \ +} \ +static inline void vec##n##_max(vec##n r, vec##n a, vec##n b) \ +{ \ + for (int 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) + +static inline 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_reflect(vec3 r, vec3 const v, vec3 const n) +{ + lm_elem p = 2.0f * vec3_mul_inner(v, n); + for (int i = 0; i < 3; ++i) + r[i] = v[i] - p * n[i]; +} + +static inline 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] = 1.0f; +} + +static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) +{ + lm_elem p = 2.0f * vec4_mul_inner(v, n); + for (int i = 0; i < 4; ++i) + r[i] = v[i] - p * n[i]; +} + +typedef vec4 mat4x4[4]; +static inline void mat4x4_identity(mat4x4 M) +{ + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + M[i][j] = i == j ? 1.0f : 0.0f; +} +static inline void mat4x4_dup(mat4x4 M, mat4x4 N) +{ + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + M[i][j] = N[i][j]; +} +static inline void mat4x4_row(vec4 r, mat4x4 M, int i) +{ + for (int k = 0; k < 4; ++k) + r[k] = M[k][i]; +} +static inline void mat4x4_col(vec4 r, mat4x4 M, int i) +{ + for (int k = 0; k < 4; ++k) + r[k] = M[i][k]; +} +static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) +{ + for (int j = 0; j < 4; ++j) + for (int i = 0; i < 4; ++i) + M[i][j] = N[j][i]; +} +static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) +{ + for (int i = 0; i < 4; ++i) + vec4_add(M[i], a[i], b[i]); +} +static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) +{ + for (int i = 0; i < 4; ++i) + vec4_sub(M[i], a[i], b[i]); +} +static inline void mat4x4_scale(mat4x4 M, mat4x4 a, lm_elem k) +{ + for (int i = 0; i < 4; ++i) + vec4_scale(M[i], a[i], k); +} +static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, lm_elem x, lm_elem y, lm_elem z) +{ + vec4_scale(M[0], a[0], x); + vec4_scale(M[1], a[1], y); + vec4_scale(M[2], a[2], z); + for (int i = 0; i < 4; ++i) + M[3][i] = a[3][i]; +} +static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) +{ + mat4x4 temp; + for (int c = 0; c < 4; ++c) { + for (int r = 0; r < 4; ++r) { + temp[c][r] = 0.0f; + for (int k = 0; k < 4; ++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) +{ + for (int j = 0; j < 4; ++j) { + r[j] = 0.0f; + for (int i = 0; i < 4; ++i) + r[j] += M[i][j] * v[i]; + } +} +static inline void mat4x4_translate(mat4x4 T, lm_elem x, lm_elem y, lm_elem 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, lm_elem x, lm_elem y, lm_elem z) +{ + vec4 t = {x, y, z, 0}; + vec4 r; + for (int i = 0; i < 4; ++i) { + mat4x4_row(r, M, i); + M[3][i] += vec4_mul_inner(r, t); + } +} +static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) +{ + for (int i = 0; i < 4; ++i) + for (int j = 0; j < 4; ++j) + M[i][j] = i < 3 && j < 3 ? a[i] * b[j] : 0.0f; +} +static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, lm_elem x, lm_elem y, lm_elem z, lm_elem angle) +{ + lm_elem s = sinf(angle); + lm_elem c = cosf(angle); + vec3 u = {x, y, z}; + + if (vec3_len(u) > 1e-4) { + vec3_norm(u, u); + mat4x4 T; + mat4x4_from_vec3_mul_outer(T, u, u); + + mat4x4 S = { + { 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); + + mat4x4 C; + mat4x4_identity(C); + mat4x4_sub(C, C, T); + + mat4x4_scale(C, C, c); + + mat4x4_add(T, T, C); + mat4x4_add(T, T, S); + + T[3][3] = 1.; + mat4x4_mul(R, M, T); + } else { + mat4x4_dup(R, M); + } +} +static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, lm_elem angle) +{ + lm_elem s = sinf(angle); + lm_elem c = cosf(angle); + mat4x4 R = { + {1.0f, 0.0f, 0.0f, 0.0f}, + {0.0f, c, s, 0.0f}, + {0.0f, -s, c, 0.0f}, + {0.0f, 0.0f, 0.0f, 1.0f} + }; + mat4x4_mul(Q, M, R); +} +static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, lm_elem angle) +{ + lm_elem s = sinf(angle); + lm_elem c = cosf(angle); + mat4x4 R = { + { c, 0.0f, s, 0.0f}, + { 0.0f, 1.0f, 0.0f, 0.0f}, + { -s, 0.0f, c, 0.0f}, + { 0.0f, 0.0f, 0.0f, 1.0f} + }; + mat4x4_mul(Q, M, R); +} +static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, lm_elem angle) +{ + lm_elem s = sinf(angle); + lm_elem c = cosf(angle); + mat4x4 R = { + { c, s, 0.0f, 0.0f}, + { -s, c, 0.0f, 0.0f}, + { 0.0f, 0.0f, 1.0f, 0.0f}, + { 0.0f, 0.0f, 0.0f, 1.0f} + }; + mat4x4_mul(Q, M, R); +} +static inline void mat4x4_invert(mat4x4 T, mat4x4 M) +{ + lm_elem s[6]; + lm_elem 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 */ + lm_elem 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; + + 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; + + 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; + + 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) +{ + mat4x4_dup(R, M); + lm_elem 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[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[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, lm_elem l, lm_elem r, lm_elem b, lm_elem t, lm_elem n, lm_elem f) +{ + M[0][0] = 2.0f * n/(r-l); + M[0][1] = M[0][2] = M[0][3] = 0.0f; + + M[1][1] = 2.0 * n/(t-b); + M[1][0] = M[1][2] = M[1][3] = 0.0f; + + M[2][0] = (r+l)/(r-l); + M[2][1] = (t+b)/(t-b); + M[2][2] = -(f+n)/(f-n); + M[2][3] = -1.0f; + + M[3][2] = -2.0f * (f * n)/(f-n); + M[3][0] = M[3][1] = M[3][3] = 0.0f; +} +static inline void mat4x4_ortho(mat4x4 M, lm_elem l, lm_elem r, lm_elem b, lm_elem t, lm_elem n, lm_elem f) +{ + M[0][0] = 2.0f/(r-l); + M[0][1] = M[0][2] = M[0][3] = 0.0f; + + M[1][1] = 2.0f/(t-b); + M[1][0] = M[1][2] = M[1][3] = 0.0f; + + M[2][2] = -2.0f/(f-n); + M[2][0] = M[2][1] = M[2][3] = 0.0f; + + M[3][0] = -(r+l)/(r-l); + M[3][1] = -(t+b)/(t-b); + M[3][2] = -(f+n)/(f-n); + M[3][3] = 1.0f; +} +static inline void mat4x4_perspective(mat4x4 m, lm_elem y_fov, lm_elem aspect, lm_elem n, lm_elem f) +{ + lm_elem const a = 1.0f / tan(y_fov / 2.0f); + + m[0][0] = a / aspect; + m[0][1] = 0.0f; + m[0][2] = 0.0f; + m[0][3] = 0.0f; + + m[1][0] = 0.0f; + m[1][1] = a; + m[1][2] = 0.0f; + m[1][3] = 0.0f; + + m[2][0] = 0.0f; + m[2][1] = 0.0f; + m[2][2] = -((f + n) / (f - n)); + m[2][3] = -1.0f; + + m[3][0] = 0.0f; + m[3][1] = 0.0f; + m[3][2] = -((2.0f * f * n) / (f - n)); + m[3][3] = 0.0f; +} +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] = 0.0f; + + m[1][0] = s[1]; + m[1][1] = t[1]; + m[1][2] = -f[1]; + m[1][3] = 0.0f; + + m[2][0] = s[2]; + m[2][1] = t[2]; + m[2][2] = -f[2]; + m[2][3] = 0.0f; + + m[3][0] = 0.0f; + m[3][1] = 0.0f; + m[3][2] = 0.0f; + m[3][3] = 1.0f; + + mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]); +} + +typedef lm_elem quat[4]; +static inline void quat_identity(quat q) +{ + q[0] = q[1] = q[2] = 0.0f; + q[3] = 1.0f; +} +static inline void quat_add(quat r, quat a, quat b) +{ + for (int i = 0; i < 4; ++i) + r[i] = a[i] + b[i]; +} +static inline void quat_sub(quat r, quat a, quat b) +{ + for (int 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, lm_elem s) +{ + for (int i = 0; i < 4; ++i) + r[i] = v[i] * s; +} +static inline lm_elem quat_inner_product(quat a, quat b) +{ + lm_elem p = 0.0f; + for (int i = 0; i < 4; ++i) + p += b[i]*a[i]; + return p; +} +static inline void quat_conj(quat r, quat q) +{ + for (int i = 0; i < 3; ++i) + r[i] = -q[i]; + r[3] = q[3]; +} +static inline void quat_rotate(quat r, lm_elem angle, vec3 axis) { + vec3 v; + vec3_scale(v, axis, sinf(angle / 2)); + for (int 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; + 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); + + 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) +{ + lm_elem a = q[3]; + lm_elem b = q[0]; + lm_elem c = q[1]; + lm_elem d = q[2]; + lm_elem a2 = a * a; + lm_elem b2 = b * b; + lm_elem c2 = c * c; + lm_elem d2 = d * d; + + M[0][0] = a2 + b2 - c2 - d2; + M[0][1] = 2.0f * (b * c + a * d); + M[0][2] = 2.0f * (b * d - a * c); + M[0][3] = 0.0f; + + M[1][0] = 2 * (b * c - a * d); + M[1][1] = a2 - b2 + c2 - d2; + M[1][2] = 2.0f * (c * d + a * b); + M[1][3] = 0.0f; + + M[2][0] = 2.0f * (b * d + a * c); + M[2][1] = 2.0f * (c * d - a * b); + M[2][2] = a2 - b2 - c2 + d2; + M[2][3] = 0.0f; + + M[3][0] = M[3][1] = M[3][2] = 0.0f; + M[3][3] = 1.0f; +} + +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] = 0.0f; + R[3][3] = 1.0f; +} + +static inline void quat_from_mat4x4(quat q, mat4x4 M) +{ + lm_elem r = 0.0f; + int i; + + int perm[] = { 0, 1, 2, 0, 1 }; + int *p = perm; + + for (int i = 0; i < 3; i++) { + lm_elem m = M[i][i]; + if (m < r) + continue; + m = r; + p = &perm[i]; + } + + r = sqrtf(1.0f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]]); + + if (r < 1e-6) { + q[0] = 1.0f; + q[1] = q[2] = q[3] = 0.0f; + return; + } + + q[0] = r/2.0f; + q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]])/(2.0f * r); + q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]])/(2.0f * r); + q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]])/(2.0f * r); +} + +#endif // LINMATH_H |