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Diffstat (limited to 'linmath.h')
-rw-r--r-- | linmath.h | 501 |
1 files changed, 501 insertions, 0 deletions
diff --git a/linmath.h b/linmath.h new file mode 100644 index 0000000..b4d386c --- /dev/null +++ b/linmath.h @@ -0,0 +1,501 @@ +/* + * Copyright (c) 2015-2016 The Khronos Group Inc. + * Copyright (c) 2015-2016 Valve Corporation + * Copyright (c) 2015-2016 LunarG, Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + * + * Relicensed from the WTFPL (http://www.wtfpl.net/faq/). + */ + +#ifndef LINMATH_H +#define LINMATH_H + +#include <math.h> + +// Converts degrees to radians. +#define degreesToRadians(angleDegrees) (angleDegrees * M_PI / 180.0) + +// Converts radians to degrees. +#define radiansToDegrees(angleRadians) (angleRadians * 180.0 / M_PI) + +typedef float vec3[3]; +static inline void vec3_add(vec3 r, vec3 const a, vec3 const b) { + int i; + for (i = 0; i < 3; ++i) r[i] = a[i] + b[i]; +} +static inline void vec3_sub(vec3 r, vec3 const a, vec3 const b) { + int i; + for (i = 0; i < 3; ++i) r[i] = a[i] - b[i]; +} +static inline void vec3_scale(vec3 r, vec3 const v, float const s) { + int i; + for (i = 0; i < 3; ++i) r[i] = v[i] * s; +} +static inline float vec3_mul_inner(vec3 const a, vec3 const 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 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 const v) { return sqrtf(vec3_mul_inner(v, v)); } +static inline void vec3_norm(vec3 r, vec3 const v) { + float k = 1.f / vec3_len(v); + vec3_scale(r, v, k); +} +static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const 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 const a, vec4 const b) { + int i; + for (i = 0; i < 4; ++i) r[i] = a[i] + b[i]; +} +static inline void vec4_sub(vec4 r, vec4 const a, vec4 const 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) { + 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) { + 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) { + 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) { + 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) { + 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; + 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) { + 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) { + 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) { + 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) { + 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) { + int k, r, c; + for (c = 0; c < 4; ++c) + for (r = 0; r < 4; ++r) { + M[c][r] = 0.f; + for (k = 0; k < 4; ++k) M[c][r] += a[k][r] * b[c][k]; + } +} +static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) { + int i, j; + for (j = 0; j < 4; ++j) { + r[j] = 0.f; + for (i = 0; i < 4; ++i) r[j] += M[i][j] * v[i]; + } +} +static inline 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) { + 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_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) { + float s = sinf(angle); + float 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, float angle) { + float s = sinf(angle); + float c = cosf(angle); + mat4x4 R = {{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) { + float s = sinf(angle); + float c = cosf(angle); + mat4x4 R = {{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) { + float s = sinf(angle); + float c = cosf(angle); + mat4x4 R = {{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_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; + + 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); + 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[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, 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 = (float)(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; +} +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]; +} +#define quat_norm vec4_norm +static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) { + quat v_ = {v[0], v[1], v[2], 0.f}; + + quat_conj(r, q); + quat_norm(r, r); + quat_mul(r, v_, r); + quat_mul(r, q, r); +} +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 |