Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 1 | /* |
Karl Schultz | dae791d | 2016-02-04 10:29:00 -0700 | [diff] [blame] | 2 | * Copyright (c) 2015-2016 The Khronos Group Inc. |
| 3 | * Copyright (c) 2015-2016 Valve Corporation |
| 4 | * Copyright (c) 2015-2016 LunarG, Inc. |
| 5 | * |
Jon Ashburn | 43b53e8 | 2016-04-19 11:30:31 -0600 | [diff] [blame^] | 6 | * Licensed under the Apache License, Version 2.0 (the "License"); |
| 7 | * you may not use this file except in compliance with the License. |
| 8 | * You may obtain a copy of the License at |
Karl Schultz | dae791d | 2016-02-04 10:29:00 -0700 | [diff] [blame] | 9 | * |
Jon Ashburn | 43b53e8 | 2016-04-19 11:30:31 -0600 | [diff] [blame^] | 10 | * http://www.apache.org/licenses/LICENSE-2.0 |
Karl Schultz | dae791d | 2016-02-04 10:29:00 -0700 | [diff] [blame] | 11 | * |
Jon Ashburn | 43b53e8 | 2016-04-19 11:30:31 -0600 | [diff] [blame^] | 12 | * Unless required by applicable law or agreed to in writing, software |
| 13 | * distributed under the License is distributed on an "AS IS" BASIS, |
| 14 | * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| 15 | * See the License for the specific language governing permissions and |
| 16 | * limitations under the License. |
Karl Schultz | dae791d | 2016-02-04 10:29:00 -0700 | [diff] [blame] | 17 | * |
| 18 | * Relicensed from the WTFPL (http://www.wtfpl.net/faq/). |
| 19 | */ |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 20 | |
| 21 | #ifndef LINMATH_H |
| 22 | #define LINMATH_H |
| 23 | |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 24 | #include <math.h> |
| 25 | |
| 26 | // Converts degrees to radians. |
| 27 | #define degreesToRadians(angleDegrees) (angleDegrees * M_PI / 180.0) |
| 28 | |
| 29 | // Converts radians to degrees. |
| 30 | #define radiansToDegrees(angleRadians) (angleRadians * 180.0 / M_PI) |
| 31 | |
| 32 | typedef float vec3[3]; |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 33 | static inline void vec3_add(vec3 r, vec3 const a, vec3 const b) { |
| 34 | int i; |
| 35 | for (i = 0; i < 3; ++i) |
| 36 | r[i] = a[i] + b[i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 37 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 38 | static inline void vec3_sub(vec3 r, vec3 const a, vec3 const b) { |
| 39 | int i; |
| 40 | for (i = 0; i < 3; ++i) |
| 41 | r[i] = a[i] - b[i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 42 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 43 | static inline void vec3_scale(vec3 r, vec3 const v, float const s) { |
| 44 | int i; |
| 45 | for (i = 0; i < 3; ++i) |
| 46 | r[i] = v[i] * s; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 47 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 48 | static inline float vec3_mul_inner(vec3 const a, vec3 const b) { |
| 49 | float p = 0.f; |
| 50 | int i; |
| 51 | for (i = 0; i < 3; ++i) |
| 52 | p += b[i] * a[i]; |
| 53 | return p; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 54 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 55 | static inline void vec3_mul_cross(vec3 r, vec3 const a, vec3 const b) { |
| 56 | r[0] = a[1] * b[2] - a[2] * b[1]; |
| 57 | r[1] = a[2] * b[0] - a[0] * b[2]; |
| 58 | r[2] = a[0] * b[1] - a[1] * b[0]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 59 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 60 | static inline float vec3_len(vec3 const v) { |
| 61 | return sqrtf(vec3_mul_inner(v, v)); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 62 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 63 | static inline void vec3_norm(vec3 r, vec3 const v) { |
| 64 | float k = 1.f / vec3_len(v); |
| 65 | vec3_scale(r, v, k); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 66 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 67 | static inline void vec3_reflect(vec3 r, vec3 const v, vec3 const n) { |
| 68 | float p = 2.f * vec3_mul_inner(v, n); |
| 69 | int i; |
| 70 | for (i = 0; i < 3; ++i) |
| 71 | r[i] = v[i] - p * n[i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 72 | } |
| 73 | |
| 74 | typedef float vec4[4]; |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 75 | static inline void vec4_add(vec4 r, vec4 const a, vec4 const b) { |
| 76 | int i; |
| 77 | for (i = 0; i < 4; ++i) |
| 78 | r[i] = a[i] + b[i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 79 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 80 | static inline void vec4_sub(vec4 r, vec4 const a, vec4 const b) { |
| 81 | int i; |
| 82 | for (i = 0; i < 4; ++i) |
| 83 | r[i] = a[i] - b[i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 84 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 85 | static inline void vec4_scale(vec4 r, vec4 v, float s) { |
| 86 | int i; |
| 87 | for (i = 0; i < 4; ++i) |
| 88 | r[i] = v[i] * s; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 89 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 90 | static inline float vec4_mul_inner(vec4 a, vec4 b) { |
| 91 | float p = 0.f; |
| 92 | int i; |
| 93 | for (i = 0; i < 4; ++i) |
| 94 | p += b[i] * a[i]; |
| 95 | return p; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 96 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 97 | static inline void vec4_mul_cross(vec4 r, vec4 a, vec4 b) { |
| 98 | r[0] = a[1] * b[2] - a[2] * b[1]; |
| 99 | r[1] = a[2] * b[0] - a[0] * b[2]; |
| 100 | r[2] = a[0] * b[1] - a[1] * b[0]; |
| 101 | r[3] = 1.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 102 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 103 | static inline float vec4_len(vec4 v) { return sqrtf(vec4_mul_inner(v, v)); } |
| 104 | static inline void vec4_norm(vec4 r, vec4 v) { |
| 105 | float k = 1.f / vec4_len(v); |
| 106 | vec4_scale(r, v, k); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 107 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 108 | static inline void vec4_reflect(vec4 r, vec4 v, vec4 n) { |
| 109 | float p = 2.f * vec4_mul_inner(v, n); |
| 110 | int i; |
| 111 | for (i = 0; i < 4; ++i) |
| 112 | r[i] = v[i] - p * n[i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 113 | } |
| 114 | |
| 115 | typedef vec4 mat4x4[4]; |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 116 | static inline void mat4x4_identity(mat4x4 M) { |
| 117 | int i, j; |
| 118 | for (i = 0; i < 4; ++i) |
| 119 | for (j = 0; j < 4; ++j) |
| 120 | M[i][j] = i == j ? 1.f : 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 121 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 122 | static inline void mat4x4_dup(mat4x4 M, mat4x4 N) { |
| 123 | int i, j; |
| 124 | for (i = 0; i < 4; ++i) |
| 125 | for (j = 0; j < 4; ++j) |
| 126 | M[i][j] = N[i][j]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 127 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 128 | static inline void mat4x4_row(vec4 r, mat4x4 M, int i) { |
| 129 | int k; |
| 130 | for (k = 0; k < 4; ++k) |
| 131 | r[k] = M[k][i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 132 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 133 | static inline void mat4x4_col(vec4 r, mat4x4 M, int i) { |
| 134 | int k; |
| 135 | for (k = 0; k < 4; ++k) |
| 136 | r[k] = M[i][k]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 137 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 138 | static inline void mat4x4_transpose(mat4x4 M, mat4x4 N) { |
| 139 | int i, j; |
| 140 | for (j = 0; j < 4; ++j) |
| 141 | for (i = 0; i < 4; ++i) |
| 142 | M[i][j] = N[j][i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 143 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 144 | static inline void mat4x4_add(mat4x4 M, mat4x4 a, mat4x4 b) { |
| 145 | int i; |
| 146 | for (i = 0; i < 4; ++i) |
| 147 | vec4_add(M[i], a[i], b[i]); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 148 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 149 | static inline void mat4x4_sub(mat4x4 M, mat4x4 a, mat4x4 b) { |
| 150 | int i; |
| 151 | for (i = 0; i < 4; ++i) |
| 152 | vec4_sub(M[i], a[i], b[i]); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 153 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 154 | static inline void mat4x4_scale(mat4x4 M, mat4x4 a, float k) { |
| 155 | int i; |
| 156 | for (i = 0; i < 4; ++i) |
| 157 | vec4_scale(M[i], a[i], k); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 158 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 159 | static inline void mat4x4_scale_aniso(mat4x4 M, mat4x4 a, float x, float y, |
| 160 | float z) { |
| 161 | int i; |
| 162 | vec4_scale(M[0], a[0], x); |
| 163 | vec4_scale(M[1], a[1], y); |
| 164 | vec4_scale(M[2], a[2], z); |
| 165 | for (i = 0; i < 4; ++i) { |
| 166 | M[3][i] = a[3][i]; |
| 167 | } |
| 168 | } |
| 169 | static inline void mat4x4_mul(mat4x4 M, mat4x4 a, mat4x4 b) { |
| 170 | int k, r, c; |
| 171 | for (c = 0; c < 4; ++c) |
| 172 | for (r = 0; r < 4; ++r) { |
| 173 | M[c][r] = 0.f; |
| 174 | for (k = 0; k < 4; ++k) |
| 175 | M[c][r] += a[k][r] * b[c][k]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 176 | } |
| 177 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 178 | static inline void mat4x4_mul_vec4(vec4 r, mat4x4 M, vec4 v) { |
| 179 | int i, j; |
| 180 | for (j = 0; j < 4; ++j) { |
| 181 | r[j] = 0.f; |
| 182 | for (i = 0; i < 4; ++i) |
| 183 | r[j] += M[i][j] * v[i]; |
| 184 | } |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 185 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 186 | static inline void mat4x4_translate(mat4x4 T, float x, float y, float z) { |
| 187 | mat4x4_identity(T); |
| 188 | T[3][0] = x; |
| 189 | T[3][1] = y; |
| 190 | T[3][2] = z; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 191 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 192 | static inline void mat4x4_translate_in_place(mat4x4 M, float x, float y, |
| 193 | float z) { |
| 194 | vec4 t = {x, y, z, 0}; |
| 195 | vec4 r; |
| 196 | int i; |
| 197 | for (i = 0; i < 4; ++i) { |
| 198 | mat4x4_row(r, M, i); |
| 199 | M[3][i] += vec4_mul_inner(r, t); |
| 200 | } |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 201 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 202 | static inline void mat4x4_from_vec3_mul_outer(mat4x4 M, vec3 a, vec3 b) { |
| 203 | int i, j; |
| 204 | for (i = 0; i < 4; ++i) |
| 205 | for (j = 0; j < 4; ++j) |
| 206 | M[i][j] = i < 3 && j < 3 ? a[i] * b[j] : 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 207 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 208 | static inline void mat4x4_rotate(mat4x4 R, mat4x4 M, float x, float y, float z, |
| 209 | float angle) { |
| 210 | float s = sinf(angle); |
| 211 | float c = cosf(angle); |
| 212 | vec3 u = {x, y, z}; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 213 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 214 | if (vec3_len(u) > 1e-4) { |
| 215 | vec3_norm(u, u); |
| 216 | mat4x4 T; |
| 217 | mat4x4_from_vec3_mul_outer(T, u, u); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 218 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 219 | mat4x4 S = {{0, u[2], -u[1], 0}, |
| 220 | {-u[2], 0, u[0], 0}, |
| 221 | {u[1], -u[0], 0, 0}, |
| 222 | {0, 0, 0, 0}}; |
| 223 | mat4x4_scale(S, S, s); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 224 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 225 | mat4x4 C; |
| 226 | mat4x4_identity(C); |
| 227 | mat4x4_sub(C, C, T); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 228 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 229 | mat4x4_scale(C, C, c); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 230 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 231 | mat4x4_add(T, T, C); |
| 232 | mat4x4_add(T, T, S); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 233 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 234 | T[3][3] = 1.; |
| 235 | mat4x4_mul(R, M, T); |
| 236 | } else { |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 237 | mat4x4_dup(R, M); |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 238 | } |
| 239 | } |
| 240 | static inline void mat4x4_rotate_X(mat4x4 Q, mat4x4 M, float angle) { |
| 241 | float s = sinf(angle); |
| 242 | float c = cosf(angle); |
| 243 | mat4x4 R = {{1.f, 0.f, 0.f, 0.f}, |
| 244 | {0.f, c, s, 0.f}, |
| 245 | {0.f, -s, c, 0.f}, |
| 246 | {0.f, 0.f, 0.f, 1.f}}; |
| 247 | mat4x4_mul(Q, M, R); |
| 248 | } |
| 249 | static inline void mat4x4_rotate_Y(mat4x4 Q, mat4x4 M, float angle) { |
| 250 | float s = sinf(angle); |
| 251 | float c = cosf(angle); |
| 252 | mat4x4 R = {{c, 0.f, s, 0.f}, |
| 253 | {0.f, 1.f, 0.f, 0.f}, |
| 254 | {-s, 0.f, c, 0.f}, |
| 255 | {0.f, 0.f, 0.f, 1.f}}; |
| 256 | mat4x4_mul(Q, M, R); |
| 257 | } |
| 258 | static inline void mat4x4_rotate_Z(mat4x4 Q, mat4x4 M, float angle) { |
| 259 | float s = sinf(angle); |
| 260 | float c = cosf(angle); |
| 261 | mat4x4 R = {{c, s, 0.f, 0.f}, |
| 262 | {-s, c, 0.f, 0.f}, |
| 263 | {0.f, 0.f, 1.f, 0.f}, |
| 264 | {0.f, 0.f, 0.f, 1.f}}; |
| 265 | mat4x4_mul(Q, M, R); |
| 266 | } |
| 267 | static inline void mat4x4_invert(mat4x4 T, mat4x4 M) { |
| 268 | float s[6]; |
| 269 | float c[6]; |
| 270 | s[0] = M[0][0] * M[1][1] - M[1][0] * M[0][1]; |
| 271 | s[1] = M[0][0] * M[1][2] - M[1][0] * M[0][2]; |
| 272 | s[2] = M[0][0] * M[1][3] - M[1][0] * M[0][3]; |
| 273 | s[3] = M[0][1] * M[1][2] - M[1][1] * M[0][2]; |
| 274 | s[4] = M[0][1] * M[1][3] - M[1][1] * M[0][3]; |
| 275 | s[5] = M[0][2] * M[1][3] - M[1][2] * M[0][3]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 276 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 277 | c[0] = M[2][0] * M[3][1] - M[3][0] * M[2][1]; |
| 278 | c[1] = M[2][0] * M[3][2] - M[3][0] * M[2][2]; |
| 279 | c[2] = M[2][0] * M[3][3] - M[3][0] * M[2][3]; |
| 280 | c[3] = M[2][1] * M[3][2] - M[3][1] * M[2][2]; |
| 281 | c[4] = M[2][1] * M[3][3] - M[3][1] * M[2][3]; |
| 282 | c[5] = M[2][2] * M[3][3] - M[3][2] * M[2][3]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 283 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 284 | /* Assumes it is invertible */ |
| 285 | float idet = 1.0f / (s[0] * c[5] - s[1] * c[4] + s[2] * c[3] + s[3] * c[2] - |
| 286 | s[4] * c[1] + s[5] * c[0]); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 287 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 288 | T[0][0] = (M[1][1] * c[5] - M[1][2] * c[4] + M[1][3] * c[3]) * idet; |
| 289 | T[0][1] = (-M[0][1] * c[5] + M[0][2] * c[4] - M[0][3] * c[3]) * idet; |
| 290 | T[0][2] = (M[3][1] * s[5] - M[3][2] * s[4] + M[3][3] * s[3]) * idet; |
| 291 | T[0][3] = (-M[2][1] * s[5] + M[2][2] * s[4] - M[2][3] * s[3]) * idet; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 292 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 293 | T[1][0] = (-M[1][0] * c[5] + M[1][2] * c[2] - M[1][3] * c[1]) * idet; |
| 294 | T[1][1] = (M[0][0] * c[5] - M[0][2] * c[2] + M[0][3] * c[1]) * idet; |
| 295 | T[1][2] = (-M[3][0] * s[5] + M[3][2] * s[2] - M[3][3] * s[1]) * idet; |
| 296 | T[1][3] = (M[2][0] * s[5] - M[2][2] * s[2] + M[2][3] * s[1]) * idet; |
| 297 | |
| 298 | T[2][0] = (M[1][0] * c[4] - M[1][1] * c[2] + M[1][3] * c[0]) * idet; |
| 299 | T[2][1] = (-M[0][0] * c[4] + M[0][1] * c[2] - M[0][3] * c[0]) * idet; |
| 300 | T[2][2] = (M[3][0] * s[4] - M[3][1] * s[2] + M[3][3] * s[0]) * idet; |
| 301 | T[2][3] = (-M[2][0] * s[4] + M[2][1] * s[2] - M[2][3] * s[0]) * idet; |
| 302 | |
| 303 | T[3][0] = (-M[1][0] * c[3] + M[1][1] * c[1] - M[1][2] * c[0]) * idet; |
| 304 | T[3][1] = (M[0][0] * c[3] - M[0][1] * c[1] + M[0][2] * c[0]) * idet; |
| 305 | T[3][2] = (-M[3][0] * s[3] + M[3][1] * s[1] - M[3][2] * s[0]) * idet; |
| 306 | T[3][3] = (M[2][0] * s[3] - M[2][1] * s[1] + M[2][2] * s[0]) * idet; |
| 307 | } |
| 308 | static inline void mat4x4_orthonormalize(mat4x4 R, mat4x4 M) { |
| 309 | mat4x4_dup(R, M); |
| 310 | float s = 1.; |
| 311 | vec3 h; |
| 312 | |
| 313 | vec3_norm(R[2], R[2]); |
| 314 | |
| 315 | s = vec3_mul_inner(R[1], R[2]); |
| 316 | vec3_scale(h, R[2], s); |
| 317 | vec3_sub(R[1], R[1], h); |
| 318 | vec3_norm(R[2], R[2]); |
| 319 | |
| 320 | s = vec3_mul_inner(R[1], R[2]); |
| 321 | vec3_scale(h, R[2], s); |
| 322 | vec3_sub(R[1], R[1], h); |
| 323 | vec3_norm(R[1], R[1]); |
| 324 | |
| 325 | s = vec3_mul_inner(R[0], R[1]); |
| 326 | vec3_scale(h, R[1], s); |
| 327 | vec3_sub(R[0], R[0], h); |
| 328 | vec3_norm(R[0], R[0]); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 329 | } |
| 330 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 331 | static inline void mat4x4_frustum(mat4x4 M, float l, float r, float b, float t, |
| 332 | float n, float f) { |
| 333 | M[0][0] = 2.f * n / (r - l); |
| 334 | M[0][1] = M[0][2] = M[0][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 335 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 336 | M[1][1] = 2.f * n / (t - b); |
| 337 | M[1][0] = M[1][2] = M[1][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 338 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 339 | M[2][0] = (r + l) / (r - l); |
| 340 | M[2][1] = (t + b) / (t - b); |
| 341 | M[2][2] = -(f + n) / (f - n); |
| 342 | M[2][3] = -1.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 343 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 344 | M[3][2] = -2.f * (f * n) / (f - n); |
| 345 | M[3][0] = M[3][1] = M[3][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 346 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 347 | static inline void mat4x4_ortho(mat4x4 M, float l, float r, float b, float t, |
| 348 | float n, float f) { |
| 349 | M[0][0] = 2.f / (r - l); |
| 350 | M[0][1] = M[0][2] = M[0][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 351 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 352 | M[1][1] = 2.f / (t - b); |
| 353 | M[1][0] = M[1][2] = M[1][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 354 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 355 | M[2][2] = -2.f / (f - n); |
| 356 | M[2][0] = M[2][1] = M[2][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 357 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 358 | M[3][0] = -(r + l) / (r - l); |
| 359 | M[3][1] = -(t + b) / (t - b); |
| 360 | M[3][2] = -(f + n) / (f - n); |
| 361 | M[3][3] = 1.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 362 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 363 | static inline void mat4x4_perspective(mat4x4 m, float y_fov, float aspect, |
| 364 | float n, float f) { |
| 365 | /* NOTE: Degrees are an unhandy unit to work with. |
| 366 | * linmath.h uses radians for everything! */ |
| 367 | float const a = (float)(1.f / tan(y_fov / 2.f)); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 368 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 369 | m[0][0] = a / aspect; |
| 370 | m[0][1] = 0.f; |
| 371 | m[0][2] = 0.f; |
| 372 | m[0][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 373 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 374 | m[1][0] = 0.f; |
| 375 | m[1][1] = a; |
| 376 | m[1][2] = 0.f; |
| 377 | m[1][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 378 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 379 | m[2][0] = 0.f; |
| 380 | m[2][1] = 0.f; |
| 381 | m[2][2] = -((f + n) / (f - n)); |
| 382 | m[2][3] = -1.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 383 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 384 | m[3][0] = 0.f; |
| 385 | m[3][1] = 0.f; |
| 386 | m[3][2] = -((2.f * f * n) / (f - n)); |
| 387 | m[3][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 388 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 389 | static inline void mat4x4_look_at(mat4x4 m, vec3 eye, vec3 center, vec3 up) { |
| 390 | /* Adapted from Android's OpenGL Matrix.java. */ |
| 391 | /* See the OpenGL GLUT documentation for gluLookAt for a description */ |
| 392 | /* of the algorithm. We implement it in a straightforward way: */ |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 393 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 394 | /* TODO: The negation of of can be spared by swapping the order of |
| 395 | * operands in the following cross products in the right way. */ |
| 396 | vec3 f; |
| 397 | vec3_sub(f, center, eye); |
| 398 | vec3_norm(f, f); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 399 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 400 | vec3 s; |
| 401 | vec3_mul_cross(s, f, up); |
| 402 | vec3_norm(s, s); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 403 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 404 | vec3 t; |
| 405 | vec3_mul_cross(t, s, f); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 406 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 407 | m[0][0] = s[0]; |
| 408 | m[0][1] = t[0]; |
| 409 | m[0][2] = -f[0]; |
| 410 | m[0][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 411 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 412 | m[1][0] = s[1]; |
| 413 | m[1][1] = t[1]; |
| 414 | m[1][2] = -f[1]; |
| 415 | m[1][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 416 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 417 | m[2][0] = s[2]; |
| 418 | m[2][1] = t[2]; |
| 419 | m[2][2] = -f[2]; |
| 420 | m[2][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 421 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 422 | m[3][0] = 0.f; |
| 423 | m[3][1] = 0.f; |
| 424 | m[3][2] = 0.f; |
| 425 | m[3][3] = 1.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 426 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 427 | mat4x4_translate_in_place(m, -eye[0], -eye[1], -eye[2]); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 428 | } |
| 429 | |
| 430 | typedef float quat[4]; |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 431 | static inline void quat_identity(quat q) { |
| 432 | q[0] = q[1] = q[2] = 0.f; |
| 433 | q[3] = 1.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 434 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 435 | static inline void quat_add(quat r, quat a, quat b) { |
| 436 | int i; |
| 437 | for (i = 0; i < 4; ++i) |
| 438 | r[i] = a[i] + b[i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 439 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 440 | static inline void quat_sub(quat r, quat a, quat b) { |
| 441 | int i; |
| 442 | for (i = 0; i < 4; ++i) |
| 443 | r[i] = a[i] - b[i]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 444 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 445 | static inline void quat_mul(quat r, quat p, quat q) { |
| 446 | vec3 w; |
| 447 | vec3_mul_cross(r, p, q); |
| 448 | vec3_scale(w, p, q[3]); |
| 449 | vec3_add(r, r, w); |
| 450 | vec3_scale(w, q, p[3]); |
| 451 | vec3_add(r, r, w); |
| 452 | r[3] = p[3] * q[3] - vec3_mul_inner(p, q); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 453 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 454 | static inline void quat_scale(quat r, quat v, float s) { |
| 455 | int i; |
| 456 | for (i = 0; i < 4; ++i) |
| 457 | r[i] = v[i] * s; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 458 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 459 | static inline float quat_inner_product(quat a, quat b) { |
| 460 | float p = 0.f; |
| 461 | int i; |
| 462 | for (i = 0; i < 4; ++i) |
| 463 | p += b[i] * a[i]; |
| 464 | return p; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 465 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 466 | static inline void quat_conj(quat r, quat q) { |
| 467 | int i; |
| 468 | for (i = 0; i < 3; ++i) |
| 469 | r[i] = -q[i]; |
| 470 | r[3] = q[3]; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 471 | } |
| 472 | #define quat_norm vec4_norm |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 473 | static inline void quat_mul_vec3(vec3 r, quat q, vec3 v) { |
| 474 | quat v_ = {v[0], v[1], v[2], 0.f}; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 475 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 476 | quat_conj(r, q); |
| 477 | quat_norm(r, r); |
| 478 | quat_mul(r, v_, r); |
| 479 | quat_mul(r, q, r); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 480 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 481 | static inline void mat4x4_from_quat(mat4x4 M, quat q) { |
| 482 | float a = q[3]; |
| 483 | float b = q[0]; |
| 484 | float c = q[1]; |
| 485 | float d = q[2]; |
| 486 | float a2 = a * a; |
| 487 | float b2 = b * b; |
| 488 | float c2 = c * c; |
| 489 | float d2 = d * d; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 490 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 491 | M[0][0] = a2 + b2 - c2 - d2; |
| 492 | M[0][1] = 2.f * (b * c + a * d); |
| 493 | M[0][2] = 2.f * (b * d - a * c); |
| 494 | M[0][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 495 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 496 | M[1][0] = 2 * (b * c - a * d); |
| 497 | M[1][1] = a2 - b2 + c2 - d2; |
| 498 | M[1][2] = 2.f * (c * d + a * b); |
| 499 | M[1][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 500 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 501 | M[2][0] = 2.f * (b * d + a * c); |
| 502 | M[2][1] = 2.f * (c * d - a * b); |
| 503 | M[2][2] = a2 - b2 - c2 + d2; |
| 504 | M[2][3] = 0.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 505 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 506 | M[3][0] = M[3][1] = M[3][2] = 0.f; |
| 507 | M[3][3] = 1.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 508 | } |
| 509 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 510 | static inline void mat4x4o_mul_quat(mat4x4 R, mat4x4 M, quat q) { |
| 511 | /* XXX: The way this is written only works for othogonal matrices. */ |
| 512 | /* TODO: Take care of non-orthogonal case. */ |
| 513 | quat_mul_vec3(R[0], q, M[0]); |
| 514 | quat_mul_vec3(R[1], q, M[1]); |
| 515 | quat_mul_vec3(R[2], q, M[2]); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 516 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 517 | R[3][0] = R[3][1] = R[3][2] = 0.f; |
| 518 | R[3][3] = 1.f; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 519 | } |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 520 | static inline void quat_from_mat4x4(quat q, mat4x4 M) { |
| 521 | float r = 0.f; |
| 522 | int i; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 523 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 524 | int perm[] = {0, 1, 2, 0, 1}; |
| 525 | int *p = perm; |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 526 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 527 | for (i = 0; i < 3; i++) { |
| 528 | float m = M[i][i]; |
| 529 | if (m < r) |
| 530 | continue; |
| 531 | m = r; |
| 532 | p = &perm[i]; |
| 533 | } |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 534 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 535 | r = sqrtf(1.f + M[p[0]][p[0]] - M[p[1]][p[1]] - M[p[2]][p[2]]); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 536 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 537 | if (r < 1e-6) { |
| 538 | q[0] = 1.f; |
| 539 | q[1] = q[2] = q[3] = 0.f; |
| 540 | return; |
| 541 | } |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 542 | |
Karl Schultz | 481756e | 2016-02-02 15:37:51 -0700 | [diff] [blame] | 543 | q[0] = r / 2.f; |
| 544 | q[1] = (M[p[0]][p[1]] - M[p[1]][p[0]]) / (2.f * r); |
| 545 | q[2] = (M[p[2]][p[0]] - M[p[0]][p[2]]) / (2.f * r); |
| 546 | q[3] = (M[p[2]][p[1]] - M[p[1]][p[2]]) / (2.f * r); |
Courtney Goeltzenleuchter | 4825f6a | 2014-10-28 10:27:47 -0600 | [diff] [blame] | 547 | } |
| 548 | |
| 549 | #endif |