Dan Albert | 287553d | 2017-02-16 10:47:51 -0800 | [diff] [blame] | 1 | /////////////////////////////////////////////////////////////////////////////////// |
| 2 | /// OpenGL Mathematics (glm.g-truc.net) |
| 3 | /// |
| 4 | /// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net) |
| 5 | /// Permission is hereby granted, free of charge, to any person obtaining a copy |
| 6 | /// of this software and associated documentation files (the "Software"), to deal |
| 7 | /// in the Software without restriction, including without limitation the rights |
| 8 | /// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell |
| 9 | /// copies of the Software, and to permit persons to whom the Software is |
| 10 | /// furnished to do so, subject to the following conditions: |
| 11 | /// |
| 12 | /// The above copyright notice and this permission notice shall be included in |
| 13 | /// all copies or substantial portions of the Software. |
| 14 | /// |
| 15 | /// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR |
| 16 | /// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
| 17 | /// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE |
| 18 | /// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER |
| 19 | /// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, |
| 20 | /// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN |
| 21 | /// THE SOFTWARE. |
| 22 | /// |
| 23 | /// @ref gtc_matrix_transform |
| 24 | /// @file glm/gtc/matrix_transform.inl |
| 25 | /// @date 2009-04-29 / 2011-06-15 |
| 26 | /// @author Christophe Riccio |
| 27 | /////////////////////////////////////////////////////////////////////////////////// |
| 28 | |
| 29 | #include "../geometric.hpp" |
| 30 | #include "../trigonometric.hpp" |
| 31 | #include "../matrix.hpp" |
| 32 | |
| 33 | namespace glm |
| 34 | { |
| 35 | template <typename T, precision P> |
| 36 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> translate |
| 37 | ( |
| 38 | detail::tmat4x4<T, P> const & m, |
| 39 | detail::tvec3<T, P> const & v |
| 40 | ) |
| 41 | { |
| 42 | detail::tmat4x4<T, P> Result(m); |
| 43 | Result[3] = m[0] * v[0] + m[1] * v[1] + m[2] * v[2] + m[3]; |
| 44 | return Result; |
| 45 | } |
| 46 | |
| 47 | template <typename T, precision P> |
| 48 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> rotate |
| 49 | ( |
| 50 | detail::tmat4x4<T, P> const & m, |
| 51 | T const & angle, |
| 52 | detail::tvec3<T, P> const & v |
| 53 | ) |
| 54 | { |
| 55 | #ifdef GLM_FORCE_RADIANS |
| 56 | T a = angle; |
| 57 | #else |
| 58 | # pragma message("GLM: rotate function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| 59 | T a = radians(angle); |
| 60 | #endif |
| 61 | T c = cos(a); |
| 62 | T s = sin(a); |
| 63 | |
| 64 | detail::tvec3<T, P> axis(normalize(v)); |
| 65 | detail::tvec3<T, P> temp((T(1) - c) * axis); |
| 66 | |
| 67 | detail::tmat4x4<T, P> Rotate(detail::tmat4x4<T, P>::_null); |
| 68 | Rotate[0][0] = c + temp[0] * axis[0]; |
| 69 | Rotate[0][1] = 0 + temp[0] * axis[1] + s * axis[2]; |
| 70 | Rotate[0][2] = 0 + temp[0] * axis[2] - s * axis[1]; |
| 71 | |
| 72 | Rotate[1][0] = 0 + temp[1] * axis[0] - s * axis[2]; |
| 73 | Rotate[1][1] = c + temp[1] * axis[1]; |
| 74 | Rotate[1][2] = 0 + temp[1] * axis[2] + s * axis[0]; |
| 75 | |
| 76 | Rotate[2][0] = 0 + temp[2] * axis[0] + s * axis[1]; |
| 77 | Rotate[2][1] = 0 + temp[2] * axis[1] - s * axis[0]; |
| 78 | Rotate[2][2] = c + temp[2] * axis[2]; |
| 79 | |
| 80 | detail::tmat4x4<T, P> Result(detail::tmat4x4<T, P>::_null); |
| 81 | Result[0] = m[0] * Rotate[0][0] + m[1] * Rotate[0][1] + m[2] * Rotate[0][2]; |
| 82 | Result[1] = m[0] * Rotate[1][0] + m[1] * Rotate[1][1] + m[2] * Rotate[1][2]; |
| 83 | Result[2] = m[0] * Rotate[2][0] + m[1] * Rotate[2][1] + m[2] * Rotate[2][2]; |
| 84 | Result[3] = m[3]; |
| 85 | return Result; |
| 86 | } |
| 87 | |
| 88 | template <typename T, precision P> |
| 89 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> rotate_slow |
| 90 | ( |
| 91 | detail::tmat4x4<T, P> const & m, |
| 92 | T const & angle, |
| 93 | detail::tvec3<T, P> const & v |
| 94 | ) |
| 95 | { |
| 96 | #ifdef GLM_FORCE_RADIANS |
| 97 | T const a = angle; |
| 98 | #else |
| 99 | # pragma message("GLM: rotate_slow function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| 100 | T const a = radians(angle); |
| 101 | #endif |
| 102 | T c = cos(a); |
| 103 | T s = sin(a); |
| 104 | detail::tmat4x4<T, P> Result; |
| 105 | |
| 106 | detail::tvec3<T, P> axis = normalize(v); |
| 107 | |
| 108 | Result[0][0] = c + (1 - c) * axis.x * axis.x; |
| 109 | Result[0][1] = (1 - c) * axis.x * axis.y + s * axis.z; |
| 110 | Result[0][2] = (1 - c) * axis.x * axis.z - s * axis.y; |
| 111 | Result[0][3] = 0; |
| 112 | |
| 113 | Result[1][0] = (1 - c) * axis.y * axis.x - s * axis.z; |
| 114 | Result[1][1] = c + (1 - c) * axis.y * axis.y; |
| 115 | Result[1][2] = (1 - c) * axis.y * axis.z + s * axis.x; |
| 116 | Result[1][3] = 0; |
| 117 | |
| 118 | Result[2][0] = (1 - c) * axis.z * axis.x + s * axis.y; |
| 119 | Result[2][1] = (1 - c) * axis.z * axis.y - s * axis.x; |
| 120 | Result[2][2] = c + (1 - c) * axis.z * axis.z; |
| 121 | Result[2][3] = 0; |
| 122 | |
| 123 | Result[3] = detail::tvec4<T, P>(0, 0, 0, 1); |
| 124 | return m * Result; |
| 125 | } |
| 126 | |
| 127 | template <typename T, precision P> |
| 128 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> scale |
| 129 | ( |
| 130 | detail::tmat4x4<T, P> const & m, |
| 131 | detail::tvec3<T, P> const & v |
| 132 | ) |
| 133 | { |
| 134 | detail::tmat4x4<T, P> Result(detail::tmat4x4<T, P>::_null); |
| 135 | Result[0] = m[0] * v[0]; |
| 136 | Result[1] = m[1] * v[1]; |
| 137 | Result[2] = m[2] * v[2]; |
| 138 | Result[3] = m[3]; |
| 139 | return Result; |
| 140 | } |
| 141 | |
| 142 | template <typename T, precision P> |
| 143 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> scale_slow |
| 144 | ( |
| 145 | detail::tmat4x4<T, P> const & m, |
| 146 | detail::tvec3<T, P> const & v |
| 147 | ) |
| 148 | { |
| 149 | detail::tmat4x4<T, P> Result(T(1)); |
| 150 | Result[0][0] = v.x; |
| 151 | Result[1][1] = v.y; |
| 152 | Result[2][2] = v.z; |
| 153 | return m * Result; |
| 154 | } |
| 155 | |
| 156 | template <typename T> |
| 157 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, defaultp> ortho |
| 158 | ( |
| 159 | T const & left, |
| 160 | T const & right, |
| 161 | T const & bottom, |
| 162 | T const & top, |
| 163 | T const & zNear, |
| 164 | T const & zFar |
| 165 | ) |
| 166 | { |
| 167 | detail::tmat4x4<T, defaultp> Result(1); |
| 168 | Result[0][0] = static_cast<T>(2) / (right - left); |
| 169 | Result[1][1] = static_cast<T>(2) / (top - bottom); |
| 170 | Result[2][2] = - T(2) / (zFar - zNear); |
| 171 | Result[3][0] = - (right + left) / (right - left); |
| 172 | Result[3][1] = - (top + bottom) / (top - bottom); |
| 173 | Result[3][2] = - (zFar + zNear) / (zFar - zNear); |
| 174 | return Result; |
| 175 | } |
| 176 | |
| 177 | template <typename T> |
| 178 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, defaultp> ortho |
| 179 | ( |
| 180 | T const & left, |
| 181 | T const & right, |
| 182 | T const & bottom, |
| 183 | T const & top |
| 184 | ) |
| 185 | { |
| 186 | detail::tmat4x4<T, defaultp> Result(1); |
| 187 | Result[0][0] = static_cast<T>(2) / (right - left); |
| 188 | Result[1][1] = static_cast<T>(2) / (top - bottom); |
| 189 | Result[2][2] = - T(1); |
| 190 | Result[3][0] = - (right + left) / (right - left); |
| 191 | Result[3][1] = - (top + bottom) / (top - bottom); |
| 192 | return Result; |
| 193 | } |
| 194 | |
| 195 | template <typename valType> |
| 196 | GLM_FUNC_QUALIFIER detail::tmat4x4<valType, defaultp> frustum |
| 197 | ( |
| 198 | valType const & left, |
| 199 | valType const & right, |
| 200 | valType const & bottom, |
| 201 | valType const & top, |
| 202 | valType const & nearVal, |
| 203 | valType const & farVal |
| 204 | ) |
| 205 | { |
| 206 | detail::tmat4x4<valType, defaultp> Result(0); |
| 207 | Result[0][0] = (valType(2) * nearVal) / (right - left); |
| 208 | Result[1][1] = (valType(2) * nearVal) / (top - bottom); |
| 209 | Result[2][0] = (right + left) / (right - left); |
| 210 | Result[2][1] = (top + bottom) / (top - bottom); |
| 211 | Result[2][2] = -(farVal + nearVal) / (farVal - nearVal); |
| 212 | Result[2][3] = valType(-1); |
| 213 | Result[3][2] = -(valType(2) * farVal * nearVal) / (farVal - nearVal); |
| 214 | return Result; |
| 215 | } |
| 216 | |
| 217 | template <typename valType> |
| 218 | GLM_FUNC_QUALIFIER detail::tmat4x4<valType, defaultp> perspective |
| 219 | ( |
| 220 | valType const & fovy, |
| 221 | valType const & aspect, |
| 222 | valType const & zNear, |
| 223 | valType const & zFar |
| 224 | ) |
| 225 | { |
| 226 | assert(aspect != valType(0)); |
| 227 | assert(zFar != zNear); |
| 228 | |
| 229 | #ifdef GLM_FORCE_RADIANS |
| 230 | valType const rad = fovy; |
| 231 | #else |
| 232 | # pragma message("GLM: perspective function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| 233 | valType const rad = glm::radians(fovy); |
| 234 | #endif |
| 235 | |
| 236 | valType tanHalfFovy = tan(rad / valType(2)); |
| 237 | |
| 238 | detail::tmat4x4<valType, defaultp> Result(valType(0)); |
| 239 | Result[0][0] = valType(1) / (aspect * tanHalfFovy); |
| 240 | Result[1][1] = valType(1) / (tanHalfFovy); |
| 241 | Result[2][2] = - (zFar + zNear) / (zFar - zNear); |
| 242 | Result[2][3] = - valType(1); |
| 243 | Result[3][2] = - (valType(2) * zFar * zNear) / (zFar - zNear); |
| 244 | return Result; |
| 245 | } |
| 246 | |
| 247 | template <typename valType> |
| 248 | GLM_FUNC_QUALIFIER detail::tmat4x4<valType, defaultp> perspectiveFov |
| 249 | ( |
| 250 | valType const & fov, |
| 251 | valType const & width, |
| 252 | valType const & height, |
| 253 | valType const & zNear, |
| 254 | valType const & zFar |
| 255 | ) |
| 256 | { |
| 257 | assert(width > valType(0)); |
| 258 | assert(height > valType(0)); |
| 259 | assert(fov > valType(0)); |
| 260 | |
| 261 | #ifdef GLM_FORCE_RADIANS |
| 262 | valType rad = fov; |
| 263 | #else |
| 264 | # pragma message("GLM: perspectiveFov function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| 265 | valType rad = glm::radians(fov); |
| 266 | #endif |
| 267 | valType h = glm::cos(valType(0.5) * rad) / glm::sin(valType(0.5) * rad); |
| 268 | valType w = h * height / width; ///todo max(width , Height) / min(width , Height)? |
| 269 | |
| 270 | detail::tmat4x4<valType, defaultp> Result(valType(0)); |
| 271 | Result[0][0] = w; |
| 272 | Result[1][1] = h; |
| 273 | Result[2][2] = - (zFar + zNear) / (zFar - zNear); |
| 274 | Result[2][3] = - valType(1); |
| 275 | Result[3][2] = - (valType(2) * zFar * zNear) / (zFar - zNear); |
| 276 | return Result; |
| 277 | } |
| 278 | |
| 279 | template <typename T> |
| 280 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, defaultp> infinitePerspective |
| 281 | ( |
| 282 | T fovy, |
| 283 | T aspect, |
| 284 | T zNear |
| 285 | ) |
| 286 | { |
| 287 | #ifdef GLM_FORCE_RADIANS |
| 288 | T const range = tan(fovy / T(2)) * zNear; |
| 289 | #else |
| 290 | # pragma message("GLM: infinitePerspective function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| 291 | T const range = tan(radians(fovy / T(2))) * zNear; |
| 292 | #endif |
| 293 | T left = -range * aspect; |
| 294 | T right = range * aspect; |
| 295 | T bottom = -range; |
| 296 | T top = range; |
| 297 | |
| 298 | detail::tmat4x4<T, defaultp> Result(T(0)); |
| 299 | Result[0][0] = (T(2) * zNear) / (right - left); |
| 300 | Result[1][1] = (T(2) * zNear) / (top - bottom); |
| 301 | Result[2][2] = - T(1); |
| 302 | Result[2][3] = - T(1); |
| 303 | Result[3][2] = - T(2) * zNear; |
| 304 | return Result; |
| 305 | } |
| 306 | |
| 307 | template <typename T> |
| 308 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, defaultp> tweakedInfinitePerspective |
| 309 | ( |
| 310 | T fovy, |
| 311 | T aspect, |
| 312 | T zNear |
| 313 | ) |
| 314 | { |
| 315 | #ifdef GLM_FORCE_RADIANS |
| 316 | T range = tan(fovy / T(2)) * zNear; |
| 317 | #else |
| 318 | # pragma message("GLM: tweakedInfinitePerspective function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.") |
| 319 | T range = tan(radians(fovy / T(2))) * zNear; |
| 320 | #endif |
| 321 | T left = -range * aspect; |
| 322 | T right = range * aspect; |
| 323 | T bottom = -range; |
| 324 | T top = range; |
| 325 | |
| 326 | detail::tmat4x4<T, defaultp> Result(T(0)); |
| 327 | Result[0][0] = (T(2) * zNear) / (right - left); |
| 328 | Result[1][1] = (T(2) * zNear) / (top - bottom); |
| 329 | Result[2][2] = static_cast<T>(0.0001) - T(1); |
| 330 | Result[2][3] = static_cast<T>(-1); |
| 331 | Result[3][2] = - (T(0.0001) - T(2)) * zNear; |
| 332 | return Result; |
| 333 | } |
| 334 | |
| 335 | template <typename T, typename U, precision P> |
| 336 | GLM_FUNC_QUALIFIER detail::tvec3<T, P> project |
| 337 | ( |
| 338 | detail::tvec3<T, P> const & obj, |
| 339 | detail::tmat4x4<T, P> const & model, |
| 340 | detail::tmat4x4<T, P> const & proj, |
| 341 | detail::tvec4<U, P> const & viewport |
| 342 | ) |
| 343 | { |
| 344 | detail::tvec4<T, P> tmp = detail::tvec4<T, P>(obj, T(1)); |
| 345 | tmp = model * tmp; |
| 346 | tmp = proj * tmp; |
| 347 | |
| 348 | tmp /= tmp.w; |
| 349 | tmp = tmp * T(0.5) + T(0.5); |
| 350 | tmp[0] = tmp[0] * T(viewport[2]) + T(viewport[0]); |
| 351 | tmp[1] = tmp[1] * T(viewport[3]) + T(viewport[1]); |
| 352 | |
| 353 | return detail::tvec3<T, P>(tmp); |
| 354 | } |
| 355 | |
| 356 | template <typename T, typename U, precision P> |
| 357 | GLM_FUNC_QUALIFIER detail::tvec3<T, P> unProject |
| 358 | ( |
| 359 | detail::tvec3<T, P> const & win, |
| 360 | detail::tmat4x4<T, P> const & model, |
| 361 | detail::tmat4x4<T, P> const & proj, |
| 362 | detail::tvec4<U, P> const & viewport |
| 363 | ) |
| 364 | { |
| 365 | detail::tmat4x4<T, P> Inverse = inverse(proj * model); |
| 366 | |
| 367 | detail::tvec4<T, P> tmp = detail::tvec4<T, P>(win, T(1)); |
| 368 | tmp.x = (tmp.x - T(viewport[0])) / T(viewport[2]); |
| 369 | tmp.y = (tmp.y - T(viewport[1])) / T(viewport[3]); |
| 370 | tmp = tmp * T(2) - T(1); |
| 371 | |
| 372 | detail::tvec4<T, P> obj = Inverse * tmp; |
| 373 | obj /= obj.w; |
| 374 | |
| 375 | return detail::tvec3<T, P>(obj); |
| 376 | } |
| 377 | |
| 378 | template <typename T, precision P, typename U> |
| 379 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> pickMatrix |
| 380 | ( |
| 381 | detail::tvec2<T, P> const & center, |
| 382 | detail::tvec2<T, P> const & delta, |
| 383 | detail::tvec4<U, P> const & viewport |
| 384 | ) |
| 385 | { |
| 386 | assert(delta.x > T(0) && delta.y > T(0)); |
| 387 | detail::tmat4x4<T, P> Result(1.0f); |
| 388 | |
| 389 | if(!(delta.x > T(0) && delta.y > T(0))) |
| 390 | return Result; // Error |
| 391 | |
| 392 | detail::tvec3<T, P> Temp( |
| 393 | (T(viewport[2]) - T(2) * (center.x - T(viewport[0]))) / delta.x, |
| 394 | (T(viewport[3]) - T(2) * (center.y - T(viewport[1]))) / delta.y, |
| 395 | T(0)); |
| 396 | |
| 397 | // Translate and scale the picked region to the entire window |
| 398 | Result = translate(Result, Temp); |
| 399 | return scale(Result, detail::tvec3<T, P>(T(viewport[2]) / delta.x, T(viewport[3]) / delta.y, T(1))); |
| 400 | } |
| 401 | |
| 402 | template <typename T, precision P> |
| 403 | GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> lookAt |
| 404 | ( |
| 405 | detail::tvec3<T, P> const & eye, |
| 406 | detail::tvec3<T, P> const & center, |
| 407 | detail::tvec3<T, P> const & up |
| 408 | ) |
| 409 | { |
| 410 | detail::tvec3<T, P> f(normalize(center - eye)); |
| 411 | detail::tvec3<T, P> s(normalize(cross(f, up))); |
| 412 | detail::tvec3<T, P> u(cross(s, f)); |
| 413 | |
| 414 | detail::tmat4x4<T, P> Result(1); |
| 415 | Result[0][0] = s.x; |
| 416 | Result[1][0] = s.y; |
| 417 | Result[2][0] = s.z; |
| 418 | Result[0][1] = u.x; |
| 419 | Result[1][1] = u.y; |
| 420 | Result[2][1] = u.z; |
| 421 | Result[0][2] =-f.x; |
| 422 | Result[1][2] =-f.y; |
| 423 | Result[2][2] =-f.z; |
| 424 | Result[3][0] =-dot(s, eye); |
| 425 | Result[3][1] =-dot(u, eye); |
| 426 | Result[3][2] = dot(f, eye); |
| 427 | return Result; |
| 428 | } |
| 429 | }//namespace glm |