| 1 | // |
| 2 | // Redistribution and use in source and binary forms, with or without |
| 3 | // modification, are permitted provided that the following conditions |
| 4 | // are met: |
| 5 | // * Redistributions of source code must retain the above copyright |
| 6 | // notice, this list of conditions and the following disclaimer. |
| 7 | // * Redistributions in binary form must reproduce the above copyright |
| 8 | // notice, this list of conditions and the following disclaimer in the |
| 9 | // documentation and/or other materials provided with the distribution. |
| 10 | // * Neither the name of NVIDIA CORPORATION nor the names of its |
| 11 | // contributors may be used to endorse or promote products derived |
| 12 | // from this software without specific prior written permission. |
| 13 | // |
| 14 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ''AS IS'' AND ANY |
| 15 | // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 16 | // IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| 17 | // PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR |
| 18 | // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| 19 | // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| 20 | // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
| 21 | // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY |
| 22 | // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 23 | // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| 24 | // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 25 | // |
| 26 | // Copyright (c) 2008-2021 NVIDIA Corporation. All rights reserved. |
| 27 | // Copyright (c) 2004-2008 AGEIA Technologies, Inc. All rights reserved. |
| 28 | // Copyright (c) 2001-2004 NovodeX AG. All rights reserved. |
| 29 | |
| 30 | #ifndef PXFOUNDATION_PXMAT33_H |
| 31 | #define PXFOUNDATION_PXMAT33_H |
| 32 | /** \addtogroup foundation |
| 33 | @{ |
| 34 | */ |
| 35 | |
| 36 | #include "foundation/PxVec3.h" |
| 37 | #include "foundation/PxQuat.h" |
| 38 | |
| 39 | #if !PX_DOXYGEN |
| 40 | namespace physx |
| 41 | { |
| 42 | #endif |
| 43 | /*! |
| 44 | \brief 3x3 matrix class |
| 45 | |
| 46 | Some clarifications, as there have been much confusion about matrix formats etc in the past. |
| 47 | |
| 48 | Short: |
| 49 | - Matrix have base vectors in columns (vectors are column matrices, 3x1 matrices). |
| 50 | - Matrix is physically stored in column major format |
| 51 | - Matrices are concaternated from left |
| 52 | |
| 53 | Long: |
| 54 | Given three base vectors a, b and c the matrix is stored as |
| 55 | |
| 56 | |a.x b.x c.x| |
| 57 | |a.y b.y c.y| |
| 58 | |a.z b.z c.z| |
| 59 | |
| 60 | Vectors are treated as columns, so the vector v is |
| 61 | |
| 62 | |x| |
| 63 | |y| |
| 64 | |z| |
| 65 | |
| 66 | And matrices are applied _before_ the vector (pre-multiplication) |
| 67 | v' = M*v |
| 68 | |
| 69 | |x'| |a.x b.x c.x| |x| |a.x*x + b.x*y + c.x*z| |
| 70 | |y'| = |a.y b.y c.y| * |y| = |a.y*x + b.y*y + c.y*z| |
| 71 | |z'| |a.z b.z c.z| |z| |a.z*x + b.z*y + c.z*z| |
| 72 | |
| 73 | |
| 74 | Physical storage and indexing: |
| 75 | To be compatible with popular 3d rendering APIs (read D3d and OpenGL) |
| 76 | the physical indexing is |
| 77 | |
| 78 | |0 3 6| |
| 79 | |1 4 7| |
| 80 | |2 5 8| |
| 81 | |
| 82 | index = column*3 + row |
| 83 | |
| 84 | which in C++ translates to M[column][row] |
| 85 | |
| 86 | The mathematical indexing is M_row,column and this is what is used for _-notation |
| 87 | so _12 is 1st row, second column and operator(row, column)! |
| 88 | |
| 89 | */ |
| 90 | class PxMat33 |
| 91 | { |
| 92 | public: |
| 93 | //! Default constructor |
| 94 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33() |
| 95 | { |
| 96 | } |
| 97 | |
| 98 | //! identity constructor |
| 99 | PX_CUDA_CALLABLE PX_INLINE PxMat33(PxIDENTITY r) |
| 100 | : column0(1.0f, 0.0f, 0.0f), column1(0.0f, 1.0f, 0.0f), column2(0.0f, 0.0f, 1.0f) |
| 101 | { |
| 102 | PX_UNUSED(r); |
| 103 | } |
| 104 | |
| 105 | //! zero constructor |
| 106 | PX_CUDA_CALLABLE PX_INLINE PxMat33(PxZERO r) : column0(0.0f), column1(0.0f), column2(0.0f) |
| 107 | { |
| 108 | PX_UNUSED(r); |
| 109 | } |
| 110 | |
| 111 | //! Construct from three base vectors |
| 112 | PX_CUDA_CALLABLE PxMat33(const PxVec3& col0, const PxVec3& col1, const PxVec3& col2) |
| 113 | : column0(col0), column1(col1), column2(col2) |
| 114 | { |
| 115 | } |
| 116 | |
| 117 | //! constructor from a scalar, which generates a multiple of the identity matrix |
| 118 | explicit PX_CUDA_CALLABLE PX_INLINE PxMat33(float r) |
| 119 | : column0(r, 0.0f, 0.0f), column1(0.0f, r, 0.0f), column2(0.0f, 0.0f, r) |
| 120 | { |
| 121 | } |
| 122 | |
| 123 | //! Construct from float[9] |
| 124 | explicit PX_CUDA_CALLABLE PX_INLINE PxMat33(float values[]) |
| 125 | : column0(values[0], values[1], values[2]) |
| 126 | , column1(values[3], values[4], values[5]) |
| 127 | , column2(values[6], values[7], values[8]) |
| 128 | { |
| 129 | } |
| 130 | |
| 131 | //! Construct from a quaternion |
| 132 | explicit PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33(const PxQuat& q) |
| 133 | { |
| 134 | const float x = q.x; |
| 135 | const float y = q.y; |
| 136 | const float z = q.z; |
| 137 | const float w = q.w; |
| 138 | |
| 139 | const float x2 = x + x; |
| 140 | const float y2 = y + y; |
| 141 | const float z2 = z + z; |
| 142 | |
| 143 | const float xx = x2 * x; |
| 144 | const float yy = y2 * y; |
| 145 | const float zz = z2 * z; |
| 146 | |
| 147 | const float xy = x2 * y; |
| 148 | const float xz = x2 * z; |
| 149 | const float xw = x2 * w; |
| 150 | |
| 151 | const float yz = y2 * z; |
| 152 | const float yw = y2 * w; |
| 153 | const float zw = z2 * w; |
| 154 | |
| 155 | column0 = PxVec3(1.0f - yy - zz, xy + zw, xz - yw); |
| 156 | column1 = PxVec3(xy - zw, 1.0f - xx - zz, yz + xw); |
| 157 | column2 = PxVec3(xz + yw, yz - xw, 1.0f - xx - yy); |
| 158 | } |
| 159 | |
| 160 | //! Copy constructor |
| 161 | PX_CUDA_CALLABLE PX_INLINE PxMat33(const PxMat33& other) |
| 162 | : column0(other.column0), column1(other.column1), column2(other.column2) |
| 163 | { |
| 164 | } |
| 165 | |
| 166 | //! Assignment operator |
| 167 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33& operator=(const PxMat33& other) |
| 168 | { |
| 169 | column0 = other.column0; |
| 170 | column1 = other.column1; |
| 171 | column2 = other.column2; |
| 172 | return *this; |
| 173 | } |
| 174 | |
| 175 | //! Construct from diagonal, off-diagonals are zero. |
| 176 | PX_CUDA_CALLABLE PX_INLINE static const PxMat33 createDiagonal(const PxVec3& d) |
| 177 | { |
| 178 | return PxMat33(PxVec3(d.x, 0.0f, 0.0f), PxVec3(0.0f, d.y, 0.0f), PxVec3(0.0f, 0.0f, d.z)); |
| 179 | } |
| 180 | |
| 181 | /** |
| 182 | \brief returns true if the two matrices are exactly equal |
| 183 | */ |
| 184 | PX_CUDA_CALLABLE PX_INLINE bool operator==(const PxMat33& m) const |
| 185 | { |
| 186 | return column0 == m.column0 && column1 == m.column1 && column2 == m.column2; |
| 187 | } |
| 188 | |
| 189 | //! Get transposed matrix |
| 190 | PX_CUDA_CALLABLE PX_FORCE_INLINE const PxMat33 getTranspose() const |
| 191 | { |
| 192 | const PxVec3 v0(column0.x, column1.x, column2.x); |
| 193 | const PxVec3 v1(column0.y, column1.y, column2.y); |
| 194 | const PxVec3 v2(column0.z, column1.z, column2.z); |
| 195 | |
| 196 | return PxMat33(v0, v1, v2); |
| 197 | } |
| 198 | |
| 199 | //! Get the real inverse |
| 200 | PX_CUDA_CALLABLE PX_INLINE const PxMat33 getInverse() const |
| 201 | { |
| 202 | const float det = getDeterminant(); |
| 203 | PxMat33 inverse; |
| 204 | |
| 205 | if(det != 0) |
| 206 | { |
| 207 | const float invDet = 1.0f / det; |
| 208 | |
| 209 | inverse.column0.x = invDet * (column1.y * column2.z - column2.y * column1.z); |
| 210 | inverse.column0.y = invDet * -(column0.y * column2.z - column2.y * column0.z); |
| 211 | inverse.column0.z = invDet * (column0.y * column1.z - column0.z * column1.y); |
| 212 | |
| 213 | inverse.column1.x = invDet * -(column1.x * column2.z - column1.z * column2.x); |
| 214 | inverse.column1.y = invDet * (column0.x * column2.z - column0.z * column2.x); |
| 215 | inverse.column1.z = invDet * -(column0.x * column1.z - column0.z * column1.x); |
| 216 | |
| 217 | inverse.column2.x = invDet * (column1.x * column2.y - column1.y * column2.x); |
| 218 | inverse.column2.y = invDet * -(column0.x * column2.y - column0.y * column2.x); |
| 219 | inverse.column2.z = invDet * (column0.x * column1.y - column1.x * column0.y); |
| 220 | |
| 221 | return inverse; |
| 222 | } |
| 223 | else |
| 224 | { |
| 225 | return PxMat33(PxIdentity); |
| 226 | } |
| 227 | } |
| 228 | |
| 229 | //! Get determinant |
| 230 | PX_CUDA_CALLABLE PX_INLINE float getDeterminant() const |
| 231 | { |
| 232 | return column0.dot(v: column1.cross(v: column2)); |
| 233 | } |
| 234 | |
| 235 | //! Unary minus |
| 236 | PX_CUDA_CALLABLE PX_INLINE const PxMat33 operator-() const |
| 237 | { |
| 238 | return PxMat33(-column0, -column1, -column2); |
| 239 | } |
| 240 | |
| 241 | //! Add |
| 242 | PX_CUDA_CALLABLE PX_INLINE const PxMat33 operator+(const PxMat33& other) const |
| 243 | { |
| 244 | return PxMat33(column0 + other.column0, column1 + other.column1, column2 + other.column2); |
| 245 | } |
| 246 | |
| 247 | //! Subtract |
| 248 | PX_CUDA_CALLABLE PX_INLINE const PxMat33 operator-(const PxMat33& other) const |
| 249 | { |
| 250 | return PxMat33(column0 - other.column0, column1 - other.column1, column2 - other.column2); |
| 251 | } |
| 252 | |
| 253 | //! Scalar multiplication |
| 254 | PX_CUDA_CALLABLE PX_INLINE const PxMat33 operator*(float scalar) const |
| 255 | { |
| 256 | return PxMat33(column0 * scalar, column1 * scalar, column2 * scalar); |
| 257 | } |
| 258 | |
| 259 | friend PxMat33 operator*(float, const PxMat33&); |
| 260 | |
| 261 | //! Matrix vector multiplication (returns 'this->transform(vec)') |
| 262 | PX_CUDA_CALLABLE PX_INLINE const PxVec3 operator*(const PxVec3& vec) const |
| 263 | { |
| 264 | return transform(other: vec); |
| 265 | } |
| 266 | |
| 267 | // a <op>= b operators |
| 268 | |
| 269 | //! Matrix multiplication |
| 270 | PX_CUDA_CALLABLE PX_FORCE_INLINE const PxMat33 operator*(const PxMat33& other) const |
| 271 | { |
| 272 | // Rows from this <dot> columns from other |
| 273 | // column0 = transform(other.column0) etc |
| 274 | return PxMat33(transform(other: other.column0), transform(other: other.column1), transform(other: other.column2)); |
| 275 | } |
| 276 | |
| 277 | //! Equals-add |
| 278 | PX_CUDA_CALLABLE PX_INLINE PxMat33& operator+=(const PxMat33& other) |
| 279 | { |
| 280 | column0 += other.column0; |
| 281 | column1 += other.column1; |
| 282 | column2 += other.column2; |
| 283 | return *this; |
| 284 | } |
| 285 | |
| 286 | //! Equals-sub |
| 287 | PX_CUDA_CALLABLE PX_INLINE PxMat33& operator-=(const PxMat33& other) |
| 288 | { |
| 289 | column0 -= other.column0; |
| 290 | column1 -= other.column1; |
| 291 | column2 -= other.column2; |
| 292 | return *this; |
| 293 | } |
| 294 | |
| 295 | //! Equals scalar multiplication |
| 296 | PX_CUDA_CALLABLE PX_INLINE PxMat33& operator*=(float scalar) |
| 297 | { |
| 298 | column0 *= scalar; |
| 299 | column1 *= scalar; |
| 300 | column2 *= scalar; |
| 301 | return *this; |
| 302 | } |
| 303 | |
| 304 | //! Equals matrix multiplication |
| 305 | PX_CUDA_CALLABLE PX_INLINE PxMat33& operator*=(const PxMat33& other) |
| 306 | { |
| 307 | *this = *this * other; |
| 308 | return *this; |
| 309 | } |
| 310 | |
| 311 | //! Element access, mathematical way! |
| 312 | PX_CUDA_CALLABLE PX_FORCE_INLINE float operator()(unsigned int row, unsigned int col) const |
| 313 | { |
| 314 | return (*this)[col][row]; |
| 315 | } |
| 316 | |
| 317 | //! Element access, mathematical way! |
| 318 | PX_CUDA_CALLABLE PX_FORCE_INLINE float& operator()(unsigned int row, unsigned int col) |
| 319 | { |
| 320 | return (*this)[col][row]; |
| 321 | } |
| 322 | |
| 323 | // Transform etc |
| 324 | |
| 325 | //! Transform vector by matrix, equal to v' = M*v |
| 326 | PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3 transform(const PxVec3& other) const |
| 327 | { |
| 328 | return column0 * other.x + column1 * other.y + column2 * other.z; |
| 329 | } |
| 330 | |
| 331 | //! Transform vector by matrix transpose, v' = M^t*v |
| 332 | PX_CUDA_CALLABLE PX_INLINE const PxVec3 transformTranspose(const PxVec3& other) const |
| 333 | { |
| 334 | return PxVec3(column0.dot(v: other), column1.dot(v: other), column2.dot(v: other)); |
| 335 | } |
| 336 | |
| 337 | PX_CUDA_CALLABLE PX_FORCE_INLINE const float* front() const |
| 338 | { |
| 339 | return &column0.x; |
| 340 | } |
| 341 | |
| 342 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3& operator[](unsigned int num) |
| 343 | { |
| 344 | return (&column0)[num]; |
| 345 | } |
| 346 | PX_CUDA_CALLABLE PX_FORCE_INLINE const PxVec3& operator[](unsigned int num) const |
| 347 | { |
| 348 | return (&column0)[num]; |
| 349 | } |
| 350 | |
| 351 | // Data, see above for format! |
| 352 | |
| 353 | PxVec3 column0, column1, column2; // the three base vectors |
| 354 | }; |
| 355 | |
| 356 | // implementation from PxQuat.h |
| 357 | PX_CUDA_CALLABLE PX_INLINE PxQuat::PxQuat(const PxMat33& m) |
| 358 | { |
| 359 | if(m.column2.z < 0) |
| 360 | { |
| 361 | if(m.column0.x > m.column1.y) |
| 362 | { |
| 363 | float t = 1 + m.column0.x - m.column1.y - m.column2.z; |
| 364 | *this = PxQuat(t, m.column0.y + m.column1.x, m.column2.x + m.column0.z, m.column1.z - m.column2.y) * |
| 365 | (0.5f / PxSqrt(a: t)); |
| 366 | } |
| 367 | else |
| 368 | { |
| 369 | float t = 1 - m.column0.x + m.column1.y - m.column2.z; |
| 370 | *this = PxQuat(m.column0.y + m.column1.x, t, m.column1.z + m.column2.y, m.column2.x - m.column0.z) * |
| 371 | (0.5f / PxSqrt(a: t)); |
| 372 | } |
| 373 | } |
| 374 | else |
| 375 | { |
| 376 | if(m.column0.x < -m.column1.y) |
| 377 | { |
| 378 | float t = 1 - m.column0.x - m.column1.y + m.column2.z; |
| 379 | *this = PxQuat(m.column2.x + m.column0.z, m.column1.z + m.column2.y, t, m.column0.y - m.column1.x) * |
| 380 | (0.5f / PxSqrt(a: t)); |
| 381 | } |
| 382 | else |
| 383 | { |
| 384 | float t = 1 + m.column0.x + m.column1.y + m.column2.z; |
| 385 | *this = PxQuat(m.column1.z - m.column2.y, m.column2.x - m.column0.z, m.column0.y - m.column1.x, t) * |
| 386 | (0.5f / PxSqrt(a: t)); |
| 387 | } |
| 388 | } |
| 389 | } |
| 390 | |
| 391 | #if !PX_DOXYGEN |
| 392 | } // namespace physx |
| 393 | #endif |
| 394 | |
| 395 | /** @} */ |
| 396 | #endif // #ifndef PXFOUNDATION_PXMAT33_H |
| 397 | |