| 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 PSFOUNDATION_PSMATHUTILS_H |
| 31 | #define PSFOUNDATION_PSMATHUTILS_H |
| 32 | |
| 33 | #include "foundation/PxPreprocessor.h" |
| 34 | #include "foundation/PxTransform.h" |
| 35 | #include "foundation/PxMat33.h" |
| 36 | #include "Ps.h" |
| 37 | #include "PsIntrinsics.h" |
| 38 | |
| 39 | // General guideline is: if it's an abstract math function, it belongs here. |
| 40 | // If it's a math function where the inputs have specific semantics (e.g. |
| 41 | // separateSwingTwist) it doesn't. |
| 42 | |
| 43 | namespace physx |
| 44 | { |
| 45 | namespace shdfnd |
| 46 | { |
| 47 | /** |
| 48 | \brief sign returns the sign of its argument. The sign of zero is undefined. |
| 49 | */ |
| 50 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 sign(const PxF32 a) |
| 51 | { |
| 52 | return intrinsics::sign(a); |
| 53 | } |
| 54 | |
| 55 | /** |
| 56 | \brief sign returns the sign of its argument. The sign of zero is undefined. |
| 57 | */ |
| 58 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 sign(const PxF64 a) |
| 59 | { |
| 60 | return (a >= 0.0) ? 1.0 : -1.0; |
| 61 | } |
| 62 | |
| 63 | /** |
| 64 | \brief sign returns the sign of its argument. The sign of zero is undefined. |
| 65 | */ |
| 66 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxI32 sign(const PxI32 a) |
| 67 | { |
| 68 | return (a >= 0) ? 1 : -1; |
| 69 | } |
| 70 | |
| 71 | /** |
| 72 | \brief Returns true if the two numbers are within eps of each other. |
| 73 | */ |
| 74 | PX_CUDA_CALLABLE PX_FORCE_INLINE bool equals(const PxF32 a, const PxF32 b, const PxF32 eps) |
| 75 | { |
| 76 | return (PxAbs(a: a - b) < eps); |
| 77 | } |
| 78 | |
| 79 | /** |
| 80 | \brief Returns true if the two numbers are within eps of each other. |
| 81 | */ |
| 82 | PX_CUDA_CALLABLE PX_FORCE_INLINE bool equals(const PxF64 a, const PxF64 b, const PxF64 eps) |
| 83 | { |
| 84 | return (PxAbs(a: a - b) < eps); |
| 85 | } |
| 86 | |
| 87 | /** |
| 88 | \brief The floor function returns a floating-point value representing the largest integer that is less than or equal to |
| 89 | x. |
| 90 | */ |
| 91 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 floor(const PxF32 a) |
| 92 | { |
| 93 | return floatFloor(x: a); |
| 94 | } |
| 95 | |
| 96 | /** |
| 97 | \brief The floor function returns a floating-point value representing the largest integer that is less than or equal to |
| 98 | x. |
| 99 | */ |
| 100 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 floor(const PxF64 a) |
| 101 | { |
| 102 | return ::floor(x: a); |
| 103 | } |
| 104 | |
| 105 | /** |
| 106 | \brief The ceil function returns a single value representing the smallest integer that is greater than or equal to x. |
| 107 | */ |
| 108 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 ceil(const PxF32 a) |
| 109 | { |
| 110 | return ::ceilf(x: a); |
| 111 | } |
| 112 | |
| 113 | /** |
| 114 | \brief The ceil function returns a double value representing the smallest integer that is greater than or equal to x. |
| 115 | */ |
| 116 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 ceil(const PxF64 a) |
| 117 | { |
| 118 | return ::ceil(x: a); |
| 119 | } |
| 120 | |
| 121 | /** |
| 122 | \brief mod returns the floating-point remainder of x / y. |
| 123 | |
| 124 | If the value of y is 0.0, mod returns a quiet NaN. |
| 125 | */ |
| 126 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 mod(const PxF32 x, const PxF32 y) |
| 127 | { |
| 128 | return PxF32(::fmodf(x: x, y: y)); |
| 129 | } |
| 130 | |
| 131 | /** |
| 132 | \brief mod returns the floating-point remainder of x / y. |
| 133 | |
| 134 | If the value of y is 0.0, mod returns a quiet NaN. |
| 135 | */ |
| 136 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 mod(const PxF64 x, const PxF64 y) |
| 137 | { |
| 138 | return ::fmod(x: x, y: y); |
| 139 | } |
| 140 | |
| 141 | /** |
| 142 | \brief Square. |
| 143 | */ |
| 144 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 sqr(const PxF32 a) |
| 145 | { |
| 146 | return a * a; |
| 147 | } |
| 148 | |
| 149 | /** |
| 150 | \brief Square. |
| 151 | */ |
| 152 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 sqr(const PxF64 a) |
| 153 | { |
| 154 | return a * a; |
| 155 | } |
| 156 | |
| 157 | /** |
| 158 | \brief Calculates x raised to the power of y. |
| 159 | */ |
| 160 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 pow(const PxF32 x, const PxF32 y) |
| 161 | { |
| 162 | return ::powf(x: x, y: y); |
| 163 | } |
| 164 | |
| 165 | /** |
| 166 | \brief Calculates x raised to the power of y. |
| 167 | */ |
| 168 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 pow(const PxF64 x, const PxF64 y) |
| 169 | { |
| 170 | return ::pow(x: x, y: y); |
| 171 | } |
| 172 | |
| 173 | /** |
| 174 | \brief Calculates e^n |
| 175 | */ |
| 176 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 exp(const PxF32 a) |
| 177 | { |
| 178 | return ::expf(x: a); |
| 179 | } |
| 180 | /** |
| 181 | |
| 182 | \brief Calculates e^n |
| 183 | */ |
| 184 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 exp(const PxF64 a) |
| 185 | { |
| 186 | return ::exp(x: a); |
| 187 | } |
| 188 | |
| 189 | /** |
| 190 | \brief Calculates 2^n |
| 191 | */ |
| 192 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 exp2(const PxF32 a) |
| 193 | { |
| 194 | return ::expf(x: a * 0.693147180559945309417f); |
| 195 | } |
| 196 | /** |
| 197 | |
| 198 | \brief Calculates 2^n |
| 199 | */ |
| 200 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 exp2(const PxF64 a) |
| 201 | { |
| 202 | return ::exp(x: a * 0.693147180559945309417); |
| 203 | } |
| 204 | |
| 205 | /** |
| 206 | \brief Calculates logarithms. |
| 207 | */ |
| 208 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 logE(const PxF32 a) |
| 209 | { |
| 210 | return ::logf(x: a); |
| 211 | } |
| 212 | |
| 213 | /** |
| 214 | \brief Calculates logarithms. |
| 215 | */ |
| 216 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 logE(const PxF64 a) |
| 217 | { |
| 218 | return ::log(x: a); |
| 219 | } |
| 220 | |
| 221 | /** |
| 222 | \brief Calculates logarithms. |
| 223 | */ |
| 224 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 log2(const PxF32 a) |
| 225 | { |
| 226 | return ::logf(x: a) / 0.693147180559945309417f; |
| 227 | } |
| 228 | |
| 229 | /** |
| 230 | \brief Calculates logarithms. |
| 231 | */ |
| 232 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 log2(const PxF64 a) |
| 233 | { |
| 234 | return ::log(x: a) / 0.693147180559945309417; |
| 235 | } |
| 236 | |
| 237 | /** |
| 238 | \brief Calculates logarithms. |
| 239 | */ |
| 240 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 log10(const PxF32 a) |
| 241 | { |
| 242 | return ::log10f(x: a); |
| 243 | } |
| 244 | |
| 245 | /** |
| 246 | \brief Calculates logarithms. |
| 247 | */ |
| 248 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 log10(const PxF64 a) |
| 249 | { |
| 250 | return ::log10(x: a); |
| 251 | } |
| 252 | |
| 253 | /** |
| 254 | \brief Converts degrees to radians. |
| 255 | */ |
| 256 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 degToRad(const PxF32 a) |
| 257 | { |
| 258 | return 0.01745329251994329547f * a; |
| 259 | } |
| 260 | |
| 261 | /** |
| 262 | \brief Converts degrees to radians. |
| 263 | */ |
| 264 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 degToRad(const PxF64 a) |
| 265 | { |
| 266 | return 0.01745329251994329547 * a; |
| 267 | } |
| 268 | |
| 269 | /** |
| 270 | \brief Converts radians to degrees. |
| 271 | */ |
| 272 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 radToDeg(const PxF32 a) |
| 273 | { |
| 274 | return 57.29577951308232286465f * a; |
| 275 | } |
| 276 | |
| 277 | /** |
| 278 | \brief Converts radians to degrees. |
| 279 | */ |
| 280 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF64 radToDeg(const PxF64 a) |
| 281 | { |
| 282 | return 57.29577951308232286465 * a; |
| 283 | } |
| 284 | |
| 285 | //! \brief compute sine and cosine at the same time. There is a 'fsincos' on PC that we probably want to use here |
| 286 | PX_CUDA_CALLABLE PX_FORCE_INLINE void sincos(const PxF32 radians, PxF32& sin, PxF32& cos) |
| 287 | { |
| 288 | /* something like: |
| 289 | _asm fld Local |
| 290 | _asm fsincos |
| 291 | _asm fstp LocalCos |
| 292 | _asm fstp LocalSin |
| 293 | */ |
| 294 | sin = PxSin(a: radians); |
| 295 | cos = PxCos(a: radians); |
| 296 | } |
| 297 | |
| 298 | /** |
| 299 | \brief uniform random number in [a,b] |
| 300 | */ |
| 301 | PX_FORCE_INLINE PxI32 rand(const PxI32 a, const PxI32 b) |
| 302 | { |
| 303 | return a + PxI32(::rand() % (b - a + 1)); |
| 304 | } |
| 305 | |
| 306 | /** |
| 307 | \brief uniform random number in [a,b] |
| 308 | */ |
| 309 | PX_FORCE_INLINE PxF32 rand(const PxF32 a, const PxF32 b) |
| 310 | { |
| 311 | return a + (b - a) * PxF32(::rand()) / PxF32(RAND_MAX); |
| 312 | } |
| 313 | |
| 314 | //! \brief return angle between two vectors in radians |
| 315 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxF32 angle(const PxVec3& v0, const PxVec3& v1) |
| 316 | { |
| 317 | const PxF32 cos = v0.dot(v: v1); // |v0|*|v1|*Cos(Angle) |
| 318 | const PxF32 sin = (v0.cross(v: v1)).magnitude(); // |v0|*|v1|*Sin(Angle) |
| 319 | return PxAtan2(x: sin, y: cos); |
| 320 | } |
| 321 | |
| 322 | //! If possible use instead fsel on the dot product /*fsel(d.dot(p),onething,anotherthing);*/ |
| 323 | //! Compares orientations (more readable, user-friendly function) |
| 324 | PX_CUDA_CALLABLE PX_FORCE_INLINE bool sameDirection(const PxVec3& d, const PxVec3& p) |
| 325 | { |
| 326 | return d.dot(v: p) >= 0.0f; |
| 327 | } |
| 328 | |
| 329 | //! Checks 2 values have different signs |
| 330 | PX_CUDA_CALLABLE PX_FORCE_INLINE IntBool differentSign(PxReal f0, PxReal f1) |
| 331 | { |
| 332 | #if !PX_EMSCRIPTEN |
| 333 | union |
| 334 | { |
| 335 | PxU32 u; |
| 336 | PxReal f; |
| 337 | } u1, u2; |
| 338 | u1.f = f0; |
| 339 | u2.f = f1; |
| 340 | return IntBool((u1.u ^ u2.u) & PX_SIGN_BITMASK); |
| 341 | #else |
| 342 | // javascript floats are 64-bits... |
| 343 | return IntBool( (f0*f1) < 0.0f ); |
| 344 | #endif |
| 345 | } |
| 346 | |
| 347 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxMat33 star(const PxVec3& v) |
| 348 | { |
| 349 | return PxMat33(PxVec3(0, v.z, -v.y), PxVec3(-v.z, 0, v.x), PxVec3(v.y, -v.x, 0)); |
| 350 | } |
| 351 | |
| 352 | PX_CUDA_CALLABLE PX_INLINE PxVec3 log(const PxQuat& q) |
| 353 | { |
| 354 | const PxReal s = q.getImaginaryPart().magnitude(); |
| 355 | if(s < 1e-12f) |
| 356 | return PxVec3(0.0f); |
| 357 | // force the half-angle to have magnitude <= pi/2 |
| 358 | PxReal halfAngle = q.w < 0 ? PxAtan2(x: -s, y: -q.w) : PxAtan2(x: s, y: q.w); |
| 359 | PX_ASSERT(halfAngle >= -PxPi / 2 && halfAngle <= PxPi / 2); |
| 360 | |
| 361 | return q.getImaginaryPart().getNormalized() * 2.f * halfAngle; |
| 362 | } |
| 363 | |
| 364 | PX_CUDA_CALLABLE PX_INLINE PxQuat exp(const PxVec3& v) |
| 365 | { |
| 366 | const PxReal m = v.magnitudeSquared(); |
| 367 | return m < 1e-24f ? PxQuat(PxIdentity) : PxQuat(PxSqrt(a: m), v * PxRecipSqrt(a: m)); |
| 368 | } |
| 369 | |
| 370 | // quat to rotate v0 t0 v1 |
| 371 | PX_CUDA_CALLABLE PX_INLINE PxQuat rotationArc(const PxVec3& v0, const PxVec3& v1) |
| 372 | { |
| 373 | const PxVec3 cross = v0.cross(v: v1); |
| 374 | const PxReal d = v0.dot(v: v1); |
| 375 | if(d <= -0.99999f) |
| 376 | return (PxAbs(a: v0.x) < 0.1f ? PxQuat(0.0f, v0.z, -v0.y, 0.0f) : PxQuat(v0.y, -v0.x, 0.0, 0.0)).getNormalized(); |
| 377 | |
| 378 | const PxReal s = PxSqrt(a: (1 + d) * 2), r = 1 / s; |
| 379 | |
| 380 | return PxQuat(cross.x * r, cross.y * r, cross.z * r, s * 0.5f).getNormalized(); |
| 381 | } |
| 382 | |
| 383 | /** |
| 384 | \brief returns largest axis |
| 385 | */ |
| 386 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxU32 largestAxis(const PxVec3& v) |
| 387 | { |
| 388 | PxU32 m = PxU32(v.y > v.x ? 1 : 0); |
| 389 | return v.z > v[m] ? 2 : m; |
| 390 | } |
| 391 | |
| 392 | /** |
| 393 | \brief returns indices for the largest axis and 2 other axii |
| 394 | */ |
| 395 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxU32 largestAxis(const PxVec3& v, PxU32& other1, PxU32& other2) |
| 396 | { |
| 397 | if(v.x >= PxMax(a: v.y, b: v.z)) |
| 398 | { |
| 399 | other1 = 1; |
| 400 | other2 = 2; |
| 401 | return 0; |
| 402 | } |
| 403 | else if(v.y >= v.z) |
| 404 | { |
| 405 | other1 = 0; |
| 406 | other2 = 2; |
| 407 | return 1; |
| 408 | } |
| 409 | else |
| 410 | { |
| 411 | other1 = 0; |
| 412 | other2 = 1; |
| 413 | return 2; |
| 414 | } |
| 415 | } |
| 416 | |
| 417 | /** |
| 418 | \brief returns axis with smallest absolute value |
| 419 | */ |
| 420 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxU32 closestAxis(const PxVec3& v) |
| 421 | { |
| 422 | PxU32 m = PxU32(PxAbs(a: v.y) > PxAbs(a: v.x) ? 1 : 0); |
| 423 | return PxAbs(a: v.z) > PxAbs(a: v[m]) ? 2 : m; |
| 424 | } |
| 425 | |
| 426 | PX_CUDA_CALLABLE PX_INLINE PxU32 closestAxis(const PxVec3& v, PxU32& j, PxU32& k) |
| 427 | { |
| 428 | // find largest 2D plane projection |
| 429 | const PxF32 absPx = PxAbs(a: v.x); |
| 430 | const PxF32 absNy = PxAbs(a: v.y); |
| 431 | const PxF32 absNz = PxAbs(a: v.z); |
| 432 | |
| 433 | PxU32 m = 0; // x biggest axis |
| 434 | j = 1; |
| 435 | k = 2; |
| 436 | if(absNy > absPx && absNy > absNz) |
| 437 | { |
| 438 | // y biggest |
| 439 | j = 2; |
| 440 | k = 0; |
| 441 | m = 1; |
| 442 | } |
| 443 | else if(absNz > absPx) |
| 444 | { |
| 445 | // z biggest |
| 446 | j = 0; |
| 447 | k = 1; |
| 448 | m = 2; |
| 449 | } |
| 450 | return m; |
| 451 | } |
| 452 | |
| 453 | /*! |
| 454 | Extend an edge along its length by a factor |
| 455 | */ |
| 456 | PX_CUDA_CALLABLE PX_FORCE_INLINE void makeFatEdge(PxVec3& p0, PxVec3& p1, PxReal fatCoeff) |
| 457 | { |
| 458 | PxVec3 delta = p1 - p0; |
| 459 | |
| 460 | const PxReal m = delta.magnitude(); |
| 461 | if(m > 0.0f) |
| 462 | { |
| 463 | delta *= fatCoeff / m; |
| 464 | p0 -= delta; |
| 465 | p1 += delta; |
| 466 | } |
| 467 | } |
| 468 | |
| 469 | //! Compute point as combination of barycentric coordinates |
| 470 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxVec3 |
| 471 | computeBarycentricPoint(const PxVec3& p0, const PxVec3& p1, const PxVec3& p2, PxReal u, PxReal v) |
| 472 | { |
| 473 | // This seems to confuse the compiler... |
| 474 | // return (1.0f - u - v)*p0 + u*p1 + v*p2; |
| 475 | const PxF32 w = 1.0f - u - v; |
| 476 | return PxVec3(w * p0.x + u * p1.x + v * p2.x, w * p0.y + u * p1.y + v * p2.y, w * p0.z + u * p1.z + v * p2.z); |
| 477 | } |
| 478 | |
| 479 | // generates a pair of quaternions (swing, twist) such that in = swing * twist, with |
| 480 | // swing.x = 0 |
| 481 | // twist.y = twist.z = 0, and twist is a unit quat |
| 482 | PX_FORCE_INLINE void separateSwingTwist(const PxQuat& q, PxQuat& swing, PxQuat& twist) |
| 483 | { |
| 484 | twist = q.x != 0.0f ? PxQuat(q.x, 0, 0, q.w).getNormalized() : PxQuat(PxIdentity); |
| 485 | swing = q * twist.getConjugate(); |
| 486 | } |
| 487 | |
| 488 | PX_FORCE_INLINE float computeSwingAngle(float swingYZ, float swingW) |
| 489 | { |
| 490 | return 4.0f * PxAtan2(x: swingYZ, y: 1.0f + swingW); // tan (t/2) = sin(t)/(1+cos t), so this is the quarter angle |
| 491 | } |
| 492 | |
| 493 | // generate two tangent vectors to a given normal |
| 494 | PX_FORCE_INLINE void normalToTangents(const PxVec3& normal, PxVec3& tangent0, PxVec3& tangent1) |
| 495 | { |
| 496 | tangent0 = PxAbs(a: normal.x) < 0.70710678f ? PxVec3(0, -normal.z, normal.y) : PxVec3(-normal.y, normal.x, 0); |
| 497 | tangent0.normalize(); |
| 498 | tangent1 = normal.cross(v: tangent0); |
| 499 | } |
| 500 | |
| 501 | /** |
| 502 | \brief computes a oriented bounding box around the scaled basis. |
| 503 | \param basis Input = skewed basis, Output = (normalized) orthogonal basis. |
| 504 | \return Bounding box extent. |
| 505 | */ |
| 506 | PX_FOUNDATION_API PxVec3 optimizeBoundingBox(PxMat33& basis); |
| 507 | |
| 508 | PX_FOUNDATION_API PxQuat slerp(const PxReal t, const PxQuat& left, const PxQuat& right); |
| 509 | |
| 510 | PX_CUDA_CALLABLE PX_INLINE PxVec3 ellipseClamp(const PxVec3& point, const PxVec3& radii) |
| 511 | { |
| 512 | // This function need to be implemented in the header file because |
| 513 | // it is included in a spu shader program. |
| 514 | |
| 515 | // finds the closest point on the ellipse to a given point |
| 516 | |
| 517 | // (p.y, p.z) is the input point |
| 518 | // (e.y, e.z) are the radii of the ellipse |
| 519 | |
| 520 | // lagrange multiplier method with Newton/Halley hybrid root-finder. |
| 521 | // see http://www.geometrictools.com/Documentation/DistancePointToEllipse2.pdf |
| 522 | // for proof of Newton step robustness and initial estimate. |
| 523 | // Halley converges much faster but sometimes overshoots - when that happens we take |
| 524 | // a newton step instead |
| 525 | |
| 526 | // converges in 1-2 iterations where D&C works well, and it's good with 4 iterations |
| 527 | // with any ellipse that isn't completely crazy |
| 528 | |
| 529 | const PxU32 MAX_ITERATIONS = 20; |
| 530 | const PxReal convergenceThreshold = 1e-4f; |
| 531 | |
| 532 | // iteration requires first quadrant but we recover generality later |
| 533 | |
| 534 | PxVec3 q(0, PxAbs(a: point.y), PxAbs(a: point.z)); |
| 535 | const PxReal tinyEps = 1e-6f; // very close to minor axis is numerically problematic but trivial |
| 536 | if(radii.y >= radii.z) |
| 537 | { |
| 538 | if(q.z < tinyEps) |
| 539 | return PxVec3(0, point.y > 0 ? radii.y : -radii.y, 0); |
| 540 | } |
| 541 | else |
| 542 | { |
| 543 | if(q.y < tinyEps) |
| 544 | return PxVec3(0, 0, point.z > 0 ? radii.z : -radii.z); |
| 545 | } |
| 546 | |
| 547 | PxVec3 denom, e2 = radii.multiply(a: radii), eq = radii.multiply(a: q); |
| 548 | |
| 549 | // we can use any initial guess which is > maximum(-e.y^2,-e.z^2) and for which f(t) is > 0. |
| 550 | // this guess works well near the axes, but is weak along the diagonals. |
| 551 | |
| 552 | PxReal t = PxMax(a: eq.y - e2.y, b: eq.z - e2.z); |
| 553 | |
| 554 | for(PxU32 i = 0; i < MAX_ITERATIONS; i++) |
| 555 | { |
| 556 | denom = PxVec3(0, 1 / (t + e2.y), 1 / (t + e2.z)); |
| 557 | PxVec3 denom2 = eq.multiply(a: denom); |
| 558 | |
| 559 | PxVec3 fv = denom2.multiply(a: denom2); |
| 560 | PxReal f = fv.y + fv.z - 1; |
| 561 | |
| 562 | // although in exact arithmetic we are guaranteed f>0, we can get here |
| 563 | // on the first iteration via catastrophic cancellation if the point is |
| 564 | // very close to the origin. In that case we just behave as if f=0 |
| 565 | |
| 566 | if(f < convergenceThreshold) |
| 567 | return e2.multiply(a: point).multiply(a: denom); |
| 568 | |
| 569 | PxReal df = fv.dot(v: denom) * -2.0f; |
| 570 | t = t - f / df; |
| 571 | } |
| 572 | |
| 573 | // we didn't converge, so clamp what we have |
| 574 | PxVec3 r = e2.multiply(a: point).multiply(a: denom); |
| 575 | return r * PxRecipSqrt(a: sqr(a: r.y / radii.y) + sqr(a: r.z / radii.z)); |
| 576 | } |
| 577 | |
| 578 | PX_CUDA_CALLABLE PX_FORCE_INLINE PxReal tanHalf(PxReal sin, PxReal cos) |
| 579 | { |
| 580 | // PT: avoids divide by zero for singularity. We return sqrt(FLT_MAX) instead of FLT_MAX |
| 581 | // to make sure the calling code doesn't generate INF values when manipulating the returned value |
| 582 | // (some joints multiply it by 4, etc). |
| 583 | if(cos==-1.0f) |
| 584 | return sin<0.0f ? -sqrtf(FLT_MAX) : sqrtf(FLT_MAX); |
| 585 | |
| 586 | // PT: half-angle formula: tan(a/2) = sin(a)/(1+cos(a)) |
| 587 | return sin / (1.0f + cos); |
| 588 | } |
| 589 | |
| 590 | PX_INLINE PxQuat quatFromTanQVector(const PxVec3& v) |
| 591 | { |
| 592 | PxReal v2 = v.dot(v); |
| 593 | if(v2 < 1e-12f) |
| 594 | return PxQuat(PxIdentity); |
| 595 | PxReal d = 1 / (1 + v2); |
| 596 | return PxQuat(v.x * 2, v.y * 2, v.z * 2, 1 - v2) * d; |
| 597 | } |
| 598 | |
| 599 | PX_FORCE_INLINE PxVec3 cross100(const PxVec3& b) |
| 600 | { |
| 601 | return PxVec3(0.0f, -b.z, b.y); |
| 602 | } |
| 603 | PX_FORCE_INLINE PxVec3 cross010(const PxVec3& b) |
| 604 | { |
| 605 | return PxVec3(b.z, 0.0f, -b.x); |
| 606 | } |
| 607 | PX_FORCE_INLINE PxVec3 cross001(const PxVec3& b) |
| 608 | { |
| 609 | return PxVec3(-b.y, b.x, 0.0f); |
| 610 | } |
| 611 | |
| 612 | PX_INLINE void decomposeVector(PxVec3& normalCompo, PxVec3& tangentCompo, const PxVec3& outwardDir, |
| 613 | const PxVec3& outwardNormal) |
| 614 | { |
| 615 | normalCompo = outwardNormal * (outwardDir.dot(v: outwardNormal)); |
| 616 | tangentCompo = outwardDir - normalCompo; |
| 617 | } |
| 618 | |
| 619 | //! \brief Return (i+1)%3 |
| 620 | // Avoid variable shift for XBox: |
| 621 | // PX_INLINE PxU32 Ps::getNextIndex3(PxU32 i) { return (1<<i) & 3; } |
| 622 | PX_INLINE PxU32 getNextIndex3(PxU32 i) |
| 623 | { |
| 624 | return (i + 1 + (i >> 1)) & 3; |
| 625 | } |
| 626 | |
| 627 | PX_INLINE PxMat33 rotFrom2Vectors(const PxVec3& from, const PxVec3& to) |
| 628 | { |
| 629 | // See bottom of http://www.euclideanspace.com/maths/algebra/matrix/orthogonal/rotation/index.htm |
| 630 | |
| 631 | // Early exit if to = from |
| 632 | if((from - to).magnitudeSquared() < 1e-4f) |
| 633 | return PxMat33(PxIdentity); |
| 634 | |
| 635 | // Early exit if to = -from |
| 636 | if((from + to).magnitudeSquared() < 1e-4f) |
| 637 | return PxMat33::createDiagonal(d: PxVec3(1.0f, -1.0f, -1.0f)); |
| 638 | |
| 639 | PxVec3 n = from.cross(v: to); |
| 640 | |
| 641 | PxReal C = from.dot(v: to), S = PxSqrt(a: 1 - C * C), CC = 1 - C; |
| 642 | |
| 643 | PxReal xx = n.x * n.x, yy = n.y * n.y, zz = n.z * n.z, xy = n.x * n.y, yz = n.y * n.z, xz = n.x * n.z; |
| 644 | |
| 645 | PxMat33 R; |
| 646 | |
| 647 | R(0, 0) = 1 + CC * (xx - 1); |
| 648 | R(0, 1) = -n.z * S + CC * xy; |
| 649 | R(0, 2) = n.y * S + CC * xz; |
| 650 | |
| 651 | R(1, 0) = n.z * S + CC * xy; |
| 652 | R(1, 1) = 1 + CC * (yy - 1); |
| 653 | R(1, 2) = -n.x * S + CC * yz; |
| 654 | |
| 655 | R(2, 0) = -n.y * S + CC * xz; |
| 656 | R(2, 1) = n.x * S + CC * yz; |
| 657 | R(2, 2) = 1 + CC * (zz - 1); |
| 658 | |
| 659 | return R; |
| 660 | } |
| 661 | |
| 662 | PX_FOUNDATION_API void integrateTransform(const PxTransform& curTrans, const PxVec3& linvel, const PxVec3& angvel, |
| 663 | PxReal timeStep, PxTransform& result); |
| 664 | |
| 665 | PX_INLINE void computeBasis(const PxVec3& dir, PxVec3& right, PxVec3& up) |
| 666 | { |
| 667 | // Derive two remaining vectors |
| 668 | if(PxAbs(a: dir.y) <= 0.9999f) |
| 669 | { |
| 670 | right = PxVec3(dir.z, 0.0f, -dir.x); |
| 671 | right.normalize(); |
| 672 | |
| 673 | // PT: normalize not needed for 'up' because dir & right are unit vectors, |
| 674 | // and by construction the angle between them is 90 degrees (i.e. sin(angle)=1) |
| 675 | up = PxVec3(dir.y * right.z, dir.z * right.x - dir.x * right.z, -dir.y * right.x); |
| 676 | } |
| 677 | else |
| 678 | { |
| 679 | right = PxVec3(1.0f, 0.0f, 0.0f); |
| 680 | |
| 681 | up = PxVec3(0.0f, dir.z, -dir.y); |
| 682 | up.normalize(); |
| 683 | } |
| 684 | } |
| 685 | |
| 686 | PX_INLINE void computeBasis(const PxVec3& p0, const PxVec3& p1, PxVec3& dir, PxVec3& right, PxVec3& up) |
| 687 | { |
| 688 | // Compute the new direction vector |
| 689 | dir = p1 - p0; |
| 690 | dir.normalize(); |
| 691 | |
| 692 | // Derive two remaining vectors |
| 693 | computeBasis(dir, right, up); |
| 694 | } |
| 695 | |
| 696 | PX_FORCE_INLINE bool isAlmostZero(const PxVec3& v) |
| 697 | { |
| 698 | if(PxAbs(a: v.x) > 1e-6f || PxAbs(a: v.y) > 1e-6f || PxAbs(a: v.z) > 1e-6f) |
| 699 | return false; |
| 700 | return true; |
| 701 | } |
| 702 | |
| 703 | } // namespace shdfnd |
| 704 | } // namespace physx |
| 705 | |
| 706 | #endif |
| 707 | |