OpenVDB  8.0.1
Math.h
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1 // Copyright Contributors to the OpenVDB Project
2 // SPDX-License-Identifier: MPL-2.0
3 //
7 
8 #ifndef OPENVDB_MATH_HAS_BEEN_INCLUDED
9 #define OPENVDB_MATH_HAS_BEEN_INCLUDED
10 
11 #include <openvdb/Platform.h>
12 #include <openvdb/version.h>
13 #include <boost/numeric/conversion/conversion_traits.hpp>
14 #include <algorithm> // for std::max()
15 #include <cassert>
16 #include <cmath> // for std::ceil(), std::fabs(), std::pow(), std::sqrt(), etc.
17 #include <cstdlib> // for abs(int)
18 #include <random>
19 #include <string>
20 #include <type_traits> // for std::is_arithmetic
21 
22 
23 // Compile pragmas
24 
25 // Intel(r) compiler fires remark #1572: floating-point equality and inequality
26 // comparisons are unrealiable when == or != is used with floating point operands.
27 #if defined(__INTEL_COMPILER)
28  #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN \
29  _Pragma("warning (push)") \
30  _Pragma("warning (disable:1572)")
31  #define OPENVDB_NO_FP_EQUALITY_WARNING_END \
32  _Pragma("warning (pop)")
33 #elif defined(__clang__)
34  #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN \
35  PRAGMA(clang diagnostic push) \
36  PRAGMA(clang diagnostic ignored "-Wfloat-equal")
37  #define OPENVDB_NO_FP_EQUALITY_WARNING_END \
38  PRAGMA(clang diagnostic pop)
39 #else
40  // For GCC, #pragma GCC diagnostic ignored "-Wfloat-equal"
41  // isn't working until gcc 4.2+,
42  // Trying
43  // #pragma GCC system_header
44  // creates other problems, most notably "warning: will never be executed"
45  // in from templates, unsure of how to work around.
46  // If necessary, could use integer based comparisons for equality
47  #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
48  #define OPENVDB_NO_FP_EQUALITY_WARNING_END
49 #endif
50 
51 
52 #ifdef OPENVDB_IS_POD
53 #undef OPENVDB_IS_POD
54 #endif
55 #define OPENVDB_IS_POD(Type) \
56 static_assert(std::is_standard_layout<Type>::value, \
57  #Type" must be a POD type (satisfy StandardLayoutType.)"); \
58 static_assert(std::is_trivial<Type>::value, \
59  #Type" must be a POD type (satisfy TrivialType.)");
60 
61 namespace openvdb {
63 namespace OPENVDB_VERSION_NAME {
64 
69 template<typename T> inline T zeroVal() { return T(0); }
71 template<> inline std::string zeroVal<std::string>() { return ""; }
73 template<> inline bool zeroVal<bool>() { return false; }
74 
75 namespace math {
76 
78 
79 inline std::string operator+(const std::string& s, bool) { return s; }
82 inline std::string operator+(const std::string& s, int) { return s; }
83 inline std::string operator+(const std::string& s, float) { return s; }
84 inline std::string operator+(const std::string& s, double) { return s; }
86 
88 template<typename Type1, typename Type2>
89 inline auto cwiseAdd(const Type1& v, const Type2 s)
90 {
92  return v + s;
94 }
95 
97 template<typename Type1, typename Type2>
98 inline bool cwiseLessThan(const Type1& a, const Type2& b)
99 {
101  return a < b;
103 }
104 
106 template<typename Type1, typename Type2>
107 inline bool cwiseGreaterThan(const Type1& a, const Type2& b)
108 {
110  return a > b;
112 }
113 
114 
115 
118 template <typename T> inline constexpr T pi() { return 3.141592653589793238462643383279502884e+00; }
119 template <> inline constexpr float pi() { return 3.141592653589793238462643383279502884e+00F; }
120 template <> inline constexpr double pi() { return 3.141592653589793238462643383279502884e+00; }
121 template <> inline constexpr long double pi() { return 3.141592653589793238462643383279502884e+00L; }
122 
123 
127 template<typename T> inline T negative(const T& val)
128 {
129 // disable unary minus on unsigned warning
130 #if defined(_MSC_VER)
131 #pragma warning(push)
132 #pragma warning(disable:4146)
133 #endif
134  return T(-val);
135 #if defined(_MSC_VER)
136 #pragma warning(pop)
137 #endif
138 }
140 template<> inline bool negative(const bool& val) { return !val; }
142 template<> inline std::string negative(const std::string& val) { return val; }
143 
144 
146 template<typename T> struct Tolerance { static T value() { return zeroVal<T>(); } };
148 template<> struct Tolerance<float> { static float value() { return 1e-8f; } };
149 template<> struct Tolerance<double> { static double value() { return 1e-15; } };
151 
153 template<typename T> struct Delta { static T value() { return zeroVal<T>(); } };
155 template<> struct Delta<float> { static float value() { return 1e-5f; } };
156 template<> struct Delta<double> { static double value() { return 1e-9; } };
158 
159 
160 // ==========> Random Values <==================
161 
164 template<typename FloatType = double, typename EngineType = std::mt19937>
165 class Rand01
166 {
167 private:
168  EngineType mEngine;
169  std::uniform_real_distribution<FloatType> mRand;
170 
171 public:
172  using ValueType = FloatType;
173 
176  Rand01(const EngineType& engine): mEngine(engine) {}
177 
180  Rand01(unsigned int seed): mEngine(static_cast<typename EngineType::result_type>(seed)) {}
181 
183  void setSeed(unsigned int seed)
184  {
185  mEngine.seed(static_cast<typename EngineType::result_type>(seed));
186  }
187 
189  const EngineType& engine() const { return mEngine; }
190 
192  FloatType operator()() { return mRand(mEngine); }
193 };
194 
196 
197 
200 template<typename IntType = int, typename EngineType = std::mt19937>
201 class RandInt
202 {
203 private:
204  using Distr = std::uniform_int_distribution<IntType>;
205  EngineType mEngine;
206  Distr mRand;
207 
208 public:
212  RandInt(const EngineType& engine, IntType imin, IntType imax):
213  mEngine(engine),
214  mRand(std::min(imin, imax), std::max(imin, imax))
215  {}
216 
220  RandInt(unsigned int seed, IntType imin, IntType imax):
221  mEngine(static_cast<typename EngineType::result_type>(seed)),
222  mRand(std::min(imin, imax), std::max(imin, imax))
223  {}
224 
226  void setRange(IntType imin, IntType imax)
227  {
228  mRand = Distr(std::min(imin, imax), std::max(imin, imax));
229  }
230 
232  void setSeed(unsigned int seed)
233  {
234  mEngine.seed(static_cast<typename EngineType::result_type>(seed));
235  }
236 
238  const EngineType& engine() const { return mEngine; }
239 
241  IntType operator()() { return mRand(mEngine); }
242 
245  IntType operator()(IntType imin, IntType imax)
246  {
247  const IntType lo = std::min(imin, imax), hi = std::max(imin, imax);
248  return mRand(mEngine, typename Distr::param_type(lo, hi));
249  }
250 };
251 
253 
254 
255 // ==========> Clamp <==================
256 
258 template<typename Type>
259 inline Type
260 Clamp(Type x, Type min, Type max)
261 {
262  assert( !(min>max) );
263  return x > min ? x < max ? x : max : min;
264 }
265 
266 
268 template<typename Type>
269 inline Type
270 Clamp01(Type x) { return x > Type(0) ? x < Type(1) ? x : Type(1) : Type(0); }
271 
272 
274 template<typename Type>
275 inline bool
276 ClampTest01(Type &x)
277 {
278  if (x >= Type(0) && x <= Type(1)) return false;
279  x = x < Type(0) ? Type(0) : Type(1);
280  return true;
281 }
282 
284 template<typename Type>
285 inline Type
287 {
288  return x > 0 ? x < 1 ? (3-2*x)*x*x : Type(1) : Type(0);
289 }
290 
293 template<typename Type>
294 inline Type
295 SmoothUnitStep(Type x, Type min, Type max)
296 {
297  assert(min < max);
298  return SmoothUnitStep((x-min)/(max-min));
299 }
300 
301 
302 // ==========> Absolute Value <==================
303 
304 
306 inline int32_t Abs(int32_t i) { return abs(i); }
308 inline int64_t Abs(int64_t i)
309 {
310 #ifdef _MSC_VER
311  return (i < int64_t(0) ? -i : i);
312 #else
313  return labs(i);
314 #endif
315 }
316 inline float Abs(float x) { return std::fabs(x); }
317 inline double Abs(double x) { return std::fabs(x); }
318 inline long double Abs(long double x) { return std::fabs(x); }
319 inline uint32_t Abs(uint32_t i) { return i; }
320 inline uint64_t Abs(uint64_t i) { return i; }
321 inline bool Abs(bool b) { return b; }
322 // On OSX size_t and uint64_t are different types
323 #if defined(__APPLE__) || defined(MACOSX)
324 inline size_t Abs(size_t i) { return i; }
325 #endif
326 
327 
328 
330 
331 
332 // ==========> Value Comparison <==================
333 
334 
336 template<typename Type>
337 inline bool
338 isZero(const Type& x)
339 {
341  return x == zeroVal<Type>();
343 }
344 
345 
348 template<typename Type>
349 inline bool
350 isApproxZero(const Type& x)
351 {
352  const Type tolerance = Type(zeroVal<Type>() + Tolerance<Type>::value());
353  return !(x > tolerance) && !(x < -tolerance);
354 }
355 
357 template<typename Type>
358 inline bool
359 isApproxZero(const Type& x, const Type& tolerance)
360 {
361  return !(x > tolerance) && !(x < -tolerance);
362 }
363 
364 
366 template<typename Type>
367 inline bool
368 isNegative(const Type& x) { return x < zeroVal<Type>(); }
369 
370 // Return false, since bool values are never less than zero.
371 template<> inline bool isNegative<bool>(const bool&) { return false; }
372 
373 
375 inline bool
376 isFinite(const float x) { return std::isfinite(x); }
377 
379 template<typename Type, typename std::enable_if<std::is_arithmetic<Type>::value, int>::type = 0>
380 inline bool
381 isFinite(const Type& x) { return std::isfinite(static_cast<double>(x)); }
382 
383 
385 inline bool
386 isInfinite(const float x) { return std::isinf(x); }
387 
389 template<typename Type, typename std::enable_if<std::is_arithmetic<Type>::value, int>::type = 0>
390 inline bool
391 isInfinite(const Type& x) { return std::isinf(static_cast<double>(x)); }
392 
393 
395 inline bool
396 isNan(const float x) { return std::isnan(x); }
397 
399 template<typename Type, typename std::enable_if<std::is_arithmetic<Type>::value, int>::type = 0>
400 inline bool
401 isNan(const Type& x) { return std::isnan(static_cast<double>(x)); }
402 
403 
405 template<typename Type>
406 inline bool
407 isApproxEqual(const Type& a, const Type& b, const Type& tolerance)
408 {
409  return !cwiseGreaterThan(Abs(a - b), tolerance);
410 }
411 
414 template<typename Type>
415 inline bool
416 isApproxEqual(const Type& a, const Type& b)
417 {
418  const Type tolerance = Type(zeroVal<Type>() + Tolerance<Type>::value());
419  return isApproxEqual(a, b, tolerance);
420 }
421 
422 #define OPENVDB_EXACT_IS_APPROX_EQUAL(T) \
423  template<> inline bool isApproxEqual<T>(const T& a, const T& b) { return a == b; } \
424  template<> inline bool isApproxEqual<T>(const T& a, const T& b, const T&) { return a == b; } \
425 
426 
429 
430 
433 template<typename Type>
434 inline bool
435 isApproxLarger(const Type& a, const Type& b, const Type& tolerance)
436 {
437  return (b - a < tolerance);
438 }
439 
440 
442 template<typename T0, typename T1>
443 inline bool
444 isExactlyEqual(const T0& a, const T1& b)
445 {
447  return a == b;
449 }
450 
451 
452 template<typename Type>
453 inline bool
454 isRelOrApproxEqual(const Type& a, const Type& b, const Type& absTol, const Type& relTol)
455 {
456  // First check to see if we are inside the absolute tolerance
457  // Necessary for numbers close to 0
458  if (!(Abs(a - b) > absTol)) return true;
459 
460  // Next check to see if we are inside the relative tolerance
461  // to handle large numbers that aren't within the abs tolerance
462  // but could be the closest floating point representation
463  double relError;
464  if (Abs(b) > Abs(a)) {
465  relError = Abs((a - b) / b);
466  } else {
467  relError = Abs((a - b) / a);
468  }
469  return (relError <= relTol);
470 }
471 
472 template<>
473 inline bool
474 isRelOrApproxEqual(const bool& a, const bool& b, const bool&, const bool&)
475 {
476  return (a == b);
477 }
478 
479 
480 // Avoid strict aliasing issues by using type punning
481 // http://cellperformance.beyond3d.com/articles/2006/06/understanding-strict-aliasing.html
482 // Using "casting through a union(2)"
483 inline int32_t
484 floatToInt32(const float aFloatValue)
485 {
486  union FloatOrInt32 { float floatValue; int32_t int32Value; };
487  const FloatOrInt32* foi = reinterpret_cast<const FloatOrInt32*>(&aFloatValue);
488  return foi->int32Value;
489 }
490 
491 
492 inline int64_t
493 doubleToInt64(const double aDoubleValue)
494 {
495  union DoubleOrInt64 { double doubleValue; int64_t int64Value; };
496  const DoubleOrInt64* dol = reinterpret_cast<const DoubleOrInt64*>(&aDoubleValue);
497  return dol->int64Value;
498 }
499 
500 
501 // aUnitsInLastPlace is the allowed difference between the least significant digits
502 // of the numbers' floating point representation
503 // Please read the reference paper before trying to use isUlpsEqual
504 // http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
505 inline bool
506 isUlpsEqual(const double aLeft, const double aRight, const int64_t aUnitsInLastPlace)
507 {
508  int64_t longLeft = doubleToInt64(aLeft);
509  // Because of 2's complement, must restore lexicographical order
510  if (longLeft < 0) {
511  longLeft = INT64_C(0x8000000000000000) - longLeft;
512  }
513 
514  int64_t longRight = doubleToInt64(aRight);
515  // Because of 2's complement, must restore lexicographical order
516  if (longRight < 0) {
517  longRight = INT64_C(0x8000000000000000) - longRight;
518  }
519 
520  int64_t difference = labs(longLeft - longRight);
521  return (difference <= aUnitsInLastPlace);
522 }
523 
524 inline bool
525 isUlpsEqual(const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)
526 {
527  int32_t intLeft = floatToInt32(aLeft);
528  // Because of 2's complement, must restore lexicographical order
529  if (intLeft < 0) {
530  intLeft = 0x80000000 - intLeft;
531  }
532 
533  int32_t intRight = floatToInt32(aRight);
534  // Because of 2's complement, must restore lexicographical order
535  if (intRight < 0) {
536  intRight = 0x80000000 - intRight;
537  }
538 
539  int32_t difference = abs(intLeft - intRight);
540  return (difference <= aUnitsInLastPlace);
541 }
542 
543 
545 
546 
547 // ==========> Pow <==================
548 
550 template<typename Type>
551 inline Type Pow2(Type x) { return x*x; }
552 
554 template<typename Type>
555 inline Type Pow3(Type x) { return x*x*x; }
556 
558 template<typename Type>
559 inline Type Pow4(Type x) { return Pow2(Pow2(x)); }
560 
562 template<typename Type>
563 Type
564 Pow(Type x, int n)
565 {
566  Type ans = 1;
567  if (n < 0) {
568  n = -n;
569  x = Type(1)/x;
570  }
571  while (n--) ans *= x;
572  return ans;
573 }
574 
576 inline float
578 Pow(float b, float e)
579 {
580  assert( b >= 0.0f && "Pow(float,float): base is negative" );
581  return powf(b,e);
582 }
583 
584 inline double
585 Pow(double b, double e)
586 {
587  assert( b >= 0.0 && "Pow(double,double): base is negative" );
588  return std::pow(b,e);
589 }
591 
592 
593 // ==========> Max <==================
594 
596 template<typename Type>
597 inline const Type&
598 Max(const Type& a, const Type& b)
599 {
600  return std::max(a,b);
601 }
602 
604 template<typename Type>
605 inline const Type&
606 Max(const Type& a, const Type& b, const Type& c)
607 {
608  return std::max(std::max(a,b), c);
609 }
610 
612 template<typename Type>
613 inline const Type&
614 Max(const Type& a, const Type& b, const Type& c, const Type& d)
615 {
616  return std::max(std::max(a,b), std::max(c,d));
617 }
618 
620 template<typename Type>
621 inline const Type&
622 Max(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e)
623 {
624  return std::max(std::max(a,b), Max(c,d,e));
625 }
626 
628 template<typename Type>
629 inline const Type&
630 Max(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e, const Type& f)
631 {
632  return std::max(Max(a,b,c), Max(d,e,f));
633 }
634 
636 template<typename Type>
637 inline const Type&
638 Max(const Type& a, const Type& b, const Type& c, const Type& d,
639  const Type& e, const Type& f, const Type& g)
640 {
641  return std::max(Max(a,b,c,d), Max(e,f,g));
642 }
643 
645 template<typename Type>
646 inline const Type&
647 Max(const Type& a, const Type& b, const Type& c, const Type& d,
648  const Type& e, const Type& f, const Type& g, const Type& h)
649 {
650  return std::max(Max(a,b,c,d), Max(e,f,g,h));
651 }
652 
653 
654 // ==========> Min <==================
655 
657 template<typename Type>
658 inline const Type&
659 Min(const Type& a, const Type& b) { return std::min(a, b); }
660 
662 template<typename Type>
663 inline const Type&
664 Min(const Type& a, const Type& b, const Type& c) { return std::min(std::min(a, b), c); }
665 
667 template<typename Type>
668 inline const Type&
669 Min(const Type& a, const Type& b, const Type& c, const Type& d)
670 {
671  return std::min(std::min(a, b), std::min(c, d));
672 }
673 
675 template<typename Type>
676 inline const Type&
677 Min(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e)
678 {
679  return std::min(std::min(a,b), Min(c,d,e));
680 }
681 
683 template<typename Type>
684 inline const Type&
685 Min(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e, const Type& f)
686 {
687  return std::min(Min(a,b,c), Min(d,e,f));
688 }
689 
691 template<typename Type>
692 inline const Type&
693 Min(const Type& a, const Type& b, const Type& c, const Type& d,
694  const Type& e, const Type& f, const Type& g)
695 {
696  return std::min(Min(a,b,c,d), Min(e,f,g));
697 }
698 
700 template<typename Type>
701 inline const Type&
702 Min(const Type& a, const Type& b, const Type& c, const Type& d,
703  const Type& e, const Type& f, const Type& g, const Type& h)
704 {
705  return std::min(Min(a,b,c,d), Min(e,f,g,h));
706 }
707 
708 
709 // ============> Exp <==================
710 
712 template<typename Type>
713 inline Type Exp(const Type& x) { return std::exp(x); }
714 
715 // ============> Sin <==================
716 
718 inline float Sin(const float& x) { return std::sin(x); }
720 
721 inline double Sin(const double& x) { return std::sin(x); }
723 
724 // ============> Cos <==================
725 
727 inline float Cos(const float& x) { return std::cos(x); }
729 
730 inline double Cos(const double& x) { return std::cos(x); }
732 
733 
735 
736 
738 template <typename Type>
739 inline int Sign(const Type &x) { return (zeroVal<Type>() < x) - (x < zeroVal<Type>()); }
740 
741 
744 template <typename Type>
745 inline bool
746 SignChange(const Type& a, const Type& b)
747 {
748  return ( (a<zeroVal<Type>()) ^ (b<zeroVal<Type>()) );
749 }
750 
751 
754 template <typename Type>
755 inline bool
756 ZeroCrossing(const Type& a, const Type& b)
757 {
758  return a * b <= zeroVal<Type>();
759 }
760 
761 
763 inline float Sqrt(float x) { return std::sqrt(x); }
765 inline double Sqrt(double x) { return std::sqrt(x); }
766 inline long double Sqrt(long double x) { return std::sqrt(x); }
768 
769 
771 inline float Cbrt(float x) { return std::cbrt(x); }
773 inline double Cbrt(double x) { return std::cbrt(x); }
774 inline long double Cbrt(long double x) { return std::cbrt(x); }
776 
777 
779 inline int Mod(int x, int y) { return (x % y); }
781 inline float Mod(float x, float y) { return std::fmod(x, y); }
782 inline double Mod(double x, double y) { return std::fmod(x, y); }
783 inline long double Mod(long double x, long double y) { return std::fmod(x, y); }
784 template<typename Type> inline Type Remainder(Type x, Type y) { return Mod(x, y); }
786 
787 
789 inline float RoundUp(float x) { return std::ceil(x); }
791 inline double RoundUp(double x) { return std::ceil(x); }
792 inline long double RoundUp(long double x) { return std::ceil(x); }
794 template<typename Type>
796 inline Type
797 RoundUp(Type x, Type base)
798 {
799  Type remainder = Remainder(x, base);
800  return remainder ? x-remainder+base : x;
801 }
802 
803 
805 inline float RoundDown(float x) { return std::floor(x); }
807 inline double RoundDown(double x) { return std::floor(x); }
808 inline long double RoundDown(long double x) { return std::floor(x); }
810 template<typename Type>
812 inline Type
813 RoundDown(Type x, Type base)
814 {
815  Type remainder = Remainder(x, base);
816  return remainder ? x-remainder : x;
817 }
818 
819 
821 inline float Round(float x) { return RoundDown(x + 0.5f); }
823 inline double Round(double x) { return RoundDown(x + 0.5); }
824 inline long double Round(long double x) { return RoundDown(x + 0.5l); }
826 
827 
830 template<typename Type>
831 inline Type
832 EuclideanRemainder(Type x) { return x - RoundDown(x); }
833 
834 
836 template<typename Type>
837 inline Type
838 IntegerPart(Type x)
839 {
840  return (x > 0 ? RoundDown(x) : RoundUp(x));
841 }
842 
844 template<typename Type>
845 inline Type
846 FractionalPart(Type x) { return Mod(x,Type(1)); }
847 
848 
850 inline int Floor(float x) { return int(RoundDown(x)); }
852 inline int Floor(double x) { return int(RoundDown(x)); }
853 inline int Floor(long double x) { return int(RoundDown(x)); }
855 
856 
858 inline int Ceil(float x) { return int(RoundUp(x)); }
860 inline int Ceil(double x) { return int(RoundUp(x)); }
861 inline int Ceil(long double x) { return int(RoundUp(x)); }
863 
864 
866 template<typename Type>
867 inline Type Chop(Type x, Type delta) { return (Abs(x) < delta ? zeroVal<Type>() : x); }
868 
869 
871 template<typename Type>
872 inline Type
873 Truncate(Type x, unsigned int digits)
874 {
875  Type tenth = Pow(10,digits);
876  return RoundDown(x*tenth+0.5)/tenth;
877 }
878 
880 
881 
884 template<typename T>
885 inline auto PrintCast(const T& val) -> typename std::enable_if<!std::is_same<T, int8_t>::value
886  && !std::is_same<T, uint8_t>::value, const T&>::type { return val; }
887 inline int32_t PrintCast(int8_t val) { return int32_t(val); }
888 inline uint32_t PrintCast(uint8_t val) { return uint32_t(val); }
889 
890 
892 
893 
895 template<typename Type>
896 inline Type
897 Inv(Type x)
898 {
899  assert(x);
900  return Type(1)/x;
901 }
902 
903 
904 enum Axis {
905  X_AXIS = 0,
906  Y_AXIS = 1,
907  Z_AXIS = 2
908 };
909 
910 // enum values are consistent with their historical mx analogs.
920 };
921 
922 
923 template <typename S, typename T>
924 struct promote {
925  using type = typename boost::numeric::conversion_traits<S, T>::supertype;
926 };
927 
928 
936 template<typename Vec3T>
937 size_t
938 MinIndex(const Vec3T& v)
939 {
940  static const size_t hashTable[8] = { 2, 1, 9, 1, 2, 9, 0, 0 };//9 is a dummy value
941  const size_t hashKey =
942  ((v[0] < v[1]) << 2) + ((v[0] < v[2]) << 1) + (v[1] < v[2]);// ?*4+?*2+?*1
943  return hashTable[hashKey];
944 }
945 
946 
954 template<typename Vec3T>
955 size_t
956 MaxIndex(const Vec3T& v)
957 {
958  static const size_t hashTable[8] = { 2, 1, 9, 1, 2, 9, 0, 0 };//9 is a dummy value
959  const size_t hashKey =
960  ((v[0] > v[1]) << 2) + ((v[0] > v[2]) << 1) + (v[1] > v[2]);// ?*4+?*2+?*1
961  return hashTable[hashKey];
962 }
963 
964 } // namespace math
965 } // namespace OPENVDB_VERSION_NAME
966 } // namespace openvdb
967 
968 #endif // OPENVDB_MATH_MATH_HAS_BEEN_INCLUDED
IntType operator()(IntType imin, IntType imax)
Return a randomly-generated integer in the new range [imin, imax], without changing the current range...
Definition: Math.h:245
Definition: Math.h:914
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
Bracket code with OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN/_END, to inhibit warnings about type conve...
Definition: Platform.h:174
bool ClampTest01(Type &x)
Return true if x is outside [0,1].
Definition: Math.h:276
Delta for small floating-point offsets.
Definition: Math.h:154
Simple generator of random numbers over the range [0, 1)
Definition: Math.h:165
Definition: Math.h:912
Definition: Math.h:924
static float value()
Definition: Math.h:148
auto cwiseAdd(const Type1 &v, const Type2 s)
Componentwise adder for POD types.
Definition: Math.h:89
bool isNegative(const Type &x)
Return true if x is less than zero.
Definition: Math.h:368
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:444
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:107
RotationOrder
Definition: Math.h:911
long double Mod(long double x, long double y)
Return the remainder of x / y.
Definition: Math.h:783
bool Abs(bool b)
Return the absolute value of the given quantity.
Definition: Math.h:321
bool isApproxLarger(const Type &a, const Type &b, const Type &tolerance)
Return true if a is larger than b to within the given tolerance, i.e., if b - a < tolerance...
Definition: Math.h:435
bool isUlpsEqual(const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)
Definition: Math.h:525
Type Clamp01(Type x)
Return x clamped to [0, 1].
Definition: Math.h:270
bool zeroVal< bool >()
Return the bool value that corresponds to zero.
Definition: Math.h:73
Type Pow4(Type x)
Return x4.
Definition: Math.h:559
Definition: Math.h:919
size_t MaxIndex(const Vec3T &v)
Return the index [0,1,2] of the largest value in a 3D vector.
Definition: Math.h:956
Definition: Coord.h:587
Rand01(unsigned int seed)
Initialize the generator.
Definition: Math.h:180
int64_t doubleToInt64(const double aDoubleValue)
Definition: Math.h:493
Type Exp(const Type &x)
Return ex.
Definition: Math.h:713
bool isZero(const Type &x)
Return true if x is exactly equal to zero.
Definition: Math.h:338
bool isNan(const Type &x)
Return true if x is a NaN (Not-A-Number) value.
Definition: Math.h:401
long double Round(long double x)
Return x rounded to the nearest integer.
Definition: Math.h:824
std::string operator+(const std::string &s, double)
Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string.
Definition: Math.h:84
Type EuclideanRemainder(Type x)
Definition: Math.h:832
int Floor(long double x)
Return the floor of x.
Definition: Math.h:853
bool SignChange(const Type &a, const Type &b)
Return true if a and b have different signs.
Definition: Math.h:746
bool ZeroCrossing(const Type &a, const Type &b)
Return true if the interval [a, b] includes zero, i.e., if either a or b is zero or if they have diff...
Definition: Math.h:756
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_END
Definition: Platform.h:175
size_t MinIndex(const Vec3T &v)
Return the index [0,1,2] of the smallest value in a 3D vector.
Definition: Math.h:938
bool isNegative< bool >(const bool &)
Definition: Math.h:371
int Sign(const Type &x)
Return the sign of the given value as an integer (either -1, 0 or 1).
Definition: Math.h:739
Type Remainder(Type x, Type y)
Return the remainder of x / y.
Definition: Math.h:784
void setSeed(unsigned int seed)
Set the seed value for the random number generator.
Definition: Math.h:183
std::string negative(const std::string &val)
Return the "negation" of the given string.
Definition: Math.h:142
int Ceil(long double x)
Return the ceiling of x.
Definition: Math.h:861
Definition: Math.h:907
const Type & Max(const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g, const Type &h)
Return the maximum of eight values.
Definition: Math.h:647
Simple random integer generator.
Definition: Math.h:201
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:101
bool isApproxZero(const Type &x, const Type &tolerance)
Return true if x is equal to zero to within the given tolerance.
Definition: Math.h:359
Definition: Math.h:913
static double value()
Definition: Math.h:149
Tolerance for floating-point comparison.
Definition: Math.h:147
Axis
Definition: Math.h:904
bool isRelOrApproxEqual(const bool &a, const bool &b, const bool &, const bool &)
Definition: Math.h:474
IntType operator()()
Return a randomly-generated integer in the current range.
Definition: Math.h:241
Type Pow2(Type x)
Return x2.
Definition: Math.h:551
double Pow(double b, double e)
Return be.
Definition: Math.h:585
Type FractionalPart(Type x)
Return the fractional part of x.
Definition: Math.h:846
Type RoundDown(Type x, Type base)
Return x rounded down to the nearest multiple of base.
Definition: Math.h:813
Type Truncate(Type x, unsigned int digits)
Return x truncated to the given number of decimal digits.
Definition: Math.h:873
constexpr long double pi()
Definition: Math.h:121
Definition: Math.h:916
void setSeed(unsigned int seed)
Set the seed value for the random number generator.
Definition: Math.h:232
RandInt(const EngineType &engine, IntType imin, IntType imax)
Initialize the generator.
Definition: Math.h:212
Type Clamp(Type x, Type min, Type max)
Return x clamped to [min, max].
Definition: Math.h:260
bool cwiseGreaterThan(const Type1 &a, const Type2 &b)
Componentwise greater than for POD types.
Definition: Math.h:107
Definition: openvdb/Exceptions.h:13
FloatType operator()()
Return a uniformly distributed random number in the range [0, 1).
Definition: Math.h:192
Type Inv(Type x)
Return the inverse of x.
Definition: Math.h:897
Definition: Math.h:918
uint32_t PrintCast(uint8_t val)
Definition: Math.h:888
#define OPENVDB_NO_FP_EQUALITY_WARNING_END
Definition: Math.h:48
Definition: Math.h:905
void setRange(IntType imin, IntType imax)
Change the range over which integers are distributed to [imin, imax].
Definition: Math.h:226
typename boost::numeric::conversion_traits< S, T >::supertype type
Definition: Math.h:925
Type SmoothUnitStep(Type x, Type min, Type max)
Return 0 if x < min, 1 if x > max or else (3 − 2 t) t², where t = (x − min)/(max − min)...
Definition: Math.h:295
Type RoundUp(Type x, Type base)
Return x rounded up to the nearest multiple of base.
Definition: Math.h:797
bool isFinite(const Type &x)
Return true if x is finite.
Definition: Math.h:381
bool cwiseLessThan(const Type1 &a, const Type2 &b)
Componentwise less than for POD types.
Definition: Math.h:98
Library and file format version numbers.
const EngineType & engine() const
Return a const reference to the random number generator.
Definition: Math.h:238
double Cos(const double &x)
Return cos x.
Definition: Math.h:730
static double value()
Definition: Math.h:156
Type Chop(Type x, Type delta)
Return x if it is greater or equal in magnitude than delta. Otherwise, return zero.
Definition: Math.h:867
Definition: Math.h:917
bool isApproxEqual(const Type &a, const Type &b)
Return true if a is equal to b to within the default floating-point comparison tolerance.
Definition: Math.h:416
#define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
Definition: Math.h:47
T zeroVal()
Return the value of type T that corresponds to zero.
Definition: Math.h:69
RandInt(unsigned int seed, IntType imin, IntType imax)
Initialize the generator.
Definition: Math.h:220
static float value()
Definition: Math.h:155
bool isInfinite(const Type &x)
Return true if x is an infinity value (either positive infinity or negative infinity).
Definition: Math.h:391
long double Sqrt(long double x)
Return the square root of a floating-point value.
Definition: Math.h:766
Rand01(const EngineType &engine)
Initialize the generator.
Definition: Math.h:176
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:103
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:153
Definition: Math.h:906
const Type & Min(const Type &a, const Type &b, const Type &c, const Type &d, const Type &e, const Type &f, const Type &g, const Type &h)
Return the minimum of eight values.
Definition: Math.h:702
int32_t floatToInt32(const float aFloatValue)
Definition: Math.h:484
long double Cbrt(long double x)
Return the cube root of a floating-point value.
Definition: Math.h:774
Type Pow3(Type x)
Return x3.
Definition: Math.h:555
Type IntegerPart(Type x)
Return the integer part of x.
Definition: Math.h:838
#define OPENVDB_EXACT_IS_APPROX_EQUAL(T)
Definition: Math.h:422
const EngineType & engine() const
Return a const reference to the random number generator.
Definition: Math.h:189
Definition: Math.h:915
double Sin(const double &x)
Return sin x.
Definition: Math.h:721