OpenVDB: Math.h Source File

OpenVDB 3.2.0

Math.h
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1 //
3 // Copyright (c) 2012-2016 DreamWorks Animation LLC
4 //
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30 //
34
35 #ifndef OPENVDB_MATH_HAS_BEEN_INCLUDED
36 #define OPENVDB_MATH_HAS_BEEN_INCLUDED
37
38 #include <assert.h>
39 #include <algorithm> // for std::max()
40 #include <cmath> // for floor(), ceil() and sqrt()
41 #include <math.h> // for pow(), fabs() etc
42 #include <cstdlib> // for srand(), abs(int)
43 #include <limits> // for std::numeric_limits<Type>::max()
44 #include <string>
45 #include <boost/numeric/conversion/conversion_traits.hpp>
46 #include <boost/math/special_functions/cbrt.hpp>
47 #include <boost/math/special_functions/fpclassify.hpp> // boost::math::isfinite
48 #include <boost/random/mersenne_twister.hpp> // for boost::random::mt19937
49 #include <boost/random/uniform_01.hpp>
50 #include <boost/random/uniform_int.hpp>
51 #include <boost/version.hpp> // for BOOST_VERSION
52 #include <openvdb/Platform.h>
53 #include <openvdb/version.h>
54
55
56 // Compile pragmas
57
58 #define PRAGMA(x) _Pragma(#x)
59
60 // Intel(r) compiler fires remark #1572: floating-point equality and inequality
61 // comparisons are unrealiable when == or != is used with floating point operands.
62 #if defined(__INTEL_COMPILER)
63 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN \
64 _Pragma("warning (push)") \
65 _Pragma("warning (disable:1572)")
66 #define OPENVDB_NO_FP_EQUALITY_WARNING_END \
67 _Pragma("warning (pop)")
68 #elif defined(__clang__)
69 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN \
70 PRAGMA(clang diagnostic push) \
71 PRAGMA(clang diagnostic ignored "-Wfloat-equal")
72 #define OPENVDB_NO_FP_EQUALITY_WARNING_END \
73 PRAGMA(clang diagnostic pop)
74 #else
75 // For GCC, #pragma GCC diagnostic ignored "-Wfloat-equal"
76 // isn't working until gcc 4.2+,
77 // Trying
78 // #pragma GCC system_header
79 // creates other problems, most notably "warning: will never be executed"
80 // in from templates, unsure of how to work around.
81 // If necessary, could use integer based comparisons for equality
82 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
83 #define OPENVDB_NO_FP_EQUALITY_WARNING_END
84 #endif
85
86 namespace openvdb {
87 OPENVDB_USE_VERSION_NAMESPACE
88 namespace OPENVDB_VERSION_NAME {
89
94 template<typename T> inline T zeroVal() { return T(0); }
96 template<> inline std::string zeroVal<std::string>() { return ""; }
98 template<> inline bool zeroVal<bool>() { return false; }
99
101
102 inline std::string operator+(const std::string& s, bool) { return s; }
105 inline std::string operator+(const std::string& s, int) { return s; }
106 inline std::string operator+(const std::string& s, float) { return s; }
107 inline std::string operator+(const std::string& s, double) { return s; }
109
110
111 namespace math {
112
116 template<typename T> inline T negative(const T& val) { return T(-val); }
118 template<> inline bool negative(const bool& val) { return !val; }
120 template<> inline std::string negative(const std::string& val) { return val; }
121
122
124 template<typename T> struct Tolerance { static T value() { return zeroVal<T>(); } };
126 template<> struct Tolerance<float> { static float value() { return 1e-8f; } };
127 template<> struct Tolerance<double> { static double value() { return 1e-15; } };
129
131 template<typename T> struct Delta { static T value() { return zeroVal<T>(); } };
133 template<> struct Delta<float> { static float value() { return 1e-5f; } };
134 template<> struct Delta<double> { static double value() { return 1e-9; } };
136
137
138 // ==========> Random Values <==================
139
142 template<typename FloatType = double, typename EngineType = boost::mt19937>
143 class Rand01
144 {
145 private:
146 EngineType mEngine;
147 boost::uniform_01<FloatType> mRand;
148
149 public:
150 typedef FloatType ValueType;
151
154 Rand01(const EngineType& engine): mEngine(engine) {}
155
158 Rand01(unsigned int seed): mEngine(static_cast<typename EngineType::result_type>(seed)) {}
159
161 void setSeed(unsigned int seed)
162 {
163 mEngine.seed(static_cast<typename EngineType::result_type>(seed));
164 }
165
167 const EngineType& engine() const { return mEngine; }
168
170 FloatType operator()() { return mRand(mEngine); }
171 };
172
173 typedef Rand01<double, boost::mt19937> Random01;
174
175
178 template<typename IntType = int, typename EngineType = boost::mt19937>
179 class RandInt
180 {
181 private:
182 #if BOOST_VERSION >= 104700
183 typedef boost::random::uniform_int_distribution<IntType> Distr;
184 #else
185 typedef boost::uniform_int<IntType> Distr;
186 #endif
187 EngineType mEngine;
188 Distr mRand;
189
190 public:
194 RandInt(const EngineType& engine, IntType imin, IntType imax):
195 mEngine(engine),
196 mRand(std::min(imin, imax), std::max(imin, imax))
197 {}
198
202 RandInt(unsigned int seed, IntType imin, IntType imax):
203 mEngine(static_cast<typename EngineType::result_type>(seed)),
204 mRand(std::min(imin, imax), std::max(imin, imax))
205 {}
206
208 void setRange(IntType imin, IntType imax)
209 {
210 mRand = Distr(std::min(imin, imax), std::max(imin, imax));
211 }
212
214 void setSeed(unsigned int seed)
215 {
216 mEngine.seed(static_cast<typename EngineType::result_type>(seed));
217 }
218
220 const EngineType& engine() const { return mEngine; }
221
223 IntType operator()() { return mRand(mEngine); }
224
227 IntType operator()(IntType imin, IntType imax)
228 {
229 const IntType lo = std::min(imin, imax), hi = std::max(imin, imax);
230 #if BOOST_VERSION >= 104700
231 return mRand(mEngine, typename Distr::param_type(lo, hi));
232 #else
233 return Distr(lo, hi)(mEngine);
234 #endif
235 }
236 };
237
238 typedef RandInt<int, boost::mt19937> RandomInt;
239
240
241 // ==========> Clamp <==================
242
244 template<typename Type>
245 inline Type
246 Clamp(Type x, Type min, Type max)
247 {
248 assert( !(min>max) );
249 return x > min ? x < max ? x : max : min;
250 }
251
252
254 template<typename Type>
255 inline Type
256 Clamp01(Type x) { return x > Type(0) ? x < Type(1) ? x : Type(1) : Type(0); }
257
258
260 template<typename Type>
261 inline bool
262 ClampTest01(Type &x)
263 {
264 if (x >= Type(0) && x <= Type(1)) return false;
265 x = x < Type(0) ? Type(0) : Type(1);
266 return true;
267 }
268
270 template<typename Type>
271 inline Type
272 SmoothUnitStep(Type x)
273 {
274 return x > 0 ? x < 1 ? (3-2*x)*x*x : Type(1) : Type(0);
275 }
276
279 template<typename Type>
280 inline Type
281 SmoothUnitStep(Type x, Type min, Type max)
282 {
283 assert(min < max);
284 return SmoothUnitStep((x-min)/(max-min));
285 }
286
287
288 // ==========> Absolute Value <==================
289
290
292 inline int32_t Abs(int32_t i) { return abs(i); }
294 inline int64_t Abs(int64_t i)
295 {
296 #ifdef _MSC_VER
297 return (i < int64_t(0) ? -i : i);
298 #else
299 return labs(i);
300 #endif
301 }
302 inline float Abs(float x) { return fabsf(x); }
303 inline double Abs(double x) { return fabs(x); }
304 inline long double Abs(long double x) { return fabsl(x); }
305 inline uint32_t Abs(uint32_t i) { return i; }
306 inline uint64_t Abs(uint64_t i) { return i; }
307 inline bool Abs(bool b) { return b; }
308 // On OSX size_t and uint64_t are different types
309 #if defined(__APPLE__) || defined(MACOSX)
310 inline size_t Abs(size_t i) { return i; }
311 #endif
312
313
314
316
317
318 // ==========> Value Comparison <==================
319
320
322 template<typename Type>
323 inline bool
324 isZero(const Type& x)
325 {
326 OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
327 return x == zeroVal<Type>();
328 OPENVDB_NO_FP_EQUALITY_WARNING_END
329 }
330
331
334 template<typename Type>
335 inline bool
336 isApproxZero(const Type& x)
337 {
338 const Type tolerance = Type(zeroVal<Type>() + Tolerance<Type>::value());
339 return !(x > tolerance) && !(x < -tolerance);
340 }
341
343 template<typename Type>
344 inline bool
345 isApproxZero(const Type& x, const Type& tolerance)
346 {
347 return !(x > tolerance) && !(x < -tolerance);
348 }
349
350
352 template<typename Type>
353 inline bool
354 isNegative(const Type& x) { return x < zeroVal<Type>(); }
355
357 template<> inline bool isNegative<bool>(const bool&) { return false; }
358
359
361 template<typename Type>
362 inline bool
363 isFinite(const Type& x) { return boost::math::isfinite(x); }
364
365
368 template<typename Type>
369 inline bool
370 isApproxEqual(const Type& a, const Type& b)
371 {
372 const Type tolerance = Type(zeroVal<Type>() + Tolerance<Type>::value());
373 return !(Abs(a - b) > tolerance);
374 }
375
376
378 template<typename Type>
379 inline bool
380 isApproxEqual(const Type& a, const Type& b, const Type& tolerance)
381 {
382 return !(Abs(a - b) > tolerance);
383 }
384
385 #define OPENVDB_EXACT_IS_APPROX_EQUAL(T) \
386 template<> inline bool isApproxEqual<T>(const T& a, const T& b) { return a == b; } \
387 template<> inline bool isApproxEqual<T>(const T& a, const T& b, const T&) { return a == b; } \
388
389
390 OPENVDB_EXACT_IS_APPROX_EQUAL(bool)
391 OPENVDB_EXACT_IS_APPROX_EQUAL(std::string)
392
393
396 template<typename Type>
397 inline bool
398 isApproxLarger(const Type& a, const Type& b, const Type& tolerance)
399 {
400 return (b - a < tolerance);
401 }
402
403
405 template<typename T0, typename T1>
406 inline bool
407 isExactlyEqual(const T0& a, const T1& b)
408 {
409 OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
410 return a == b;
411 OPENVDB_NO_FP_EQUALITY_WARNING_END
412 }
413
414
415 template<typename Type>
416 inline bool
417 isRelOrApproxEqual(const Type& a, const Type& b, const Type& absTol, const Type& relTol)
418 {
419 // First check to see if we are inside the absolute tolerance
420 // Necessary for numbers close to 0
421 if (!(Abs(a - b) > absTol)) return true;
422
423 // Next check to see if we are inside the relative tolerance
424 // to handle large numbers that aren't within the abs tolerance
425 // but could be the closest floating point representation
426 double relError;
427 if (Abs(b) > Abs(a)) {
428 relError = Abs((a - b) / b);
429 } else {
430 relError = Abs((a - b) / a);
431 }
432 return (relError <= relTol);
433 }
434
435 template<>
436 inline bool
437 isRelOrApproxEqual(const bool& a, const bool& b, const bool&, const bool&)
438 {
439 return (a == b);
440 }
441
442
443 // Avoid strict aliasing issues by using type punning
444 // http://cellperformance.beyond3d.com/articles/2006/06/understanding-strict-aliasing.html
445 // Using "casting through a union(2)"
446 inline int32_t
447 floatToInt32(const float aFloatValue)
448 {
449 union FloatOrInt32 { float floatValue; int32_t int32Value; };
450 const FloatOrInt32* foi = reinterpret_cast<const FloatOrInt32*>(&aFloatValue);
451 return foi->int32Value;
452 }
453
454
455 inline int64_t
456 doubleToInt64(const double aDoubleValue)
457 {
458 union DoubleOrInt64 { double doubleValue; int64_t int64Value; };
459 const DoubleOrInt64* dol = reinterpret_cast<const DoubleOrInt64*>(&aDoubleValue);
460 return dol->int64Value;
461 }
462
463
464 // aUnitsInLastPlace is the allowed difference between the least significant digits
465 // of the numbers' floating point representation
466 // Please read the reference paper before trying to use isUlpsEqual
467 // http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
468 inline bool
469 isUlpsEqual(const double aLeft, const double aRight, const int64_t aUnitsInLastPlace)
470 {
471 int64_t longLeft = doubleToInt64(aLeft);
472 // Because of 2's complement, must restore lexicographical order
473 if (longLeft < 0) {
474 longLeft = INT64_C(0x8000000000000000) - longLeft;
475 }
476
477 int64_t longRight = doubleToInt64(aRight);
478 // Because of 2's complement, must restore lexicographical order
479 if (longRight < 0) {
480 longRight = INT64_C(0x8000000000000000) - longRight;
481 }
482
483 int64_t difference = labs(longLeft - longRight);
484 return (difference <= aUnitsInLastPlace);
485 }
486
487 inline bool
488 isUlpsEqual(const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)
489 {
490 int32_t intLeft = floatToInt32(aLeft);
491 // Because of 2's complement, must restore lexicographical order
492 if (intLeft < 0) {
493 intLeft = 0x80000000 - intLeft;
494 }
495
496 int32_t intRight = floatToInt32(aRight);
497 // Because of 2's complement, must restore lexicographical order
498 if (intRight < 0) {
499 intRight = 0x80000000 - intRight;
500 }
501
502 int32_t difference = abs(intLeft - intRight);
503 return (difference <= aUnitsInLastPlace);
504 }
505
506
508
509
510 // ==========> Pow <==================
511
513 template<typename Type>
514 inline Type Pow2(Type x) { return x*x; }
515
517 template<typename Type>
518 inline Type Pow3(Type x) { return x*x*x; }
519
521 template<typename Type>
522 inline Type Pow4(Type x) { return Pow2(Pow2(x)); }
523
525 template<typename Type>
526 Type
527 Pow(Type x, int n)
528 {
529 Type ans = 1;
530 if (n < 0) {
531 n = -n;
532 x = Type(1)/x;
533 }
534 while (n--) ans *= x;
535 return ans;
536 }
537
539 inline float
541 Pow(float b, float e)
542 {
543 assert( b >= 0.0f && "Pow(float,float): base is negative" );
544 return powf(b,e);
545 }
546
547 inline double
548 Pow(double b, double e)
549 {
550 assert( b >= 0.0 && "Pow(double,double): base is negative" );
551 return pow(b,e);
552 }
554
555
556 // ==========> Max <==================
557
559 template<typename Type>
560 inline const Type&
561 Max(const Type& a, const Type& b)
562 {
563 return std::max(a,b) ;
564 }
565
567 template<typename Type>
568 inline const Type&
569 Max(const Type& a, const Type& b, const Type& c)
570 {
571 return std::max( std::max(a,b), c ) ;
572 }
573
575 template<typename Type>
576 inline const Type&
577 Max(const Type& a, const Type& b, const Type& c, const Type& d)
578 {
579 return std::max(std::max(a,b), std::max(c,d));
580 }
581
583 template<typename Type>
584 inline const Type&
585 Max(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e)
586 {
587 return std::max(std::max(a,b), Max(c,d,e));
588 }
589
591 template<typename Type>
592 inline const Type&
593 Max(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e, const Type& f)
594 {
595 return std::max(Max(a,b,c), Max(d,e,f));
596 }
597
599 template<typename Type>
600 inline const Type&
601 Max(const Type& a, const Type& b, const Type& c, const Type& d,
602 const Type& e, const Type& f, const Type& g)
603 {
604 return std::max(Max(a,b,c,d), Max(e,f,g));
605 }
606
608 template<typename Type>
609 inline const Type&
610 Max(const Type& a, const Type& b, const Type& c, const Type& d,
611 const Type& e, const Type& f, const Type& g, const Type& h)
612 {
613 return std::max(Max(a,b,c,d), Max(e,f,g,h));
614 }
615
616
617 // ==========> Min <==================
618
620 template<typename Type>
621 inline const Type&
622 Min(const Type& a, const Type& b) { return std::min(a, b); }
623
625 template<typename Type>
626 inline const Type&
627 Min(const Type& a, const Type& b, const Type& c) { return std::min(std::min(a, b), c); }
628
630 template<typename Type>
631 inline const Type&
632 Min(const Type& a, const Type& b, const Type& c, const Type& d)
633 {
634 return std::min(std::min(a, b), std::min(c, d));
635 }
636
638 template<typename Type>
639 inline const Type&
640 Min(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e)
641 {
642 return std::min(std::min(a,b), Min(c,d,e));
643 }
644
646 template<typename Type>
647 inline const Type&
648 Min(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e, const Type& f)
649 {
650 return std::min(Min(a,b,c), Min(d,e,f));
651 }
652
654 template<typename Type>
655 inline const Type&
656 Min(const Type& a, const Type& b, const Type& c, const Type& d,
657 const Type& e, const Type& f, const Type& g)
658 {
659 return std::min(Min(a,b,c,d), Min(e,f,g));
660 }
661
663 template<typename Type>
664 inline const Type&
665 Min(const Type& a, const Type& b, const Type& c, const Type& d,
666 const Type& e, const Type& f, const Type& g, const Type& h)
667 {
668 return std::min(Min(a,b,c,d), Min(e,f,g,h));
669 }
670
671
672 // ============> Exp <==================
673
675 template<typename Type>
676 inline Type Exp(const Type& x) { return std::exp(x); }
677
678 // ============> Sin <==================
679
681 inline float Sin(const float& x) { return sinf(x); }
683
684 inline double Sin(const double& x) { return sin(x); }
686
687 // ============> Cos <==================
688
690 inline float Cos(const float& x) { return cosf(x); }
692
693 inline double Cos(const double& x) { return cos(x); }
695
696
698
699
701 template <typename Type>
702 inline int Sign(const Type &x) { return (zeroVal<Type>() < x) - (x < zeroVal<Type>()); }
703
704
707 template <typename Type>
708 inline bool
709 SignChange(const Type& a, const Type& b)
710 {
711 return ( (a<zeroVal<Type>()) ^ (b<zeroVal<Type>()) );
712 }
713
714
717 template <typename Type>
718 inline bool
719 ZeroCrossing(const Type& a, const Type& b)
720 {
721 return a * b <= zeroVal<Type>();
722 }
723
724
726 inline float Sqrt(float x) { return sqrtf(x); }
728 inline double Sqrt(double x) { return sqrt(x); }
729 inline long double Sqrt(long double x) { return sqrtl(x); }
731
732
734 inline float Cbrt(float x) { return boost::math::cbrt(x); }
736 inline double Cbrt(double x) { return boost::math::cbrt(x); }
737 inline long double Cbrt(long double x) { return boost::math::cbrt(x); }
739
740
742 inline int Mod(int x, int y) { return (x % y); }
744 inline float Mod(float x, float y) { return fmodf(x,y); }
745 inline double Mod(double x, double y) { return fmod(x,y); }
746 inline long double Mod(long double x, long double y) { return fmodl(x,y); }
747 template<typename Type> inline Type Remainder(Type x, Type y) { return Mod(x,y); }
749
750
752 inline float RoundUp(float x) { return ceilf(x); }
754 inline double RoundUp(double x) { return ceil(x); }
755 inline long double RoundUp(long double x) { return ceill(x); }
757 template<typename Type>
759 inline Type
760 RoundUp(Type x, Type base)
761 {
762 Type remainder = Remainder(x, base);
763 return remainder ? x-remainder+base : x;
764 }
765
766
768 inline float RoundDown(float x) { return floorf(x); }
770 inline double RoundDown(double x) { return floor(x); }
771 inline long double RoundDown(long double x) { return floorl(x); }
773 template<typename Type>
775 inline Type
776 RoundDown(Type x, Type base)
777 {
778 Type remainder = Remainder(x, base);
779 return remainder ? x-remainder : x;
780 }
781
782
784 inline float Round(float x) { return RoundDown(x + 0.5f); }
786 inline double Round(double x) { return RoundDown(x + 0.5); }
787 inline long double Round(long double x) { return RoundDown(x + 0.5l); }
789
790
793 template<typename Type>
794 inline Type
795 EuclideanRemainder(Type x) { return x - RoundDown(x); }
796
797
799 template<typename Type>
800 inline Type
801 IntegerPart(Type x)
802 {
803 return (x > 0 ? RoundDown(x) : RoundUp(x));
804 }
805
807 template<typename Type>
808 inline Type
809 FractionalPart(Type x) { return Mod(x,Type(1)); }
810
811
813 inline int Floor(float x) { return int(RoundDown(x)); }
815 inline int Floor(double x) { return int(RoundDown(x)); }
816 inline int Floor(long double x) { return int(RoundDown(x)); }
818
819
821 inline int Ceil(float x) { return int(RoundUp(x)); }
823 inline int Ceil(double x) { return int(RoundUp(x)); }
824 inline int Ceil(long double x) { return int(RoundUp(x)); }
826
827
829 template<typename Type>
830 inline Type Chop(Type x, Type delta) { return (Abs(x) < delta ? zeroVal<Type>() : x); }
831
832
834 template<typename Type>
835 inline Type
836 Truncate(Type x, unsigned int digits)
837 {
838 Type tenth = Pow(10,digits);
839 return RoundDown(x*tenth+0.5)/tenth;
840 }
841
842
844
845
847 template<typename Type>
848 inline Type
849 Inv(Type x)
850 {
851 assert(x);
852 return Type(1)/x;
853 }
854
855
856 enum Axis {
857 X_AXIS = 0,
858 Y_AXIS = 1,
859 Z_AXIS = 2
860 };
861
862 // enum values are consistent with their historical mx analogs.
863 enum RotationOrder {
864 XYZ_ROTATION = 0,
865 XZY_ROTATION,
866 YXZ_ROTATION,
867 YZX_ROTATION,
868 ZXY_ROTATION,
869 ZYX_ROTATION,
870 XZX_ROTATION,
871 ZXZ_ROTATION
872 };
873
874
875 template <typename S, typename T>
876 struct promote {
877 typedef typename boost::numeric::conversion_traits<S, T>::supertype type;
878 };
879
880
888 template<typename Vec3T>
889 size_t
890 MinIndex(const Vec3T& v)
891 {
892 #ifndef _MSC_VER // Visual C++ doesn't guarantee thread-safe initialization of local statics
893 static
894 #endif
895 const size_t hashTable[8] = { 2, 1, 9, 1, 2, 9, 0, 0 };//9 is a dummy value
896 const size_t hashKey =
897 ((v[0] < v[1]) << 2) + ((v[0] < v[2]) << 1) + (v[1] < v[2]);// ?*4+?*2+?*1
898 return hashTable[hashKey];
899 }
900
901
909 template<typename Vec3T>
910 size_t
911 MaxIndex(const Vec3T& v)
912 {
913 #ifndef _MSC_VER // Visual C++ doesn't guarantee thread-safe initialization of local statics
914 static
915 #endif
916 const size_t hashTable[8] = { 2, 1, 9, 1, 2, 9, 0, 0 };//9 is a dummy value
917 const size_t hashKey =
918 ((v[0] > v[1]) << 2) + ((v[0] > v[2]) << 1) + (v[1] > v[2]);// ?*4+?*2+?*1
919 return hashTable[hashKey];
920 }
921
922 } // namespace math
923 } // namespace OPENVDB_VERSION_NAME
924 } // namespace openvdb
925
926 #endif // OPENVDB_MATH_MATH_HAS_BEEN_INCLUDED
927
928 // Copyright (c) 2012-2016 DreamWorks Animation LLC
929 // All rights reserved. This software is distributed under the
930 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v3_2_0::math::Cbrt
long double Cbrt(long double x)
Return the cube root of a floating-point value.
Definition: Math.h:737
openvdb::v3_2_0::math::isApproxEqual
bool isApproxEqual(const Type &a, const Type &b, const Type &tolerance)
Return true if a is equal to b to within the given tolerance.
Definition: Math.h:380
openvdb::v3_2_0::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:407
openvdb::v3_2_0::math::X_AXIS
Definition: Math.h:857
openvdb::v3_2_0::math::Delta
Delta for small floating-point offsets.
Definition: Math.h:132
openvdb::v3_2_0::math::Rand01::ValueType
FloatType ValueType
Definition: Math.h:150
openvdb::v3_2_0::math::XZX_ROTATION
Definition: Math.h:870
openvdb::v3_2_0::math::isFinite
bool isFinite(const Type &x)
Return true if x is finite.
Definition: Math.h:363
openvdb::v3_2_0::math::Rand01::engine
const EngineType & engine() const
Return a const reference to the random number generator.
Definition: Math.h:167
openvdb::v3_2_0::math::Rand01::Rand01
Rand01(const EngineType &engine)
Initialize the generator.
Definition: Math.h:154
openvdb::v3_2_0::math::RandInt::engine
const EngineType & engine() const
Return a const reference to the random number generator.
Definition: Math.h:220
openvdb::v3_2_0::math::Tolerance< double >::value
static double value()
Definition: Math.h:127
openvdb::v3_2_0::math::Pow2
Type Pow2(Type x)
Return .
Definition: Math.h:514
openvdb::v3_2_0::math::Truncate
Type Truncate(Type x, unsigned int digits)
Return x truncated to the given number of decimal digits.
Definition: Math.h:836
openvdb::v3_2_0::math::Remainder
Type Remainder(Type x, Type y)
Return the remainder of x / y.
Definition: Math.h:747
openvdb::v3_2_0::math::Rand01
Simple generator of random numbers over the range [0, 1)
Definition: Math.h:143
openvdb::v3_2_0::math::isApproxLarger
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:398
openvdb::v3_2_0::math::Pow3
Type Pow3(Type x)
Return .
Definition: Math.h:518
openvdb::v3_2_0::math::isZero
bool isZero(const Type &x)
Return true if x is exactly equal to zero.
Definition: Math.h:324
openvdb::v3_2_0::math::RoundDown
Type RoundDown(Type x, Type base)
Return x rounded down to the nearest multiple of base.
Definition: Math.h:776
openvdb::v3_2_0::math::isNegative< bool >
bool isNegative< bool >(const bool &)
Return false, since bool values are never less than zero.
Definition: Math.h:357
openvdb::v3_2_0::math::Y_AXIS
Definition: Math.h:858
openvdb::v3_2_0::math::Clamp
Type Clamp(Type x, Type min, Type max)
Return x clamped to [min, max].
Definition: Math.h:246
openvdb::v3_2_0::tools::composite::max
const boost::disable_if_c< VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:132
openvdb::v3_2_0::math::Chop
Type Chop(Type x, Type delta)
Return x if it is greater or equal in magnitude than delta. Otherwise, return zero.
Definition: Math.h:830
openvdb::v3_2_0::math::isRelOrApproxEqual
bool isRelOrApproxEqual(const bool &a, const bool &b, const bool &, const bool &)
Definition: Math.h:437
openvdb::v3_2_0::math::XZY_ROTATION
Definition: Math.h:865
openvdb::v3_2_0::math::ZXY_ROTATION
Definition: Math.h:868
openvdb::v3_2_0::math::negative
std::string negative(const std::string &val)
Return the "negation" of the given string.
Definition: Math.h:120
openvdb::v3_2_0::math::RandInt
Simple random integer generator.
Definition: Math.h:179
openvdb::v3_2_0::math::Mod
long double Mod(long double x, long double y)
Return the remainder of x / y.
Definition: Math.h:746
openvdb::v3_2_0::math::RandInt::setSeed
void setSeed(unsigned int seed)
Set the seed value for the random number generator.
Definition: Math.h:214
openvdb::v3_2_0::math::ZXZ_ROTATION
Definition: Math.h:871
openvdb::v3_2_0::math::YXZ_ROTATION
Definition: Math.h:866
openvdb::v3_2_0::math::Exp
Type Exp(const Type &x)
Return .
Definition: Math.h:676
openvdb::v3_2_0::math::Delta< float >::value
static float value()
Definition: Math.h:133
openvdb::v3_2_0::math::Delta< double >::value
static double value()
Definition: Math.h:134
openvdb::v3_2_0::math::XYZ_ROTATION
Definition: Math.h:864
openvdb::v3_2_0::math::Tolerance< float >::value
static float value()
Definition: Math.h:126
openvdb::v3_2_0::math::RotationOrder
RotationOrder
Definition: Math.h:863
openvdb::v3_2_0::math::Rand01::Rand01
Rand01(unsigned int seed)
Initialize the generator.
Definition: Math.h:158
openvdb::v3_2_0::math::Sign
int Sign(const Type &x)
Return the sign of the given value as an integer (either -1, 0 or 1).
Definition: Math.h:702
openvdb::v3_2_0::math::Ceil
int Ceil(long double x)
Return the ceiling of x.
Definition: Math.h:824
openvdb::v3_2_0::math::SmoothUnitStep
Type SmoothUnitStep(Type x, Type min, Type max)
Return 0 if x < min, 1 if x > max or else , where .
Definition: Math.h:281
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
Definition: version.h:43
openvdb::v3_2_0::math::Clamp01
Type Clamp01(Type x)
Return x clamped to [0, 1].
Definition: Math.h:256
openvdb::v3_2_0::math::ClampTest01
bool ClampTest01(Type &x)
Return true if x is outside [0,1].
Definition: Math.h:262
openvdb::v3_2_0::math::RandInt::setRange
void setRange(IntType imin, IntType imax)
Change the range over which integers are distributed to [imin, imax].
Definition: Math.h:208
openvdb::v3_2_0::math::Cos
double Cos(const double &x)
Return .
Definition: Math.h:693
openvdb::v3_2_0::math::Floor
int Floor(long double x)
Return the floor of x.
Definition: Math.h:816
openvdb::v3_2_0::math::RandomInt
RandInt< int, boost::mt19937 > RandomInt
Definition: Math.h:238
openvdb::v3_2_0::math::RoundUp
Type RoundUp(Type x, Type base)
Return x rounded up to the nearest multiple of base.
Definition: Math.h:760
openvdb::v3_2_0::math::RandInt::operator()
IntType operator()()
Return a randomly-generated integer in the current range.
Definition: Math.h:223
openvdb::v3_2_0::math::Min
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:665
openvdb
Definition: Exceptions.h:39
openvdb::v3_2_0::math::Random01
Rand01< double, boost::mt19937 > Random01
Definition: Math.h:173
openvdb::v3_2_0::math::Tolerance
Tolerance for floating-point comparison.
Definition: Math.h:125
openvdb::v3_2_0::math::Rand01::operator()
FloatType operator()()
Return a uniformly distributed random number in the range [0, 1).
Definition: Math.h:170
openvdb::v3_2_0::math::RandInt::operator()
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:227
OPENVDB_NO_FP_EQUALITY_WARNING_END
#define OPENVDB_NO_FP_EQUALITY_WARNING_END
Definition: Math.h:83
openvdb::v3_2_0::math::SignChange
bool SignChange(const Type &a, const Type &b)
Return true if a and b have different signs.
Definition: Math.h:709
openvdb::v3_2_0::math::EuclideanRemainder
Type EuclideanRemainder(Type x)
Definition: Math.h:795
openvdb::v3_2_0::math::Rand01::setSeed
void setSeed(unsigned int seed)
Set the seed value for the random number generator.
Definition: Math.h:161
openvdb::v3_2_0::math::FractionalPart
Type FractionalPart(Type x)
Return the fractional part of x.
Definition: Math.h:809
openvdb::v3_2_0::math::Z_AXIS
Definition: Math.h:859
version.h
openvdb::v3_2_0::math::Sin
double Sin(const double &x)
Return .
Definition: Math.h:684
openvdb::v3_2_0::math::promote::type
boost::numeric::conversion_traits< S, T >::supertype type
Definition: Math.h:877
openvdb::v3_2_0::math::doubleToInt64
int64_t doubleToInt64(const double aDoubleValue)
Definition: Math.h:456
openvdb::v3_2_0::math::Max
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:610
OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
#define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
Definition: Math.h:82
openvdb::v3_2_0::math::Sqrt
long double Sqrt(long double x)
Return the square root of a floating-point value.
Definition: Math.h:729
openvdb::v3_2_0::operator+
std::string operator+(const std::string &s, double)
Needed to support the (zeroVal<ValueType>() + val) idiom when ValueType is std::string.
Definition: Math.h:107
openvdb::v3_2_0::math::MaxIndex
size_t MaxIndex(const Vec3T &v)
Return the index [0,1,2] of the largest value in a 3D vector.
Definition: Math.h:911
openvdb::v3_2_0::math::Abs
bool Abs(bool b)
Return the absolute value of the given quantity.
Definition: Math.h:307
openvdb::v3_2_0::math::YZX_ROTATION
Definition: Math.h:867
openvdb::v3_2_0::math::Inv
Type Inv(Type x)
Return the inverse of x.
Definition: Math.h:849
openvdb::v3_2_0::math::isNegative
bool isNegative(const Type &x)
Return true if x is less than zero.
Definition: Math.h:354
openvdb::v3_2_0::math::Axis
Axis
Definition: Math.h:856
openvdb::v3_2_0::math::Pow
double Pow(double b, double e)
Return .
Definition: Math.h:548
openvdb::v3_2_0::math::RandInt::RandInt
RandInt(unsigned int seed, IntType imin, IntType imax)
Initialize the generator.
Definition: Math.h:202
openvdb::v3_2_0::math::ZeroCrossing
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:719
openvdb::v3_2_0::zeroVal< bool >
bool zeroVal< bool >()
Return the bool value that corresponds to zero.
Definition: Math.h:98
openvdb::v3_2_0::math::ZYX_ROTATION
Definition: Math.h:869
openvdb::v3_2_0::math::Round
long double Round(long double x)
Return x rounded to the nearest integer.
Definition: Math.h:787
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:71
openvdb::v3_2_0::math::Pow4
Type Pow4(Type x)
Return .
Definition: Math.h:522
openvdb::v3_2_0::math::IntegerPart
Type IntegerPart(Type x)
Return the integer part of x.
Definition: Math.h:801
openvdb::v3_2_0::math::isUlpsEqual
bool isUlpsEqual(const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)
Definition: Math.h:488
openvdb::v3_2_0::math::MinIndex
size_t MinIndex(const Vec3T &v)
Return the index [0,1,2] of the smallest value in a 3D vector.
Definition: Math.h:890
openvdb::v3_2_0::math::promote
Definition: Math.h:876
openvdb::v3_2_0::math::RandInt::RandInt
RandInt(const EngineType &engine, IntType imin, IntType imax)
Initialize the generator.
Definition: Math.h:194
OPENVDB_EXACT_IS_APPROX_EQUAL
#define OPENVDB_EXACT_IS_APPROX_EQUAL(T)
Definition: Math.h:385
openvdb::v3_2_0::math::isApproxZero
bool isApproxZero(const Type &x, const Type &tolerance)
Return true if x is equal to zero to within the given tolerance.
Definition: Math.h:345
openvdb::v3_2_0::math::floatToInt32
int32_t floatToInt32(const float aFloatValue)
Definition: Math.h:447
Platform.h
openvdb::v3_2_0::zeroVal
T zeroVal()
Return the value of type T that corresponds to zero.
Definition: Math.h:94
openvdb::v3_2_0::tools::composite::min
const boost::disable_if_c< VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:128