OpenVDB 5.1.0

Math.h
Go to the documentation of this file.
1 //
3 // Copyright (c) 2012-2018 DreamWorks Animation LLC
4 //
5 // All rights reserved. This software is distributed under the
6 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
7 //
8 // Redistributions of source code must retain the above copyright
9 // and license notice and the following restrictions and disclaimer.
10 //
11 // * Neither the name of DreamWorks Animation nor the names of
12 // its contributors may be used to endorse or promote products derived
13 // from this software without specific prior written permission.
14 //
15 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
16 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
17 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
18 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
19 // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY INDIRECT, INCIDENTAL,
20 // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
21 // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
22 // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
23 // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
24 // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
25 // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
26 // IN NO EVENT SHALL THE COPYRIGHT HOLDERS' AND CONTRIBUTORS' AGGREGATE
27 // LIABILITY FOR ALL CLAIMS REGARDLESS OF THEIR BASIS EXCEED US$250.00.
28 //
30 //
34
35 #ifndef OPENVDB_MATH_HAS_BEEN_INCLUDED
36 #define OPENVDB_MATH_HAS_BEEN_INCLUDED
37
38 #include <openvdb/Platform.h>
39 #include <openvdb/version.h>
40 #include <boost/numeric/conversion/conversion_traits.hpp>
41 #include <algorithm> // for std::max()
42 #include <cassert>
43 #include <cmath> // for std::ceil(), std::fabs(), std::pow(), std::sqrt(), etc.
44 #include <cstdlib> // for abs(int)
45 #include <random>
46 #include <string>
47 #include <type_traits> // for std::is_arithmetic
48
49
50 // Compile pragmas
51
52 // Intel(r) compiler fires remark #1572: floating-point equality and inequality
53 // comparisons are unrealiable when == or != is used with floating point operands.
54 #if defined(__INTEL_COMPILER)
55 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN \
56 _Pragma("warning (push)") \
57 _Pragma("warning (disable:1572)")
58 #define OPENVDB_NO_FP_EQUALITY_WARNING_END \
59 _Pragma("warning (pop)")
60 #elif defined(__clang__)
61 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN \
62 PRAGMA(clang diagnostic push) \
63 PRAGMA(clang diagnostic ignored "-Wfloat-equal")
64 #define OPENVDB_NO_FP_EQUALITY_WARNING_END \
65 PRAGMA(clang diagnostic pop)
66 #else
67 // For GCC, #pragma GCC diagnostic ignored "-Wfloat-equal"
68 // isn't working until gcc 4.2+,
69 // Trying
70 // #pragma GCC system_header
71 // creates other problems, most notably "warning: will never be executed"
72 // in from templates, unsure of how to work around.
73 // If necessary, could use integer based comparisons for equality
74 #define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
75 #define OPENVDB_NO_FP_EQUALITY_WARNING_END
76 #endif
77
78 namespace openvdb {
79 OPENVDB_USE_VERSION_NAMESPACE
80 namespace OPENVDB_VERSION_NAME {
81
86 template<typename T> inline T zeroVal() { return T(0); }
88 template<> inline std::string zeroVal<std::string>() { return ""; }
90 template<> inline bool zeroVal<bool>() { return false; }
91
93
94 inline std::string operator+(const std::string& s, bool) { return s; }
97 inline std::string operator+(const std::string& s, int) { return s; }
98 inline std::string operator+(const std::string& s, float) { return s; }
99 inline std::string operator+(const std::string& s, double) { return s; }
101
102
103 namespace math {
104
108 template<typename T> inline T negative(const T& val) { return T(-val); }
110 template<> inline bool negative(const bool& val) { return !val; }
112 template<> inline std::string negative(const std::string& val) { return val; }
113
114
116 template<typename T> struct Tolerance { static T value() { return zeroVal<T>(); } };
118 template<> struct Tolerance<float> { static float value() { return 1e-8f; } };
119 template<> struct Tolerance<double> { static double value() { return 1e-15; } };
121
123 template<typename T> struct Delta { static T value() { return zeroVal<T>(); } };
125 template<> struct Delta<float> { static float value() { return 1e-5f; } };
126 template<> struct Delta<double> { static double value() { return 1e-9; } };
128
129
130 // ==========> Random Values <==================
131
134 template<typename FloatType = double, typename EngineType = std::mt19937>
135 class Rand01
136 {
137 private:
138 EngineType mEngine;
139 std::uniform_real_distribution<FloatType> mRand;
140
141 public:
142 using ValueType = FloatType;
143
146 Rand01(const EngineType& engine): mEngine(engine) {}
147
150 Rand01(unsigned int seed): mEngine(static_cast<typename EngineType::result_type>(seed)) {}
151
153 void setSeed(unsigned int seed)
154 {
155 mEngine.seed(static_cast<typename EngineType::result_type>(seed));
156 }
157
159 const EngineType& engine() const { return mEngine; }
160
162 FloatType operator()() { return mRand(mEngine); }
163 };
164
165 using Random01 = Rand01<double, std::mt19937>;
166
167
170 template<typename IntType = int, typename EngineType = std::mt19937>
171 class RandInt
172 {
173 private:
174 using Distr = std::uniform_int_distribution<IntType>;
175 EngineType mEngine;
176 Distr mRand;
177
178 public:
182 RandInt(const EngineType& engine, IntType imin, IntType imax):
183 mEngine(engine),
184 mRand(std::min(imin, imax), std::max(imin, imax))
185 {}
186
190 RandInt(unsigned int seed, IntType imin, IntType imax):
191 mEngine(static_cast<typename EngineType::result_type>(seed)),
192 mRand(std::min(imin, imax), std::max(imin, imax))
193 {}
194
196 void setRange(IntType imin, IntType imax)
197 {
198 mRand = Distr(std::min(imin, imax), std::max(imin, imax));
199 }
200
202 void setSeed(unsigned int seed)
203 {
204 mEngine.seed(static_cast<typename EngineType::result_type>(seed));
205 }
206
208 const EngineType& engine() const { return mEngine; }
209
211 IntType operator()() { return mRand(mEngine); }
212
215 IntType operator()(IntType imin, IntType imax)
216 {
217 const IntType lo = std::min(imin, imax), hi = std::max(imin, imax);
218 return mRand(mEngine, typename Distr::param_type(lo, hi));
219 }
220 };
221
222 using RandomInt = RandInt<int, std::mt19937>;
223
224
225 // ==========> Clamp <==================
226
228 template<typename Type>
229 inline Type
230 Clamp(Type x, Type min, Type max)
231 {
232 assert( !(min>max) );
233 return x > min ? x < max ? x : max : min;
234 }
235
236
238 template<typename Type>
239 inline Type
240 Clamp01(Type x) { return x > Type(0) ? x < Type(1) ? x : Type(1) : Type(0); }
241
242
244 template<typename Type>
245 inline bool
246 ClampTest01(Type &x)
247 {
248 if (x >= Type(0) && x <= Type(1)) return false;
249 x = x < Type(0) ? Type(0) : Type(1);
250 return true;
251 }
252
254 template<typename Type>
255 inline Type
256 SmoothUnitStep(Type x)
257 {
258 return x > 0 ? x < 1 ? (3-2*x)*x*x : Type(1) : Type(0);
259 }
260
263 template<typename Type>
264 inline Type
265 SmoothUnitStep(Type x, Type min, Type max)
266 {
267 assert(min < max);
268 return SmoothUnitStep((x-min)/(max-min));
269 }
270
271
272 // ==========> Absolute Value <==================
273
274
276 inline int32_t Abs(int32_t i) { return abs(i); }
278 inline int64_t Abs(int64_t i)
279 {
280 #ifdef _MSC_VER
281 return (i < int64_t(0) ? -i : i);
282 #else
283 return labs(i);
284 #endif
285 }
286 inline float Abs(float x) { return std::fabs(x); }
287 inline double Abs(double x) { return std::fabs(x); }
288 inline long double Abs(long double x) { return std::fabs(x); }
289 inline uint32_t Abs(uint32_t i) { return i; }
290 inline uint64_t Abs(uint64_t i) { return i; }
291 inline bool Abs(bool b) { return b; }
292 // On OSX size_t and uint64_t are different types
293 #if defined(__APPLE__) || defined(MACOSX)
294 inline size_t Abs(size_t i) { return i; }
295 #endif
296
297
298
300
301
302 // ==========> Value Comparison <==================
303
304
306 template<typename Type>
307 inline bool
308 isZero(const Type& x)
309 {
310 OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
311 return x == zeroVal<Type>();
312 OPENVDB_NO_FP_EQUALITY_WARNING_END
313 }
314
315
318 template<typename Type>
319 inline bool
320 isApproxZero(const Type& x)
321 {
322 const Type tolerance = Type(zeroVal<Type>() + Tolerance<Type>::value());
323 return !(x > tolerance) && !(x < -tolerance);
324 }
325
327 template<typename Type>
328 inline bool
329 isApproxZero(const Type& x, const Type& tolerance)
330 {
331 return !(x > tolerance) && !(x < -tolerance);
332 }
333
334
336 template<typename Type>
337 inline bool
338 isNegative(const Type& x) { return x < zeroVal<Type>(); }
339
340 // Return false, since bool values are never less than zero.
341 template<> inline bool isNegative<bool>(const bool&) { return false; }
342
343
345 inline bool
346 isFinite(const float x) { return std::isfinite(x); }
347
349 template<typename Type, typename std::enable_if<std::is_arithmetic<Type>::value, int>::type = 0>
350 inline bool
351 isFinite(const Type& x) { return std::isfinite(static_cast<double>(x)); }
352
353
356 template<typename Type>
357 inline bool
358 isApproxEqual(const Type& a, const Type& b)
359 {
360 const Type tolerance = Type(zeroVal<Type>() + Tolerance<Type>::value());
361 return !(Abs(a - b) > tolerance);
362 }
363
364
366 template<typename Type>
367 inline bool
368 isApproxEqual(const Type& a, const Type& b, const Type& tolerance)
369 {
370 return !(Abs(a - b) > tolerance);
371 }
372
373 #define OPENVDB_EXACT_IS_APPROX_EQUAL(T) \
374 template<> inline bool isApproxEqual<T>(const T& a, const T& b) { return a == b; } \
375 template<> inline bool isApproxEqual<T>(const T& a, const T& b, const T&) { return a == b; } \
376
377
378 OPENVDB_EXACT_IS_APPROX_EQUAL(bool)
379 OPENVDB_EXACT_IS_APPROX_EQUAL(std::string)
380
381
384 template<typename Type>
385 inline bool
386 isApproxLarger(const Type& a, const Type& b, const Type& tolerance)
387 {
388 return (b - a < tolerance);
389 }
390
391
393 template<typename T0, typename T1>
394 inline bool
395 isExactlyEqual(const T0& a, const T1& b)
396 {
397 OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
398 return a == b;
399 OPENVDB_NO_FP_EQUALITY_WARNING_END
400 }
401
402
403 template<typename Type>
404 inline bool
405 isRelOrApproxEqual(const Type& a, const Type& b, const Type& absTol, const Type& relTol)
406 {
407 // First check to see if we are inside the absolute tolerance
408 // Necessary for numbers close to 0
409 if (!(Abs(a - b) > absTol)) return true;
410
411 // Next check to see if we are inside the relative tolerance
412 // to handle large numbers that aren't within the abs tolerance
413 // but could be the closest floating point representation
414 double relError;
415 if (Abs(b) > Abs(a)) {
416 relError = Abs((a - b) / b);
417 } else {
418 relError = Abs((a - b) / a);
419 }
420 return (relError <= relTol);
421 }
422
423 template<>
424 inline bool
425 isRelOrApproxEqual(const bool& a, const bool& b, const bool&, const bool&)
426 {
427 return (a == b);
428 }
429
430
431 // Avoid strict aliasing issues by using type punning
432 // http://cellperformance.beyond3d.com/articles/2006/06/understanding-strict-aliasing.html
433 // Using "casting through a union(2)"
434 inline int32_t
435 floatToInt32(const float aFloatValue)
436 {
437 union FloatOrInt32 { float floatValue; int32_t int32Value; };
438 const FloatOrInt32* foi = reinterpret_cast<const FloatOrInt32*>(&aFloatValue);
439 return foi->int32Value;
440 }
441
442
443 inline int64_t
444 doubleToInt64(const double aDoubleValue)
445 {
446 union DoubleOrInt64 { double doubleValue; int64_t int64Value; };
447 const DoubleOrInt64* dol = reinterpret_cast<const DoubleOrInt64*>(&aDoubleValue);
448 return dol->int64Value;
449 }
450
451
452 // aUnitsInLastPlace is the allowed difference between the least significant digits
453 // of the numbers' floating point representation
454 // Please read the reference paper before trying to use isUlpsEqual
455 // http://www.cygnus-software.com/papers/comparingfloats/comparingfloats.htm
456 inline bool
457 isUlpsEqual(const double aLeft, const double aRight, const int64_t aUnitsInLastPlace)
458 {
459 int64_t longLeft = doubleToInt64(aLeft);
460 // Because of 2's complement, must restore lexicographical order
461 if (longLeft < 0) {
462 longLeft = INT64_C(0x8000000000000000) - longLeft;
463 }
464
465 int64_t longRight = doubleToInt64(aRight);
466 // Because of 2's complement, must restore lexicographical order
467 if (longRight < 0) {
468 longRight = INT64_C(0x8000000000000000) - longRight;
469 }
470
471 int64_t difference = labs(longLeft - longRight);
472 return (difference <= aUnitsInLastPlace);
473 }
474
475 inline bool
476 isUlpsEqual(const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)
477 {
478 int32_t intLeft = floatToInt32(aLeft);
479 // Because of 2's complement, must restore lexicographical order
480 if (intLeft < 0) {
481 intLeft = 0x80000000 - intLeft;
482 }
483
484 int32_t intRight = floatToInt32(aRight);
485 // Because of 2's complement, must restore lexicographical order
486 if (intRight < 0) {
487 intRight = 0x80000000 - intRight;
488 }
489
490 int32_t difference = abs(intLeft - intRight);
491 return (difference <= aUnitsInLastPlace);
492 }
493
494
496
497
498 // ==========> Pow <==================
499
501 template<typename Type>
502 inline Type Pow2(Type x) { return x*x; }
503
505 template<typename Type>
506 inline Type Pow3(Type x) { return x*x*x; }
507
509 template<typename Type>
510 inline Type Pow4(Type x) { return Pow2(Pow2(x)); }
511
513 template<typename Type>
514 Type
515 Pow(Type x, int n)
516 {
517 Type ans = 1;
518 if (n < 0) {
519 n = -n;
520 x = Type(1)/x;
521 }
522 while (n--) ans *= x;
523 return ans;
524 }
525
527 inline float
529 Pow(float b, float e)
530 {
531 assert( b >= 0.0f && "Pow(float,float): base is negative" );
532 return powf(b,e);
533 }
534
535 inline double
536 Pow(double b, double e)
537 {
538 assert( b >= 0.0 && "Pow(double,double): base is negative" );
539 return std::pow(b,e);
540 }
542
543
544 // ==========> Max <==================
545
547 template<typename Type>
548 inline const Type&
549 Max(const Type& a, const Type& b)
550 {
551 return std::max(a,b);
552 }
553
555 template<typename Type>
556 inline const Type&
557 Max(const Type& a, const Type& b, const Type& c)
558 {
559 return std::max(std::max(a,b), c);
560 }
561
563 template<typename Type>
564 inline const Type&
565 Max(const Type& a, const Type& b, const Type& c, const Type& d)
566 {
567 return std::max(std::max(a,b), std::max(c,d));
568 }
569
571 template<typename Type>
572 inline const Type&
573 Max(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e)
574 {
575 return std::max(std::max(a,b), Max(c,d,e));
576 }
577
579 template<typename Type>
580 inline const Type&
581 Max(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e, const Type& f)
582 {
583 return std::max(Max(a,b,c), Max(d,e,f));
584 }
585
587 template<typename Type>
588 inline const Type&
589 Max(const Type& a, const Type& b, const Type& c, const Type& d,
590 const Type& e, const Type& f, const Type& g)
591 {
592 return std::max(Max(a,b,c,d), Max(e,f,g));
593 }
594
596 template<typename Type>
597 inline const Type&
598 Max(const Type& a, const Type& b, const Type& c, const Type& d,
599 const Type& e, const Type& f, const Type& g, const Type& h)
600 {
601 return std::max(Max(a,b,c,d), Max(e,f,g,h));
602 }
603
604
605 // ==========> Min <==================
606
608 template<typename Type>
609 inline const Type&
610 Min(const Type& a, const Type& b) { return std::min(a, b); }
611
613 template<typename Type>
614 inline const Type&
615 Min(const Type& a, const Type& b, const Type& c) { return std::min(std::min(a, b), c); }
616
618 template<typename Type>
619 inline const Type&
620 Min(const Type& a, const Type& b, const Type& c, const Type& d)
621 {
622 return std::min(std::min(a, b), std::min(c, d));
623 }
624
626 template<typename Type>
627 inline const Type&
628 Min(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e)
629 {
630 return std::min(std::min(a,b), Min(c,d,e));
631 }
632
634 template<typename Type>
635 inline const Type&
636 Min(const Type& a, const Type& b, const Type& c, const Type& d, const Type& e, const Type& f)
637 {
638 return std::min(Min(a,b,c), Min(d,e,f));
639 }
640
642 template<typename Type>
643 inline const Type&
644 Min(const Type& a, const Type& b, const Type& c, const Type& d,
645 const Type& e, const Type& f, const Type& g)
646 {
647 return std::min(Min(a,b,c,d), Min(e,f,g));
648 }
649
651 template<typename Type>
652 inline const Type&
653 Min(const Type& a, const Type& b, const Type& c, const Type& d,
654 const Type& e, const Type& f, const Type& g, const Type& h)
655 {
656 return std::min(Min(a,b,c,d), Min(e,f,g,h));
657 }
658
659
660 // ============> Exp <==================
661
663 template<typename Type>
664 inline Type Exp(const Type& x) { return std::exp(x); }
665
666 // ============> Sin <==================
667
669 inline float Sin(const float& x) { return std::sin(x); }
671
672 inline double Sin(const double& x) { return std::sin(x); }
674
675 // ============> Cos <==================
676
678 inline float Cos(const float& x) { return std::cos(x); }
680
681 inline double Cos(const double& x) { return std::cos(x); }
683
684
686
687
689 template <typename Type>
690 inline int Sign(const Type &x) { return (zeroVal<Type>() < x) - (x < zeroVal<Type>()); }
691
692
695 template <typename Type>
696 inline bool
697 SignChange(const Type& a, const Type& b)
698 {
699 return ( (a<zeroVal<Type>()) ^ (b<zeroVal<Type>()) );
700 }
701
702
705 template <typename Type>
706 inline bool
707 ZeroCrossing(const Type& a, const Type& b)
708 {
709 return a * b <= zeroVal<Type>();
710 }
711
712
714 inline float Sqrt(float x) { return std::sqrt(x); }
716 inline double Sqrt(double x) { return std::sqrt(x); }
717 inline long double Sqrt(long double x) { return std::sqrt(x); }
719
720
722 inline float Cbrt(float x) { return std::cbrt(x); }
724 inline double Cbrt(double x) { return std::cbrt(x); }
725 inline long double Cbrt(long double x) { return std::cbrt(x); }
727
728
730 inline int Mod(int x, int y) { return (x % y); }
732 inline float Mod(float x, float y) { return std::fmod(x, y); }
733 inline double Mod(double x, double y) { return std::fmod(x, y); }
734 inline long double Mod(long double x, long double y) { return std::fmod(x, y); }
735 template<typename Type> inline Type Remainder(Type x, Type y) { return Mod(x, y); }
737
738
740 inline float RoundUp(float x) { return std::ceil(x); }
742 inline double RoundUp(double x) { return std::ceil(x); }
743 inline long double RoundUp(long double x) { return std::ceil(x); }
745 template<typename Type>
747 inline Type
748 RoundUp(Type x, Type base)
749 {
750 Type remainder = Remainder(x, base);
751 return remainder ? x-remainder+base : x;
752 }
753
754
756 inline float RoundDown(float x) { return std::floor(x); }
758 inline double RoundDown(double x) { return std::floor(x); }
759 inline long double RoundDown(long double x) { return std::floor(x); }
761 template<typename Type>
763 inline Type
764 RoundDown(Type x, Type base)
765 {
766 Type remainder = Remainder(x, base);
767 return remainder ? x-remainder : x;
768 }
769
770
772 inline float Round(float x) { return RoundDown(x + 0.5f); }
774 inline double Round(double x) { return RoundDown(x + 0.5); }
775 inline long double Round(long double x) { return RoundDown(x + 0.5l); }
777
778
781 template<typename Type>
782 inline Type
783 EuclideanRemainder(Type x) { return x - RoundDown(x); }
784
785
787 template<typename Type>
788 inline Type
789 IntegerPart(Type x)
790 {
791 return (x > 0 ? RoundDown(x) : RoundUp(x));
792 }
793
795 template<typename Type>
796 inline Type
797 FractionalPart(Type x) { return Mod(x,Type(1)); }
798
799
801 inline int Floor(float x) { return int(RoundDown(x)); }
803 inline int Floor(double x) { return int(RoundDown(x)); }
804 inline int Floor(long double x) { return int(RoundDown(x)); }
806
807
809 inline int Ceil(float x) { return int(RoundUp(x)); }
811 inline int Ceil(double x) { return int(RoundUp(x)); }
812 inline int Ceil(long double x) { return int(RoundUp(x)); }
814
815
817 template<typename Type>
818 inline Type Chop(Type x, Type delta) { return (Abs(x) < delta ? zeroVal<Type>() : x); }
819
820
822 template<typename Type>
823 inline Type
824 Truncate(Type x, unsigned int digits)
825 {
826 Type tenth = Pow(10,digits);
827 return RoundDown(x*tenth+0.5)/tenth;
828 }
829
830
832
833
836 template<typename T>
837 inline auto PrintCast(const T& val) -> typename std::enable_if<!std::is_same<T, int8_t>::value
838 && !std::is_same<T, uint8_t>::value, const T&>::type { return val; }
839 inline int32_t PrintCast(int8_t val) { return int32_t(val); }
840 inline uint32_t PrintCast(uint8_t val) { return uint32_t(val); }
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 using type = typename boost::numeric::conversion_traits<S, T>::supertype;
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) 2012-2018 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::v5_1::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:329
openvdb::v5_1::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:395
openvdb::v5_1::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:690
openvdb::v5_1::math::RandInt::operator()
IntType operator()()
Return a randomly-generated integer in the current range.
Definition: Math.h:211
openvdb::v5_1::math::Exp
Type Exp(const Type &x)
Return ex.
Definition: Math.h:664
openvdb::v5_1::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:653
openvdb::v5_1::math::IntegerPart
Type IntegerPart(Type x)
Return the integer part of x.
Definition: Math.h:789
openvdb::v5_1::math::Truncate
Type Truncate(Type x, unsigned int digits)
Return x truncated to the given number of decimal digits.
Definition: Math.h:824
openvdb::v5_1::zeroVal
T zeroVal()
Return the value of type T that corresponds to zero.
Definition: Math.h:86
openvdb::v5_1::math::negative
std::string negative(const std::string &val)
Return the "negation" of the given string.
Definition: Math.h:112
openvdb::v5_1::math::Pow
double Pow(double b, double e)
Return be.
Definition: Math.h:536
openvdb::v5_1::math::Axis
Axis
Definition: Math.h:856
openvdb::v5_1::math::isZero
bool isZero(const Type &x)
Return true if x is exactly equal to zero.
Definition: Math.h:308
openvdb::v5_1::zeroVal< bool >
bool zeroVal< bool >()
Return the bool value that corresponds to zero.
Definition: Math.h:90
openvdb::v5_1::math::RandInt::setRange
void setRange(IntType imin, IntType imax)
Change the range over which integers are distributed to [imin, imax].
Definition: Math.h:196
openvdb::v5_1::math::YZX_ROTATION
Definition: Math.h:867
openvdb::v5_1::math::Pow4
Type Pow4(Type x)
Return x4.
Definition: Math.h:510
openvdb::v5_1::math::XZY_ROTATION
Definition: Math.h:865
openvdb::v5_1::math::XYZ_ROTATION
Definition: Math.h:864
openvdb::v5_1::math::EuclideanRemainder
Type EuclideanRemainder(Type x)
Definition: Math.h:783
openvdb::v5_1::math::YXZ_ROTATION
Definition: Math.h:866
openvdb::v5_1::math::RandInt::engine
const EngineType & engine() const
Return a const reference to the random number generator.
Definition: Math.h:208
openvdb::v5_1::math::Clamp01
Type Clamp01(Type x)
Return x clamped to [0, 1].
Definition: Math.h:240
openvdb::v5_1::math::ClampTest01
bool ClampTest01(Type &x)
Return true if x is outside [0,1].
Definition: Math.h:246
openvdb::v5_1::math::Clamp
Type Clamp(Type x, Type min, Type max)
Return x clamped to [min, max].
Definition: Math.h:230
openvdb::v5_1::math::PrintCast
uint32_t PrintCast(uint8_t val)
Definition: Math.h:840
openvdb::v5_1::math::Cbrt
long double Cbrt(long double x)
Return the cube root of a floating-point value.
Definition: Math.h:725
openvdb::v5_1::math::Rand01::operator()
FloatType operator()()
Return a uniformly distributed random number in the range [0, 1).
Definition: Math.h:162
openvdb::v5_1::math::Abs
bool Abs(bool b)
Return the absolute value of the given quantity.
Definition: Math.h:291
openvdb::v5_1::math::Tolerance
Tolerance for floating-point comparison.
Definition: Math.h:117
openvdb::v5_1::math::Pow2
Type Pow2(Type x)
Return x2.
Definition: Math.h:502
openvdb::v5_1::math::Delta< float >::value
static float value()
Definition: Math.h:125
openvdb::v5_1::math::Mod
long double Mod(long double x, long double y)
Return the remainder of x / y.
Definition: Math.h:734
openvdb::v5_1::math::FractionalPart
Type FractionalPart(Type x)
Return the fractional part of x.
Definition: Math.h:797
openvdb::v5_1::math::isRelOrApproxEqual
bool isRelOrApproxEqual(const bool &a, const bool &b, const bool &, const bool &)
Definition: Math.h:425
openvdb::v5_1::math::Sqrt
long double Sqrt(long double x)
Return the square root of a floating-point value.
Definition: Math.h:717
openvdb::v5_1::math::Rand01
Simple generator of random numbers over the range [0, 1)
Definition: Math.h:135
openvdb::v5_1::math::Remainder
Type Remainder(Type x, Type y)
Return the remainder of x / y.
Definition: Math.h:735
openvdb::v5_1::math::RandInt::RandInt
RandInt(unsigned int seed, IntType imin, IntType imax)
Initialize the generator.
Definition: Math.h:190
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:136
openvdb::v5_1::math::XZX_ROTATION
Definition: Math.h:870
openvdb::v5_1::math::SmoothUnitStep
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:265
openvdb::v5_1::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:215
openvdb::v5_1::math::RotationOrder
RotationOrder
Definition: Math.h:863
openvdb::v5_1::math::isNegative< bool >
bool isNegative< bool >(const bool &)
Definition: Math.h:341
openvdb::v5_1::math::Rand01::Rand01
Rand01(unsigned int seed)
Initialize the generator.
Definition: Math.h:150
openvdb::v5_1::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:386
openvdb::v5_1::math::isUlpsEqual
bool isUlpsEqual(const float aLeft, const float aRight, const int32_t aUnitsInLastPlace)
Definition: Math.h:476
openvdb::v5_1::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:368
openvdb::v5_1::math::ZYX_ROTATION
Definition: Math.h:869
openvdb
Definition: Exceptions.h:40
openvdb::v5_1::math::isNegative
bool isNegative(const Type &x)
Return true if x is less than zero.
Definition: Math.h:338
openvdb::v5_1::math::Z_AXIS
Definition: Math.h:859
openvdb::v5_1::math::Pow3
Type Pow3(Type x)
Return x3.
Definition: Math.h:506
openvdb::v5_1::math::Delta
Delta for small floating-point offsets.
Definition: Math.h:124
openvdb::v5_1::math::Round
long double Round(long double x)
Return x rounded to the nearest integer.
Definition: Math.h:775
openvdb::v5_1::math::Cos
double Cos(const double &x)
Return cos x.
Definition: Math.h:681
OPENVDB_NO_FP_EQUALITY_WARNING_END
#define OPENVDB_NO_FP_EQUALITY_WARNING_END
Definition: Math.h:75
openvdb::v5_1::math::RoundUp
Type RoundUp(Type x, Type base)
Return x rounded up to the nearest multiple of base.
Definition: Math.h:748
openvdb::v5_1::math::Y_AXIS
Definition: Math.h:858
openvdb::v5_1::math::promote
Definition: Math.h:876
version.h
Library and file format version numbers.
openvdb::v5_1::math::Rand01::Rand01
Rand01(const EngineType &engine)
Initialize the generator.
Definition: Math.h:146
OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
#define OPENVDB_NO_FP_EQUALITY_WARNING_BEGIN
Definition: Math.h:74
openvdb::v5_1::math::Ceil
int Ceil(long double x)
Return the ceiling of x.
Definition: Math.h:812
openvdb::v5_1::tools::composite::min
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:129
openvdb::v5_1::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:707
openvdb::v5_1::math::Inv
Type Inv(Type x)
Return the inverse of x.
Definition: Math.h:849
openvdb::v5_1::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::v5_1::math::ZXY_ROTATION
Definition: Math.h:868
openvdb::v5_1::math::Sin
double Sin(const double &x)
Return sin x.
Definition: Math.h:672
openvdb::v5_1::math::SignChange
bool SignChange(const Type &a, const Type &b)
Return true if a and b have different signs.
Definition: Math.h:697
openvdb::v5_1::math::X_AXIS
Definition: Math.h:857
openvdb::v5_1::math::Rand01< double, RandomGenerator >::ValueType
double ValueType
Definition: Math.h:142
openvdb::v5_1::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:598
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:188
openvdb::v5_1::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::v5_1::math::Rand01::engine
const EngineType & engine() const
Return a const reference to the random number generator.
Definition: Math.h:159
openvdb::v5_1::math::RoundDown
Type RoundDown(Type x, Type base)
Return x rounded down to the nearest multiple of base.
Definition: Math.h:764
openvdb::v5_1::math::Delta< double >::value
static double value()
Definition: Math.h:126
openvdb::v5_1::math::Rand01::setSeed
void setSeed(unsigned int seed)
Set the seed value for the random number generator.
Definition: Math.h:153
openvdb::v5_1::math::RandInt::setSeed
void setSeed(unsigned int seed)
Set the seed value for the random number generator.
Definition: Math.h:202
openvdb::v5_1::math::RandInt::RandInt
RandInt(const EngineType &engine, IntType imin, IntType imax)
Initialize the generator.
Definition: Math.h:182
openvdb::v5_1::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:133
openvdb::v5_1::math::Floor
int Floor(long double x)
Return the floor of x.
Definition: Math.h:804
openvdb::v5_1::math::doubleToInt64
int64_t doubleToInt64(const double aDoubleValue)
Definition: Math.h:444
openvdb::v5_1::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:99
openvdb::v5_1::math::floatToInt32
int32_t floatToInt32(const float aFloatValue)
Definition: Math.h:435
openvdb::v5_1::math::RandInt
Simple random integer generator.
Definition: Math.h:171
openvdb::v5_1::math::ZXZ_ROTATION
Definition: Math.h:871
openvdb::v5_1::math::Tolerance< float >::value
static float value()
Definition: Math.h:118
OPENVDB_EXACT_IS_APPROX_EQUAL
#define OPENVDB_EXACT_IS_APPROX_EQUAL(T)
Definition: Math.h:373
openvdb::v5_1::math::isFinite
bool isFinite(const Type &x)
Return true if x is finite.
Definition: Math.h:351
openvdb::v5_1::math::Tolerance< double >::value
static double value()
Definition: Math.h:119
openvdb::v5_1::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:818
openvdb::v5_1::math::promote::type
typename boost::numeric::conversion_traits< S, T >::supertype type
Definition: Math.h:877
Platform.h