OpenVDB 5.1.0

Vec3.h
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1 //
3 // Copyright (c) 2012-2018 DreamWorks Animation LLC
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30
31 #ifndef OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
32 #define OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
33
34 #include <openvdb/Exceptions.h>
35 #include "Math.h"
36 #include "Tuple.h"
37 #include <algorithm>
38 #include <cmath>
39 #include <type_traits>
40
41
42 namespace openvdb {
43 OPENVDB_USE_VERSION_NAMESPACE
44 namespace OPENVDB_VERSION_NAME {
45 namespace math {
46
47 template<typename T> class Mat3;
48
49 template<typename T>
50 class Vec3: public Tuple<3, T>
51 {
52 public:
53 using value_type = T;
54 using ValueType = T;
55
57 Vec3() {}
58
60 explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
61
63 Vec3(T x, T y, T z)
64 {
65 this->mm[0] = x;
66 this->mm[1] = y;
67 this->mm[2] = z;
68 }
69
71 template <typename Source>
72 Vec3(Source *a)
73 {
74 this->mm[0] = a[0];
75 this->mm[1] = a[1];
76 this->mm[2] = a[2];
77 }
78
81 template<typename Source>
82 explicit Vec3(const Tuple<3, Source> &v)
83 {
84 this->mm[0] = static_cast<T>(v[0]);
85 this->mm[1] = static_cast<T>(v[1]);
86 this->mm[2] = static_cast<T>(v[2]);
87 }
88
92 template<typename Other>
93 explicit Vec3(Other val,
94 typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
95 {
96 this->mm[0] = this->mm[1] = this->mm[2] = static_cast<T>(val);
97 }
98
101 template<typename Other>
102 Vec3(const Vec3<Other>& v)
103 {
104 this->mm[0] = static_cast<T>(v[0]);
105 this->mm[1] = static_cast<T>(v[1]);
106 this->mm[2] = static_cast<T>(v[2]);
107 }
108
110 T& x() { return this->mm[0]; }
111 T& y() { return this->mm[1]; }
112 T& z() { return this->mm[2]; }
113
115 T x() const { return this->mm[0]; }
116 T y() const { return this->mm[1]; }
117 T z() const { return this->mm[2]; }
118
119 T* asPointer() { return this->mm; }
120 const T* asPointer() const { return this->mm; }
121
123 T& operator()(int i) { return this->mm[i]; }
124
126 T operator()(int i) const { return this->mm[i]; }
127
130 const Vec3<T>& init(T x=0, T y=0, T z=0)
131 {
132 this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
133 return *this;
134 }
135
136
138 const Vec3<T>& setZero()
139 {
140 this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
141 return *this;
142 }
143
146 template<typename Source>
147 const Vec3<T>& operator=(const Vec3<Source> &v)
148 {
149 // note: don't static_cast because that suppresses warnings
150 this->mm[0] = v[0];
151 this->mm[1] = v[1];
152 this->mm[2] = v[2];
153
154 return *this;
155 }
156
158 bool eq(const Vec3<T> &v, T eps = static_cast<T>(1.0e-7)) const
159 {
160 return isRelOrApproxEqual(this->mm[0], v.mm[0], eps, eps) &&
161 isRelOrApproxEqual(this->mm[1], v.mm[1], eps, eps) &&
162 isRelOrApproxEqual(this->mm[2], v.mm[2], eps, eps);
163 }
164
165
167 Vec3<T> operator-() const { return Vec3<T>(-this->mm[0], -this->mm[1], -this->mm[2]); }
168
171 template <typename T0, typename T1>
172 const Vec3<T>& add(const Vec3<T0> &v1, const Vec3<T1> &v2)
173 {
174 this->mm[0] = v1[0] + v2[0];
175 this->mm[1] = v1[1] + v2[1];
176 this->mm[2] = v1[2] + v2[2];
177
178 return *this;
179 }
180
183 template <typename T0, typename T1>
184 const Vec3<T>& sub(const Vec3<T0> &v1, const Vec3<T1> &v2)
185 {
186 this->mm[0] = v1[0] - v2[0];
187 this->mm[1] = v1[1] - v2[1];
188 this->mm[2] = v1[2] - v2[2];
189
190 return *this;
191 }
192
195 template <typename T0, typename T1>
196 const Vec3<T>& scale(T0 scale, const Vec3<T1> &v)
197 {
198 this->mm[0] = scale * v[0];
199 this->mm[1] = scale * v[1];
200 this->mm[2] = scale * v[2];
201
202 return *this;
203 }
204
205 template <typename T0, typename T1>
206 const Vec3<T> &div(T0 scale, const Vec3<T1> &v)
207 {
208 this->mm[0] = v[0] / scale;
209 this->mm[1] = v[1] / scale;
210 this->mm[2] = v[2] / scale;
211
212 return *this;
213 }
214
216 T dot(const Vec3<T> &v) const
217 {
218 return
219 this->mm[0]*v.mm[0] +
220 this->mm[1]*v.mm[1] +
221 this->mm[2]*v.mm[2];
222 }
223
225 T length() const
226 {
227 return static_cast<T>(sqrt(double(
228 this->mm[0]*this->mm[0] +
229 this->mm[1]*this->mm[1] +
230 this->mm[2]*this->mm[2])));
231 }
232
233
236 T lengthSqr() const
237 {
238 return
239 this->mm[0]*this->mm[0] +
240 this->mm[1]*this->mm[1] +
241 this->mm[2]*this->mm[2];
242 }
243
245 Vec3<T> cross(const Vec3<T> &v) const
246 {
247 return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1],
248 this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2],
249 this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]);
250 }
251
252
254 const Vec3<T>& cross(const Vec3<T> &v1, const Vec3<T> &v2)
255 {
256 // assert(this!=&v1);
257 // assert(this!=&v2);
258 this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1];
259 this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2];
260 this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0];
261 return *this;
262 }
263
265 template <typename S>
266 const Vec3<T> &operator*=(S scalar)
267 {
268 this->mm[0] = static_cast<T>(this->mm[0] * scalar);
269 this->mm[1] = static_cast<T>(this->mm[1] * scalar);
270 this->mm[2] = static_cast<T>(this->mm[2] * scalar);
271 return *this;
272 }
273
275 template <typename S>
276 const Vec3<T> &operator*=(const Vec3<S> &v1)
277 {
278 this->mm[0] *= v1[0];
279 this->mm[1] *= v1[1];
280 this->mm[2] *= v1[2];
281 return *this;
282 }
283
285 template <typename S>
286 const Vec3<T> &operator/=(S scalar)
287 {
288 this->mm[0] /= scalar;
289 this->mm[1] /= scalar;
290 this->mm[2] /= scalar;
291 return *this;
292 }
293
295 template <typename S>
296 const Vec3<T> &operator/=(const Vec3<S> &v1)
297 {
298 this->mm[0] /= v1[0];
299 this->mm[1] /= v1[1];
300 this->mm[2] /= v1[2];
301 return *this;
302 }
303
305 template <typename S>
306 const Vec3<T> &operator+=(S scalar)
307 {
308 this->mm[0] = static_cast<T>(this->mm[0] + scalar);
309 this->mm[1] = static_cast<T>(this->mm[1] + scalar);
310 this->mm[2] = static_cast<T>(this->mm[2] + scalar);
311 return *this;
312 }
313
315 template <typename S>
316 const Vec3<T> &operator+=(const Vec3<S> &v1)
317 {
318 this->mm[0] += v1[0];
319 this->mm[1] += v1[1];
320 this->mm[2] += v1[2];
321 return *this;
322 }
323
325 template <typename S>
326 const Vec3<T> &operator-=(S scalar)
327 {
328 this->mm[0] -= scalar;
329 this->mm[1] -= scalar;
330 this->mm[2] -= scalar;
331 return *this;
332 }
333
335 template <typename S>
336 const Vec3<T> &operator-=(const Vec3<S> &v1)
337 {
338 this->mm[0] -= v1[0];
339 this->mm[1] -= v1[1];
340 this->mm[2] -= v1[2];
341 return *this;
342 }
343
346 inline const Vec3<T>& exp()
347 {
348 this->mm[0] = std::exp(this->mm[0]);
349 this->mm[1] = std::exp(this->mm[1]);
350 this->mm[2] = std::exp(this->mm[2]);
351 return *this;
352 }
353
356 inline const Vec3<T>& log()
357 {
358 this->mm[0] = std::log(this->mm[0]);
359 this->mm[1] = std::log(this->mm[1]);
360 this->mm[2] = std::log(this->mm[2]);
361 return *this;
362 }
363
365 inline T sum() const
366 {
367 return this->mm[0] + this->mm[1] + this->mm[2];
368 }
369
371 inline T product() const
372 {
373 return this->mm[0] * this->mm[1] * this->mm[2];
374 }
375
377 bool normalize(T eps = T(1.0e-7))
378 {
379 T d = length();
380 if (isApproxEqual(d, T(0), eps)) {
381 return false;
382 }
383 *this *= (T(1) / d);
384 return true;
385 }
386
387
389 Vec3<T> unit(T eps=0) const
390 {
391 T d;
392 return unit(eps, d);
393 }
394
396 Vec3<T> unit(T eps, T& len) const
397 {
398 len = length();
399 if (isApproxEqual(len, T(0), eps)) {
400 OPENVDB_THROW(ArithmeticError, "Normalizing null 3-vector");
401 }
402 return *this / len;
403 }
404
406 Vec3<T> unitSafe() const
407 {
408 T l2 = lengthSqr();
409 return l2 ? *this / static_cast<T>(sqrt(l2)) : Vec3<T>(1, 0 ,0);
410 }
411
412 // Number of cols, rows, elements
413 static unsigned numRows() { return 1; }
414 static unsigned numColumns() { return 3; }
415 static unsigned numElements() { return 3; }
416
419 T component(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
420 {
421 T l = onto.length();
422 if (isApproxEqual(l, T(0), eps)) return 0;
423
424 return dot(onto)*(T(1)/l);
425 }
426
429 Vec3<T> projection(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
430 {
431 T l = onto.lengthSqr();
432 if (isApproxEqual(l, T(0), eps)) return Vec3::zero();
433
434 return onto*(dot(onto)*(T(1)/l));
435 }
436
440 Vec3<T> getArbPerpendicular() const
441 {
442 Vec3<T> u;
443 T l;
444
445 if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
446 // v.x or v.z is the largest magnitude component, swap them
447 l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
448 l = static_cast<T>(T(1)/sqrt(double(l)));
449 u.mm[0] = -this->mm[2]*l;
450 u.mm[1] = T(0);
451 u.mm[2] = +this->mm[0]*l;
452 } else {
453 // W.y or W.z is the largest magnitude component, swap them
454 l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
455 l = static_cast<T>(T(1)/sqrt(double(l)));
456 u.mm[0] = T(0);
457 u.mm[1] = +this->mm[2]*l;
458 u.mm[2] = -this->mm[1]*l;
459 }
460
461 return u;
462 }
463
465 Vec3<T> sorted() const
466 {
467 Vec3<T> r(*this);
468 if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
469 if( r.mm[1] > r.mm[2] ) std::swap(r.mm[1], r.mm[2]);
470 if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
471 return r;
472 }
473
475 Vec3<T> reversed() const
476 {
477 return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]);
478 }
479
481 static Vec3<T> zero() { return Vec3<T>(0, 0, 0); }
482 static Vec3<T> ones() { return Vec3<T>(1, 1, 1); }
483 };
484
485
487 template <typename T0, typename T1>
488 inline bool operator==(const Vec3<T0> &v0, const Vec3<T1> &v1)
489 {
490 return isExactlyEqual(v0[0], v1[0]) && isExactlyEqual(v0[1], v1[1])
491 && isExactlyEqual(v0[2], v1[2]);
492 }
493
495 template <typename T0, typename T1>
496 inline bool operator!=(const Vec3<T0> &v0, const Vec3<T1> &v1) { return !(v0==v1); }
497
499 template <typename S, typename T>
500 inline Vec3<typename promote<S, T>::type> operator*(S scalar, const Vec3<T> &v) { return v*scalar; }
501
503 template <typename S, typename T>
504 inline Vec3<typename promote<S, T>::type> operator*(const Vec3<T> &v, S scalar)
505 {
506 Vec3<typename promote<S, T>::type> result(v);
507 result *= scalar;
508 return result;
509 }
510
512 template <typename T0, typename T1>
513 inline Vec3<typename promote<T0, T1>::type> operator*(const Vec3<T0> &v0, const Vec3<T1> &v1)
514 {
515 Vec3<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1], v0[2] * v1[2]);
516 return result;
517 }
518
519
521 template <typename S, typename T>
522 inline Vec3<typename promote<S, T>::type> operator/(S scalar, const Vec3<T> &v)
523 {
524 return Vec3<typename promote<S, T>::type>(scalar/v[0], scalar/v[1], scalar/v[2]);
525 }
526
528 template <typename S, typename T>
529 inline Vec3<typename promote<S, T>::type> operator/(const Vec3<T> &v, S scalar)
530 {
531 Vec3<typename promote<S, T>::type> result(v);
532 result /= scalar;
533 return result;
534 }
535
537 template <typename T0, typename T1>
538 inline Vec3<typename promote<T0, T1>::type> operator/(const Vec3<T0> &v0, const Vec3<T1> &v1)
539 {
540 Vec3<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1], v0[2] / v1[2]);
541 return result;
542 }
543
545 template <typename T0, typename T1>
546 inline Vec3<typename promote<T0, T1>::type> operator+(const Vec3<T0> &v0, const Vec3<T1> &v1)
547 {
548 Vec3<typename promote<T0, T1>::type> result(v0);
549 result += v1;
550 return result;
551 }
552
554 template <typename S, typename T>
555 inline Vec3<typename promote<S, T>::type> operator+(const Vec3<T> &v, S scalar)
556 {
557 Vec3<typename promote<S, T>::type> result(v);
558 result += scalar;
559 return result;
560 }
561
563 template <typename T0, typename T1>
564 inline Vec3<typename promote<T0, T1>::type> operator-(const Vec3<T0> &v0, const Vec3<T1> &v1)
565 {
566 Vec3<typename promote<T0, T1>::type> result(v0);
567 result -= v1;
568 return result;
569 }
570
572 template <typename S, typename T>
573 inline Vec3<typename promote<S, T>::type> operator-(const Vec3<T> &v, S scalar)
574 {
575 Vec3<typename promote<S, T>::type> result(v);
576 result -= scalar;
577 return result;
578 }
579
582 template <typename T>
583 inline T angle(const Vec3<T> &v1, const Vec3<T> &v2)
584 {
585 Vec3<T> c = v1.cross(v2);
586 return static_cast<T>(atan2(c.length(), v1.dot(v2)));
587 }
588
589 template <typename T>
590 inline bool
591 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b)
592 {
593 return a.eq(b);
594 }
595 template <typename T>
596 inline bool
597 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b, const Vec3<T>& eps)
598 {
599 return isApproxEqual(a.x(), b.x(), eps.x()) &&
600 isApproxEqual(a.y(), b.y(), eps.y()) &&
601 isApproxEqual(a.z(), b.z(), eps.z());
602 }
603
604 template<typename T>
605 inline Vec3<T>
606 Abs(const Vec3<T>& v)
607 {
608 return Vec3<T>(Abs(v[0]), Abs(v[1]), Abs(v[2]));
609 }
610
613 template <typename T>
614 inline void orthonormalize(Vec3<T> &v1, Vec3<T> &v2, Vec3<T> &v3)
615 {
616 // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
617 // orthonormalization produces vectors u0, u1, and u2 as follows,
618 //
619 // u0 = v0/|v0|
620 // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
621 // u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
622 //
623 // where |A| indicates length of vector A and A*B indicates dot
624 // product of vectors A and B.
625
626 // compute u0
627 v1.normalize();
628
629 // compute u1
630 T d0 = v1.dot(v2);
631 v2 -= v1*d0;
632 v2.normalize();
633
634 // compute u2
635 T d1 = v2.dot(v3);
636 d0 = v1.dot(v3);
637 v3 -= v1*d0 + v2*d1;
638 v3.normalize();
639 }
640
645
647 template <typename T>
648 inline Vec3<T> minComponent(const Vec3<T> &v1, const Vec3<T> &v2)
649 {
650 return Vec3<T>(
651 std::min(v1.x(), v2.x()),
652 std::min(v1.y(), v2.y()),
653 std::min(v1.z(), v2.z()));
654 }
655
657 template <typename T>
658 inline Vec3<T> maxComponent(const Vec3<T> &v1, const Vec3<T> &v2)
659 {
660 return Vec3<T>(
661 std::max(v1.x(), v2.x()),
662 std::max(v1.y(), v2.y()),
663 std::max(v1.z(), v2.z()));
664 }
665
668 template <typename T>
669 inline Vec3<T> Exp(Vec3<T> v) { return v.exp(); }
670
673 template <typename T>
674 inline Vec3<T> Log(Vec3<T> v) { return v.log(); }
675
676 using Vec3i = Vec3<int32_t>;
677 using Vec3ui = Vec3<uint32_t>;
678 using Vec3s = Vec3<float>;
679 using Vec3d = Vec3<double>;
680
681 } // namespace math
682 } // namespace OPENVDB_VERSION_NAME
683 } // namespace openvdb
684
685 #endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
686
687 // Copyright (c) 2012-2018 DreamWorks Animation LLC
688 // All rights reserved. This software is distributed under the
689 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
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::operator*
Vec3< typename promote< T0, T1 >::type > operator*(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Multiply corresponding elements of v0 and v1 and return the result.
Definition: Vec3.h:513
openvdb::v5_1::math::unit
MatType unit(const MatType &mat, typename MatType::value_type eps=1.0e-8)
Return a copy of the given matrix with its upper 3×3 rows normalized.
Definition: Mat.h:678
openvdb::v5_1::math::Vec3::operator-=
const Vec3< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec3.h:326
openvdb::v5_1::math::operator/
Vec3< typename promote< T0, T1 >::type > operator/(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Divide corresponding elements of v0 and v1 and return the result.
Definition: Vec3.h:538
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v5_1::math::Vec3::ones
static Vec3< T > ones()
Definition: Vec3.h:482
openvdb::v5_1::math::Vec3::Vec3
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition: Vec3.h:60
openvdb::v5_1::math::angle
T angle(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Vec3.h:583
openvdb::v5_1::math::Vec3::Vec3
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:72
openvdb::v5_1::math::Exp
Vec3< T > Exp(Vec3< T > v)
Return a vector with the exponent applied to each of the components of the input vector.
Definition: Vec3.h:669
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:109
openvdb::v5_1::math::Vec3::operator*=
const Vec3< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition: Vec3.h:266
openvdb::v5_1::math::Vec3::projection
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:429
openvdb::v5_1::math::Vec3::log
const Vec3< T > & log()
Definition: Vec3.h:356
openvdb::v5_1::math::Vec3::length
T length() const
Length of the vector.
Definition: Vec3.h:225
openvdb::v5_1::math::Vec3::operator+=
const Vec3< T > & operator+=(const Vec3< S > &v1)
Add each element of the given vector to the corresponding element of this vector. ...
Definition: Vec3.h:316
openvdb::v5_1::math::Vec3::asPointer
const T * asPointer() const
Definition: Vec3.h:120
openvdb::v5_1::math::Vec3::reversed
Vec3< T > reversed() const
Return the vector (z, y, x)
Definition: Vec3.h:475
openvdb::v5_1::math::Vec3::unit
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:389
openvdb::v5_1::math::Vec3
Definition: Mat.h:197
openvdb::v5_1::math::minComponent
Vec3< T > minComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec3.h:648
openvdb::v5_1::math::Vec3::init
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:130
openvdb::v5_1::math::scale
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:645
openvdb::v5_1::math::Vec3::product
T product() const
Return the product of all the vector components.
Definition: Vec3.h:371
openvdb::v5_1::math::Vec3::operator+=
const Vec3< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec3.h:306
openvdb::v5_1::math::Vec3::exp
const Vec3< T > & exp()
Definition: Vec3.h:346
openvdb::v5_1::math::Vec3::unitSafe
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition: Vec3.h:406
openvdb::v5_1::math::Vec3::numRows
static unsigned numRows()
Definition: Vec3.h:413
openvdb::v5_1::math::Vec3::x
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:115
openvdb::v5_1::math::Vec3::Vec3
Vec3()
Trivial constructor, the vector is NOT initialized.
Definition: Vec3.h:57
openvdb::v5_1::math::Vec3::zero
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:481
openvdb::v5_1::math::Conversion
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:49
openvdb::v5_1::math::operator-
Vec3< typename promote< S, T >::type > operator-(const Vec3< T > &v, S scalar)
Subtract scalar from each element of the given vector and return the result.
Definition: Vec3.h:573
Exceptions.h
openvdb::v5_1::math::Vec3::add
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:172
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:136
openvdb::v5_1::math::Vec3< Real >::value_type
Real value_type
Definition: Vec3.h:53
openvdb::v5_1::math::Vec3::operator-
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:167
openvdb::v5_1::math::Vec3::dot
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:216
openvdb::v5_1::math::operator!=
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:496
openvdb::v5_1::math::Vec3::operator()
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:123
openvdb::v5_1::math::Vec3::numColumns
static unsigned numColumns()
Definition: Vec3.h:414
openvdb::v5_1::math::Vec3::scale
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:196
openvdb::v5_1::math::Vec3::component
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:419
openvdb::v5_1::ArithmeticError
Definition: Exceptions.h:83
openvdb::v5_1::math::Vec3::operator/=
const Vec3< T > & operator/=(const Vec3< S > &v1)
Divide each element of this vector by the corresponding element of the given vector.
Definition: Vec3.h:296
openvdb::v5_1::math::Vec3< Real >::ValueType
Real ValueType
Definition: Vec3.h:54
openvdb::v5_1::math::Abs
Vec3< T > Abs(const Vec3< T > &v)
Definition: Vec3.h:606
openvdb::v5_1::math::Vec3::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:110
openvdb
Definition: Exceptions.h:40
openvdb::v5_1::math::Vec3::normalize
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:377
openvdb::v5_1::math::Vec3::numElements
static unsigned numElements()
Definition: Vec3.h:415
openvdb::v5_1::math::operator==
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:488
openvdb::v5_1::math::Vec3::sub
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:184
openvdb::v5_1::math::Vec3::y
T y() const
Definition: Vec3.h:116
openvdb::v5_1::math::Tuple
Definition: Tuple.h:55
openvdb::v5_1::math::Vec3::sum
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:365
openvdb::v5_1::math::Vec3::z
T z() const
Definition: Vec3.h:117
openvdb::v5_1::math::Vec3::sorted
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition: Vec3.h:465
openvdb::v5_1::math::Vec3::Vec3
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:102
openvdb::v5_1::math::Vec3::Vec3
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition: Vec3.h:82
openvdb::v5_1::math::Vec3::cross
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:245
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::Vec3::operator=
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:147
openvdb::v5_1::math::Vec3::cross
const Vec3< T > & cross(const Vec3< T > &v1, const Vec3< T > &v2)
this = v1 cross v2, v1 and v2 must be distinct objects than "this"
Definition: Vec3.h:254
openvdb::v5_1::math::operator+
Vec3< typename promote< S, T >::type > operator+(const Vec3< T > &v, S scalar)
Add scalar to each element of the given vector and return the result.
Definition: Vec3.h:555
openvdb::v5_1::math::Vec3::Vec3
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:63
Tuple.h
openvdb::v5_1::math::isRelOrApproxEqual
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:405
openvdb::v5_1::math::Vec3::asPointer
T * asPointer()
Definition: Vec3.h:119
openvdb::v5_1::math::maxComponent
Vec3< T > maxComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec3.h:658
openvdb::v5_1::math::Vec3::operator-=
const Vec3< T > & operator-=(const Vec3< S > &v1)
Subtract each element of the given vector from the corresponding element of this vector.
Definition: Vec3.h:336
openvdb::v5_1::math::Log
Vec3< T > Log(Vec3< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec3.h:674
openvdb::v5_1::math::Vec3::eq
bool eq(const Vec3< T > &v, T eps=static_cast< T >(1.0e-7)) const
Test if "this" vector is equivalent to vector v with tolerance of eps.
Definition: Vec3.h:158
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:188
openvdb::v5_1::math::Vec3::Vec3
Vec3(Other val, typename std::enable_if< std::is_arithmetic< Other >::value, Conversion >::type=Conversion{})
Construct a vector all of whose components have the given value, which may be of an arithmetic type d...
Definition: Vec3.h:93
openvdb::v5_1::math::orthonormalize
void orthonormalize(Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)
Definition: Vec3.h:614
openvdb::v5_1::math::Vec3::getArbPerpendicular
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:440
openvdb::v5_1::math::Vec3::div
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:206
openvdb::v5_1::math::Vec3::unit
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:396
openvdb::v5_1::math::isApproxEqual
bool isApproxEqual(const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)
Definition: Vec3.h:597
openvdb::v5_1::math::Vec3::lengthSqr
T lengthSqr() const
Definition: Vec3.h:236
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::Vec3::operator/=
const Vec3< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec3.h:286
openvdb::v5_1::math::Vec3::setZero
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:138
openvdb::v5_1::math::Vec3::operator*=
const Vec3< T > & operator*=(const Vec3< S > &v1)
Multiply each element of this vector by the corresponding element of the given vector.
Definition: Vec3.h:276
openvdb::v5_1::math::Vec3::operator()
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:126
openvdb::v5_1::math::Vec3::z
T & z()
Definition: Vec3.h:112
openvdb::v5_1::math::Vec3::y
T & y()
Definition: Vec3.h:111