OpenVDB: Vec3.h Source File

OpenVDB 4.0.2

Vec3.h
Go to the documentation of this file.
1 //
3 // Copyright (c) 2012-2017 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
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 <cmath>
38 #include <type_traits>
39
40
41 namespace openvdb {
42 OPENVDB_USE_VERSION_NAMESPACE
43 namespace OPENVDB_VERSION_NAME {
44 namespace math {
45
46 template<typename T> class Mat3;
47
48 template<typename T>
49 class Vec3: public Tuple<3, T>
50 {
51 public:
52 typedef T value_type;
53 typedef T ValueType;
54
56 Vec3() {}
57
59 explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
60
62 Vec3(T x, T y, T z)
63 {
64 this->mm[0] = x;
65 this->mm[1] = y;
66 this->mm[2] = z;
67 }
68
70 template <typename Source>
71 Vec3(Source *a)
72 {
73 this->mm[0] = a[0];
74 this->mm[1] = a[1];
75 this->mm[2] = a[2];
76 }
77
80 template<typename Source>
81 explicit Vec3(const Tuple<3, Source> &v)
82 {
83 this->mm[0] = static_cast<T>(v[0]);
84 this->mm[1] = static_cast<T>(v[1]);
85 this->mm[2] = static_cast<T>(v[2]);
86 }
87
91 template<typename Other>
92 explicit Vec3(Other val,
93 typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
94 {
95 this->mm[0] = this->mm[1] = this->mm[2] = static_cast<T>(val);
96 }
97
100 template<typename Other>
101 Vec3(const Vec3<Other>& v)
102 {
103 this->mm[0] = static_cast<T>(v[0]);
104 this->mm[1] = static_cast<T>(v[1]);
105 this->mm[2] = static_cast<T>(v[2]);
106 }
107
109 T& x() { return this->mm[0]; }
110 T& y() { return this->mm[1]; }
111 T& z() { return this->mm[2]; }
112
114 T x() const { return this->mm[0]; }
115 T y() const { return this->mm[1]; }
116 T z() const { return this->mm[2]; }
117
118 T* asPointer() { return this->mm; }
119 const T* asPointer() const { return this->mm; }
120
122 T& operator()(int i) { return this->mm[i]; }
123
125 T operator()(int i) const { return this->mm[i]; }
126
129 const Vec3<T>& init(T x=0, T y=0, T z=0)
130 {
131 this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
132 return *this;
133 }
134
135
137 const Vec3<T>& setZero()
138 {
139 this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
140 return *this;
141 }
142
145 template<typename Source>
146 const Vec3<T>& operator=(const Vec3<Source> &v)
147 {
148 // note: don't static_cast because that suppresses warnings
149 this->mm[0] = v[0];
150 this->mm[1] = v[1];
151 this->mm[2] = v[2];
152
153 return *this;
154 }
155
157 bool eq(const Vec3<T> &v, T eps = static_cast<T>(1.0e-7)) const
158 {
159 return isRelOrApproxEqual(this->mm[0], v.mm[0], eps, eps) &&
160 isRelOrApproxEqual(this->mm[1], v.mm[1], eps, eps) &&
161 isRelOrApproxEqual(this->mm[2], v.mm[2], eps, eps);
162 }
163
164
166 Vec3<T> operator-() const { return Vec3<T>(-this->mm[0], -this->mm[1], -this->mm[2]); }
167
170 template <typename T0, typename T1>
171 const Vec3<T>& add(const Vec3<T0> &v1, const Vec3<T1> &v2)
172 {
173 this->mm[0] = v1[0] + v2[0];
174 this->mm[1] = v1[1] + v2[1];
175 this->mm[2] = v1[2] + v2[2];
176
177 return *this;
178 }
179
182 template <typename T0, typename T1>
183 const Vec3<T>& sub(const Vec3<T0> &v1, const Vec3<T1> &v2)
184 {
185 this->mm[0] = v1[0] - v2[0];
186 this->mm[1] = v1[1] - v2[1];
187 this->mm[2] = v1[2] - v2[2];
188
189 return *this;
190 }
191
194 template <typename T0, typename T1>
195 const Vec3<T>& scale(T0 scale, const Vec3<T1> &v)
196 {
197 this->mm[0] = scale * v[0];
198 this->mm[1] = scale * v[1];
199 this->mm[2] = scale * v[2];
200
201 return *this;
202 }
203
204 template <typename T0, typename T1>
205 const Vec3<T> &div(T0 scale, const Vec3<T1> &v)
206 {
207 this->mm[0] = v[0] / scale;
208 this->mm[1] = v[1] / scale;
209 this->mm[2] = v[2] / scale;
210
211 return *this;
212 }
213
215 T dot(const Vec3<T> &v) const
216 {
217 return
218 this->mm[0]*v.mm[0] +
219 this->mm[1]*v.mm[1] +
220 this->mm[2]*v.mm[2];
221 }
222
224 T length() const
225 {
226 return static_cast<T>(sqrt(double(
227 this->mm[0]*this->mm[0] +
228 this->mm[1]*this->mm[1] +
229 this->mm[2]*this->mm[2])));
230 }
231
232
235 T lengthSqr() const
236 {
237 return
238 this->mm[0]*this->mm[0] +
239 this->mm[1]*this->mm[1] +
240 this->mm[2]*this->mm[2];
241 }
242
244 Vec3<T> cross(const Vec3<T> &v) const
245 {
246 return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1],
247 this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2],
248 this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]);
249 }
250
251
253 const Vec3<T>& cross(const Vec3<T> &v1, const Vec3<T> &v2)
254 {
255 // assert(this!=&v1);
256 // assert(this!=&v2);
257 this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1];
258 this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2];
259 this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0];
260 return *this;
261 }
262
264 template <typename S>
265 const Vec3<T> &operator*=(S scalar)
266 {
267 this->mm[0] = static_cast<T>(this->mm[0] * scalar);
268 this->mm[1] = static_cast<T>(this->mm[1] * scalar);
269 this->mm[2] = static_cast<T>(this->mm[2] * scalar);
270 return *this;
271 }
272
274 template <typename S>
275 const Vec3<T> &operator*=(const Vec3<S> &v1)
276 {
277 this->mm[0] *= v1[0];
278 this->mm[1] *= v1[1];
279 this->mm[2] *= v1[2];
280 return *this;
281 }
282
284 template <typename S>
285 const Vec3<T> &operator/=(S scalar)
286 {
287 this->mm[0] /= scalar;
288 this->mm[1] /= scalar;
289 this->mm[2] /= scalar;
290 return *this;
291 }
292
294 template <typename S>
295 const Vec3<T> &operator/=(const Vec3<S> &v1)
296 {
297 this->mm[0] /= v1[0];
298 this->mm[1] /= v1[1];
299 this->mm[2] /= v1[2];
300 return *this;
301 }
302
304 template <typename S>
305 const Vec3<T> &operator+=(S scalar)
306 {
307 this->mm[0] = static_cast<T>(this->mm[0] + scalar);
308 this->mm[1] = static_cast<T>(this->mm[1] + scalar);
309 this->mm[2] = static_cast<T>(this->mm[2] + scalar);
310 return *this;
311 }
312
314 template <typename S>
315 const Vec3<T> &operator+=(const Vec3<S> &v1)
316 {
317 this->mm[0] += v1[0];
318 this->mm[1] += v1[1];
319 this->mm[2] += v1[2];
320 return *this;
321 }
322
324 template <typename S>
325 const Vec3<T> &operator-=(S scalar)
326 {
327 this->mm[0] -= scalar;
328 this->mm[1] -= scalar;
329 this->mm[2] -= scalar;
330 return *this;
331 }
332
334 template <typename S>
335 const Vec3<T> &operator-=(const Vec3<S> &v1)
336 {
337 this->mm[0] -= v1[0];
338 this->mm[1] -= v1[1];
339 this->mm[2] -= v1[2];
340 return *this;
341 }
342
345 inline const Vec3<T>& exp()
346 {
347 this->mm[0] = std::exp(this->mm[0]);
348 this->mm[1] = std::exp(this->mm[1]);
349 this->mm[2] = std::exp(this->mm[2]);
350 return *this;
351 }
352
355 inline const Vec3<T>& log()
356 {
357 this->mm[0] = std::log(this->mm[0]);
358 this->mm[1] = std::log(this->mm[1]);
359 this->mm[2] = std::log(this->mm[2]);
360 return *this;
361 }
362
364 inline T sum() const
365 {
366 return this->mm[0] + this->mm[1] + this->mm[2];
367 }
368
370 inline T product() const
371 {
372 return this->mm[0] * this->mm[1] * this->mm[2];
373 }
374
376 bool normalize(T eps = T(1.0e-7))
377 {
378 T d = length();
379 if (isApproxEqual(d, T(0), eps)) {
380 return false;
381 }
382 *this *= (T(1) / d);
383 return true;
384 }
385
386
388 Vec3<T> unit(T eps=0) const
389 {
390 T d;
391 return unit(eps, d);
392 }
393
395 Vec3<T> unit(T eps, T& len) const
396 {
397 len = length();
398 if (isApproxEqual(len, T(0), eps)) {
399 OPENVDB_THROW(ArithmeticError, "Normalizing null 3-vector");
400 }
401 return *this / len;
402 }
403
405 Vec3<T> unitSafe() const
406 {
407 T l2 = lengthSqr();
408 return l2 ? *this / static_cast<T>(sqrt(l2)) : Vec3<T>(1, 0 ,0);
409 }
410
411 // Number of cols, rows, elements
412 static unsigned numRows() { return 1; }
413 static unsigned numColumns() { return 3; }
414 static unsigned numElements() { return 3; }
415
418 T component(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
419 {
420 T l = onto.length();
421 if (isApproxEqual(l, T(0), eps)) return 0;
422
423 return dot(onto)*(T(1)/l);
424 }
425
428 Vec3<T> projection(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
429 {
430 T l = onto.lengthSqr();
431 if (isApproxEqual(l, T(0), eps)) return Vec3::zero();
432
433 return onto*(dot(onto)*(T(1)/l));
434 }
435
439 Vec3<T> getArbPerpendicular() const
440 {
441 Vec3<T> u;
442 T l;
443
444 if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
445 // v.x or v.z is the largest magnitude component, swap them
446 l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
447 l = static_cast<T>(T(1)/sqrt(double(l)));
448 u.mm[0] = -this->mm[2]*l;
449 u.mm[1] = T(0);
450 u.mm[2] = +this->mm[0]*l;
451 } else {
452 // W.y or W.z is the largest magnitude component, swap them
453 l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
454 l = static_cast<T>(T(1)/sqrt(double(l)));
455 u.mm[0] = T(0);
456 u.mm[1] = +this->mm[2]*l;
457 u.mm[2] = -this->mm[1]*l;
458 }
459
460 return u;
461 }
462
464 Vec3<T> sorted() const
465 {
466 Vec3<T> r(*this);
467 if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
468 if( r.mm[1] > r.mm[2] ) std::swap(r.mm[1], r.mm[2]);
469 if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
470 return r;
471 }
472
474 Vec3<T> reversed() const
475 {
476 return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]);
477 }
478
480 static Vec3<T> zero() { return Vec3<T>(0, 0, 0); }
481 static Vec3<T> ones() { return Vec3<T>(1, 1, 1); }
482 };
483
484
486 template <typename T0, typename T1>
487 inline bool operator==(const Vec3<T0> &v0, const Vec3<T1> &v1)
488 {
489 return isExactlyEqual(v0[0], v1[0]) && isExactlyEqual(v0[1], v1[1])
490 && isExactlyEqual(v0[2], v1[2]);
491 }
492
494 template <typename T0, typename T1>
495 inline bool operator!=(const Vec3<T0> &v0, const Vec3<T1> &v1) { return !(v0==v1); }
496
498 template <typename S, typename T>
499 inline Vec3<typename promote<S, T>::type> operator*(S scalar, const Vec3<T> &v) { return v*scalar; }
500
502 template <typename S, typename T>
503 inline Vec3<typename promote<S, T>::type> operator*(const Vec3<T> &v, S scalar)
504 {
505 Vec3<typename promote<S, T>::type> result(v);
506 result *= scalar;
507 return result;
508 }
509
511 template <typename T0, typename T1>
512 inline Vec3<typename promote<T0, T1>::type> operator*(const Vec3<T0> &v0, const Vec3<T1> &v1)
513 {
514 Vec3<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1], v0[2] * v1[2]);
515 return result;
516 }
517
518
520 template <typename S, typename T>
521 inline Vec3<typename promote<S, T>::type> operator/(S scalar, const Vec3<T> &v)
522 {
523 return Vec3<typename promote<S, T>::type>(scalar/v[0], scalar/v[1], scalar/v[2]);
524 }
525
527 template <typename S, typename T>
528 inline Vec3<typename promote<S, T>::type> operator/(const Vec3<T> &v, S scalar)
529 {
530 Vec3<typename promote<S, T>::type> result(v);
531 result /= scalar;
532 return result;
533 }
534
536 template <typename T0, typename T1>
537 inline Vec3<typename promote<T0, T1>::type> operator/(const Vec3<T0> &v0, const Vec3<T1> &v1)
538 {
539 Vec3<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1], v0[2] / v1[2]);
540 return result;
541 }
542
544 template <typename T0, typename T1>
545 inline Vec3<typename promote<T0, T1>::type> operator+(const Vec3<T0> &v0, const Vec3<T1> &v1)
546 {
547 Vec3<typename promote<T0, T1>::type> result(v0);
548 result += v1;
549 return result;
550 }
551
553 template <typename S, typename T>
554 inline Vec3<typename promote<S, T>::type> operator+(const Vec3<T> &v, S scalar)
555 {
556 Vec3<typename promote<S, T>::type> result(v);
557 result += scalar;
558 return result;
559 }
560
562 template <typename T0, typename T1>
563 inline Vec3<typename promote<T0, T1>::type> operator-(const Vec3<T0> &v0, const Vec3<T1> &v1)
564 {
565 Vec3<typename promote<T0, T1>::type> result(v0);
566 result -= v1;
567 return result;
568 }
569
571 template <typename S, typename T>
572 inline Vec3<typename promote<S, T>::type> operator-(const Vec3<T> &v, S scalar)
573 {
574 Vec3<typename promote<S, T>::type> result(v);
575 result -= scalar;
576 return result;
577 }
578
581 template <typename T>
582 inline T angle(const Vec3<T> &v1, const Vec3<T> &v2)
583 {
584 Vec3<T> c = v1.cross(v2);
585 return static_cast<T>(atan2(c.length(), v1.dot(v2)));
586 }
587
588 template <typename T>
589 inline bool
590 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b)
591 {
592 return a.eq(b);
593 }
594 template <typename T>
595 inline bool
596 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b, const Vec3<T>& eps)
597 {
598 return isApproxEqual(a.x(), b.x(), eps.x()) &&
599 isApproxEqual(a.y(), b.y(), eps.y()) &&
600 isApproxEqual(a.z(), b.z(), eps.z());
601 }
602
603 template<typename T>
604 inline Vec3<T>
605 Abs(const Vec3<T>& v)
606 {
607 return Vec3<T>(Abs(v[0]), Abs(v[1]), Abs(v[2]));
608 }
609
612 template <typename T>
613 inline void orthonormalize(Vec3<T> &v1, Vec3<T> &v2, Vec3<T> &v3)
614 {
615 // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
616 // orthonormalization produces vectors u0, u1, and u2 as follows,
617 //
618 // u0 = v0/|v0|
619 // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
620 // u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
621 //
622 // where |A| indicates length of vector A and A*B indicates dot
623 // product of vectors A and B.
624
625 // compute u0
626 v1.normalize();
627
628 // compute u1
629 T d0 = v1.dot(v2);
630 v2 -= v1*d0;
631 v2.normalize();
632
633 // compute u2
634 T d1 = v2.dot(v3);
635 d0 = v1.dot(v3);
636 v3 -= v1*d0 + v2*d1;
637 v3.normalize();
638 }
639
644
646 template <typename T>
647 inline Vec3<T> minComponent(const Vec3<T> &v1, const Vec3<T> &v2)
648 {
649 return Vec3<T>(
650 std::min(v1.x(), v2.x()),
651 std::min(v1.y(), v2.y()),
652 std::min(v1.z(), v2.z()));
653 }
654
656 template <typename T>
657 inline Vec3<T> maxComponent(const Vec3<T> &v1, const Vec3<T> &v2)
658 {
659 return Vec3<T>(
660 std::max(v1.x(), v2.x()),
661 std::max(v1.y(), v2.y()),
662 std::max(v1.z(), v2.z()));
663 }
664
667 template <typename T>
668 inline Vec3<T> Exp(Vec3<T> v) { return v.exp(); }
669
672 template <typename T>
673 inline Vec3<T> Log(Vec3<T> v) { return v.log(); }
674
675 typedef Vec3<int32_t> Vec3i;
676 typedef Vec3<uint32_t> Vec3ui;
677 typedef Vec3<float> Vec3s;
678 typedef Vec3<double> Vec3d;
679
680 } // namespace math
681 } // namespace OPENVDB_VERSION_NAME
682 } // namespace openvdb
683
684 #endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
685
686 // Copyright (c) 2012-2017 DreamWorks Animation LLC
687 // All rights reserved. This software is distributed under the
688 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v4_0_2::math::operator-
Vec3< typename promote< S, T >::type > operator-(const Vec3< T > &v, S scalar)
Returns V, where for .
Definition: Vec3.h:572
openvdb::v4_0_2::math::Vec3::add
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:171
openvdb::v4_0_2::math::angle
T angle(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Vec3.h:582
openvdb::v4_0_2::math::Vec3::Vec3
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:71
openvdb::v4_0_2::math::Vec3::Vec3
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:101
openvdb::v4_0_2::math::Conversion
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:48
openvdb::v4_0_2::math::Vec3::log
const Vec3< T > & log()
Definition: Vec3.h:355
openvdb::v4_0_2::math::operator!=
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:495
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v4_0_2::math::Vec3::dot
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:215
openvdb::v4_0_2::math::operator*
Vec3< typename promote< T0, T1 >::type > operator*(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Returns V, where for .
Definition: Vec3.h:512
openvdb::v4_0_2::math::Vec3::z
T & z()
Definition: Vec3.h:111
openvdb::v4_0_2::math::Vec3::numElements
static unsigned numElements()
Definition: Vec3.h:414
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:101
openvdb::v4_0_2::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:391
openvdb::v4_0_2::math::Vec3::projection
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:428
openvdb::v4_0_2::math::Vec3::numColumns
static unsigned numColumns()
Definition: Vec3.h:413
i
tbb::atomic< Index32 > i
Definition: LeafBuffer.h:71
openvdb::v4_0_2::ArithmeticError
Definition: Exceptions.h:82
openvdb::v4_0_2::math::Vec3::operator+=
const Vec3< T > & operator+=(const Vec3< S > &v1)
Returns v0, where for .
Definition: Vec3.h:315
openvdb::v4_0_2::math::isRelOrApproxEqual
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:401
openvdb::v4_0_2::math::Vec3::value_type
T value_type
Definition: Vec3.h:52
openvdb::v4_0_2::math::orthonormalize
void orthonormalize(Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)
Definition: Vec3.h:613
openvdb::v4_0_2::math::Vec3::unit
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:388
openvdb::v4_0_2::math::Vec3::ones
static Vec3< T > ones()
Definition: Vec3.h:481
openvdb::v4_0_2::math::Vec3i
Vec3< int32_t > Vec3i
Definition: Vec3.h:675
openvdb::v4_0_2::math::Vec3
Definition: Mat.h:195
openvdb::v4_0_2::math::Vec3::numRows
static unsigned numRows()
Definition: Vec3.h:412
openvdb::v4_0_2::math::Vec3s
Vec3< float > Vec3s
Definition: Vec3.h:677
openvdb::v4_0_2::math::Vec3::operator/=
const Vec3< T > & operator/=(S scalar)
Returns v, where for .
Definition: Vec3.h:285
openvdb::v4_0_2::math::scale
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:643
openvdb::v4_0_2::math::Vec3::sub
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:183
openvdb::v4_0_2::math::Vec3::ValueType
T ValueType
Definition: Vec3.h:53
openvdb::v4_0_2::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:133
openvdb::v4_0_2::tools::composite::min
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:129
openvdb::v4_0_2::math::isApproxEqual
bool isApproxEqual(const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)
Definition: Vec3.h:596
openvdb::v4_0_2::math::Vec3::asPointer
T * asPointer()
Definition: Vec3.h:118
Exceptions.h
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
Definition: version.h:43
openvdb::v4_0_2::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:668
openvdb::v4_0_2::math::Vec3::reversed
Vec3< T > reversed() const
Return the vector (z, y, x)
Definition: Vec3.h:474
openvdb::v4_0_2::math::Vec3ui
Vec3< uint32_t > Vec3ui
Definition: Vec3.h:676
openvdb::v4_0_2::math::Vec3::x
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:114
openvdb::v4_0_2::math::Vec3::div
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:205
openvdb::v4_0_2::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:81
openvdb::v4_0_2::math::Vec3::Vec3
Vec3()
Trivial constructor, the vector is NOT initialized.
Definition: Vec3.h:56
openvdb::v4_0_2::math::Vec3::operator*=
const Vec3< T > & operator*=(const Vec3< S > &v1)
Returns v0, where for .
Definition: Vec3.h:275
openvdb::v4_0_2::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:673
openvdb::v4_0_2::math::Vec3::normalize
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:376
openvdb
Definition: Exceptions.h:39
openvdb::v4_0_2::math::Vec3::zero
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:480
openvdb::v4_0_2::math::operator==
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:487
openvdb::v4_0_2::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:253
openvdb::v4_0_2::math::Vec3::cross
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:244
openvdb::v4_0_2::math::Vec3::component
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:418
openvdb::v4_0_2::math::Vec3::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:109
openvdb::v4_0_2::math::Vec3d
Vec3< double > Vec3d
Definition: Vec3.h:678
openvdb::v4_0_2::math::Vec3::operator()
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:122
openvdb::v4_0_2::math::Vec3::y
T & y()
Definition: Vec3.h:110
openvdb::v4_0_2::math::Vec3::sum
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:364
openvdb::v4_0_2::math::operator/
Vec3< typename promote< T0, T1 >::type > operator/(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Returns V, where for .
Definition: Vec3.h:537
openvdb::v4_0_2::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:157
openvdb::v4_0_2::math::Vec3::init
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:129
openvdb::v4_0_2::math::Vec3::getArbPerpendicular
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:439
openvdb::v4_0_2::math::Vec3::length
T length() const
Length of the vector.
Definition: Vec3.h:224
openvdb::v4_0_2::math::Vec3::setZero
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:137
openvdb::v4_0_2::math::Vec3::sorted
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition: Vec3.h:464
openvdb::v4_0_2::math::Vec3::z
T z() const
Definition: Vec3.h:116
openvdb::v4_0_2::math::Vec3::asPointer
const T * asPointer() const
Definition: Vec3.h:119
openvdb::v4_0_2::math::Vec3::operator-
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:166
openvdb::v4_0_2::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 3x3 rows normalized.
Definition: Mat.h:676
openvdb::v4_0_2::math::Vec3::product
T product() const
Return the product of all the vector components.
Definition: Vec3.h:370
openvdb::v4_0_2::math::Vec3::operator()
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:125
openvdb::v4_0_2::math::Vec3::operator=
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:146
openvdb::v4_0_2::math::Vec3::exp
const Vec3< T > & exp()
Definition: Vec3.h:345
Tuple.h
openvdb::v4_0_2::math::Vec3::operator-=
const Vec3< T > & operator-=(const Vec3< S > &v1)
Returns v0, where for .
Definition: Vec3.h:335
openvdb::v4_0_2::math::Abs
Vec3< T > Abs(const Vec3< T > &v)
Definition: Vec3.h:605
openvdb::v4_0_2::math::Tuple
Definition: Tuple.h:54
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:71
openvdb::v4_0_2::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:92
openvdb::v4_0_2::math::Vec3::Vec3
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition: Vec3.h:59
openvdb::v4_0_2::math::Vec3::operator+=
const Vec3< T > & operator+=(S scalar)
Returns v, where for .
Definition: Vec3.h:305
openvdb::v4_0_2::math::minComponent
Vec3< T > minComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec3.h:647
openvdb::v4_0_2::math::Vec3::scale
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:195
openvdb::v4_0_2::math::Vec3::y
T y() const
Definition: Vec3.h:115
openvdb::v4_0_2::math::Vec3::Vec3
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:62
openvdb::v4_0_2::math::Vec3::lengthSqr
T lengthSqr() const
Definition: Vec3.h:235
openvdb::v4_0_2::math::Vec3::operator/=
const Vec3< T > & operator/=(const Vec3< S > &v1)
Returns v0, where for .
Definition: Vec3.h:295
openvdb::v4_0_2::math::Vec3::operator*=
const Vec3< T > & operator*=(S scalar)
Returns v, where for .
Definition: Vec3.h:265
openvdb::v4_0_2::math::Vec3::unitSafe
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition: Vec3.h:405
openvdb::v4_0_2::math::Vec3::operator-=
const Vec3< T > & operator-=(S scalar)
Returns v, where for .
Definition: Vec3.h:325
openvdb::v4_0_2::math::maxComponent
Vec3< T > maxComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec3.h:657
openvdb::v4_0_2::math::operator+
Vec3< typename promote< S, T >::type > operator+(const Vec3< T > &v, S scalar)
Returns V, where for .
Definition: Vec3.h:554
openvdb::v4_0_2::math::Vec3::unit
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:395