OpenVDB  3.2.0
Vec3.h
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30 
31 #ifndef OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
32 #define OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
33 
34 #include <cmath>
35 #include <openvdb/Exceptions.h>
36 #include "Math.h"
37 #include "Tuple.h"
38 
39 namespace openvdb {
41 namespace OPENVDB_VERSION_NAME {
42 namespace math {
43 
44 template<typename T> class Mat3;
45 
46 template<typename T>
47 class Vec3: public Tuple<3, T>
48 {
49 public:
50  typedef T value_type;
51  typedef T ValueType;
52 
54  Vec3() {}
55 
57  explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
58 
60  Vec3(T x, T y, T z)
61  {
62  this->mm[0] = x;
63  this->mm[1] = y;
64  this->mm[2] = z;
65  }
66 
68  template <typename Source>
69  Vec3(Source *a)
70  {
71  this->mm[0] = a[0];
72  this->mm[1] = a[1];
73  this->mm[2] = a[2];
74  }
75 
78  template<typename Source>
79  explicit Vec3(const Tuple<3, Source> &v)
80  {
81  this->mm[0] = static_cast<T>(v[0]);
82  this->mm[1] = static_cast<T>(v[1]);
83  this->mm[2] = static_cast<T>(v[2]);
84  }
85 
88  template<typename Other>
89  Vec3(const Vec3<Other>& v)
90  {
91  this->mm[0] = static_cast<T>(v[0]);
92  this->mm[1] = static_cast<T>(v[1]);
93  this->mm[2] = static_cast<T>(v[2]);
94  }
95 
97  T& x() { return this->mm[0]; }
98  T& y() { return this->mm[1]; }
99  T& z() { return this->mm[2]; }
100 
102  T x() const { return this->mm[0]; }
103  T y() const { return this->mm[1]; }
104  T z() const { return this->mm[2]; }
105 
106  T* asPointer() { return this->mm; }
107  const T* asPointer() const { return this->mm; }
108 
110  T& operator()(int i) { return this->mm[i]; }
111 
113  T operator()(int i) const { return this->mm[i]; }
114 
117  const Vec3<T>& init(T x=0, T y=0, T z=0)
118  {
119  this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
120  return *this;
121  }
122 
123 
125  const Vec3<T>& setZero()
126  {
127  this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
128  return *this;
129  }
130 
133  template<typename Source>
134  const Vec3<T>& operator=(const Vec3<Source> &v)
135  {
136  // note: don't static_cast because that suppresses warnings
137  this->mm[0] = v[0];
138  this->mm[1] = v[1];
139  this->mm[2] = v[2];
140 
141  return *this;
142  }
143 
145  bool eq(const Vec3<T> &v, T eps = static_cast<T>(1.0e-7)) const
146  {
147  return isRelOrApproxEqual(this->mm[0], v.mm[0], eps, eps) &&
148  isRelOrApproxEqual(this->mm[1], v.mm[1], eps, eps) &&
149  isRelOrApproxEqual(this->mm[2], v.mm[2], eps, eps);
150  }
151 
152 
154  Vec3<T> operator-() const { return Vec3<T>(-this->mm[0], -this->mm[1], -this->mm[2]); }
155 
158  template <typename T0, typename T1>
159  const Vec3<T>& add(const Vec3<T0> &v1, const Vec3<T1> &v2)
160  {
161  this->mm[0] = v1[0] + v2[0];
162  this->mm[1] = v1[1] + v2[1];
163  this->mm[2] = v1[2] + v2[2];
164 
165  return *this;
166  }
167 
170  template <typename T0, typename T1>
171  const Vec3<T>& sub(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>& scale(T0 scale, const Vec3<T1> &v)
184  {
185  this->mm[0] = scale * v[0];
186  this->mm[1] = scale * v[1];
187  this->mm[2] = scale * v[2];
188 
189  return *this;
190  }
191 
192  template <typename T0, typename T1>
193  const Vec3<T> &div(T0 scale, const Vec3<T1> &v)
194  {
195  this->mm[0] = v[0] / scale;
196  this->mm[1] = v[1] / scale;
197  this->mm[2] = v[2] / scale;
198 
199  return *this;
200  }
201 
203  T dot(const Vec3<T> &v) const
204  {
205  return
206  this->mm[0]*v.mm[0] +
207  this->mm[1]*v.mm[1] +
208  this->mm[2]*v.mm[2];
209  }
210 
212  T length() const
213  {
214  return static_cast<T>(sqrt(double(
215  this->mm[0]*this->mm[0] +
216  this->mm[1]*this->mm[1] +
217  this->mm[2]*this->mm[2])));
218  }
219 
220 
223  T lengthSqr() const
224  {
225  return
226  this->mm[0]*this->mm[0] +
227  this->mm[1]*this->mm[1] +
228  this->mm[2]*this->mm[2];
229  }
230 
232  Vec3<T> cross(const Vec3<T> &v) const
233  {
234  return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1],
235  this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2],
236  this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]);
237  }
238 
239 
241  const Vec3<T>& cross(const Vec3<T> &v1, const Vec3<T> &v2)
242  {
243  // assert(this!=&v1);
244  // assert(this!=&v2);
245  this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1];
246  this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2];
247  this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0];
248  return *this;
249  }
250 
252  template <typename S>
253  const Vec3<T> &operator*=(S scalar)
254  {
255  this->mm[0] = static_cast<T>(this->mm[0] * scalar);
256  this->mm[1] = static_cast<T>(this->mm[1] * scalar);
257  this->mm[2] = static_cast<T>(this->mm[2] * scalar);
258  return *this;
259  }
260 
262  template <typename S>
263  const Vec3<T> &operator*=(const Vec3<S> &v1)
264  {
265  this->mm[0] *= v1[0];
266  this->mm[1] *= v1[1];
267  this->mm[2] *= v1[2];
268  return *this;
269  }
270 
272  template <typename S>
273  const Vec3<T> &operator/=(S scalar)
274  {
275  this->mm[0] /= scalar;
276  this->mm[1] /= scalar;
277  this->mm[2] /= scalar;
278  return *this;
279  }
280 
282  template <typename S>
283  const Vec3<T> &operator/=(const Vec3<S> &v1)
284  {
285  this->mm[0] /= v1[0];
286  this->mm[1] /= v1[1];
287  this->mm[2] /= v1[2];
288  return *this;
289  }
290 
292  template <typename S>
293  const Vec3<T> &operator+=(S scalar)
294  {
295  this->mm[0] = static_cast<T>(this->mm[0] + scalar);
296  this->mm[1] = static_cast<T>(this->mm[1] + scalar);
297  this->mm[2] = static_cast<T>(this->mm[2] + scalar);
298  return *this;
299  }
300 
302  template <typename S>
303  const Vec3<T> &operator+=(const Vec3<S> &v1)
304  {
305  this->mm[0] += v1[0];
306  this->mm[1] += v1[1];
307  this->mm[2] += v1[2];
308  return *this;
309  }
310 
312  template <typename S>
313  const Vec3<T> &operator-=(S scalar)
314  {
315  this->mm[0] -= scalar;
316  this->mm[1] -= scalar;
317  this->mm[2] -= scalar;
318  return *this;
319  }
320 
322  template <typename S>
323  const Vec3<T> &operator-=(const Vec3<S> &v1)
324  {
325  this->mm[0] -= v1[0];
326  this->mm[1] -= v1[1];
327  this->mm[2] -= v1[2];
328  return *this;
329  }
330 
333  inline const Vec3<T>& exp()
334  {
335  this->mm[0] = std::exp(this->mm[0]);
336  this->mm[1] = std::exp(this->mm[1]);
337  this->mm[2] = std::exp(this->mm[2]);
338  return *this;
339  }
340 
342  inline T sum() const
343  {
344  return this->mm[0] + this->mm[1] + this->mm[2];
345  }
346 
348  bool normalize(T eps = T(1.0e-7))
349  {
350  T d = length();
351  if (isApproxEqual(d, T(0), eps)) {
352  return false;
353  }
354  *this *= (T(1) / d);
355  return true;
356  }
357 
358 
360  Vec3<T> unit(T eps=0) const
361  {
362  T d;
363  return unit(eps, d);
364  }
365 
367  Vec3<T> unit(T eps, T& len) const
368  {
369  len = length();
370  if (isApproxEqual(len, T(0), eps)) {
371  OPENVDB_THROW(ArithmeticError, "Normalizing null 3-vector");
372  }
373  return *this / len;
374  }
375 
376  // Number of cols, rows, elements
377  static unsigned numRows() { return 1; }
378  static unsigned numColumns() { return 3; }
379  static unsigned numElements() { return 3; }
380 
383  T component(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
384  {
385  T l = onto.length();
386  if (isApproxEqual(l, T(0), eps)) return 0;
387 
388  return dot(onto)*(T(1)/l);
389  }
390 
393  Vec3<T> projection(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
394  {
395  T l = onto.lengthSqr();
396  if (isApproxEqual(l, T(0), eps)) return Vec3::zero();
397 
398  return onto*(dot(onto)*(T(1)/l));
399  }
400 
405  {
406  Vec3<T> u;
407  T l;
408 
409  if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
410  // v.x or v.z is the largest magnitude component, swap them
411  l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
412  l = static_cast<T>(T(1)/sqrt(double(l)));
413  u.mm[0] = -this->mm[2]*l;
414  u.mm[1] = (T)0.0;
415  u.mm[2] = +this->mm[0]*l;
416  } else {
417  // W.y or W.z is the largest magnitude component, swap them
418  l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
419  l = static_cast<T>(T(1)/sqrt(double(l)));
420  u.mm[0] = (T)0.0;
421  u.mm[1] = +this->mm[2]*l;
422  u.mm[2] = -this->mm[1]*l;
423  }
424 
425  return u;
426  }
427 
429  bool isNan() const { return isnan(this->mm[0]) || isnan(this->mm[1]) || isnan(this->mm[2]); }
430 
432  bool isInfinite() const
433  {
434  return isinf(this->mm[0]) || isinf(this->mm[1]) || isinf(this->mm[2]);
435  }
436 
438  bool isFinite() const
439  {
440  return finite(this->mm[0]) && finite(this->mm[1]) && finite(this->mm[2]);
441  }
442 
444  static Vec3<T> zero() { return Vec3<T>(0, 0, 0); }
445 };
446 
447 
449 template <typename T0, typename T1>
450 inline bool operator==(const Vec3<T0> &v0, const Vec3<T1> &v1)
451 {
452  return isExactlyEqual(v0[0], v1[0]) && isExactlyEqual(v0[1], v1[1])
453  && isExactlyEqual(v0[2], v1[2]);
454 }
455 
457 template <typename T0, typename T1>
458 inline bool operator!=(const Vec3<T0> &v0, const Vec3<T1> &v1) { return !(v0==v1); }
459 
461 template <typename S, typename T>
462 inline Vec3<typename promote<S, T>::type> operator*(S scalar, const Vec3<T> &v) { return v*scalar; }
463 
465 template <typename S, typename T>
467 {
469  result *= scalar;
470  return result;
471 }
472 
474 template <typename T0, typename T1>
476 {
477  Vec3<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1], v0[2] * v1[2]);
478  return result;
479 }
480 
481 
483 template <typename S, typename T>
485 {
486  return Vec3<typename promote<S, T>::type>(scalar/v[0], scalar/v[1], scalar/v[2]);
487 }
488 
490 template <typename S, typename T>
492 {
494  result /= scalar;
495  return result;
496 }
497 
499 template <typename T0, typename T1>
501 {
502  Vec3<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1], v0[2] / v1[2]);
503  return result;
504 }
505 
507 template <typename T0, typename T1>
509 {
511  result += v1;
512  return result;
513 }
514 
516 template <typename S, typename T>
518 {
520  result += scalar;
521  return result;
522 }
523 
525 template <typename T0, typename T1>
527 {
529  result -= v1;
530  return result;
531 }
532 
534 template <typename S, typename T>
536 {
538  result -= scalar;
539  return result;
540 }
541 
544 template <typename T>
545 inline T angle(const Vec3<T> &v1, const Vec3<T> &v2)
546 {
547  Vec3<T> c = v1.cross(v2);
548  return static_cast<T>(atan2(c.length(), v1.dot(v2)));
549 }
550 
551 template <typename T>
552 inline bool
553 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b)
554 {
555  return a.eq(b);
556 }
557 template <typename T>
558 inline bool
559 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b, const Vec3<T>& eps)
560 {
561  return isApproxEqual(a.x(), b.x(), eps.x()) &&
562  isApproxEqual(a.y(), b.y(), eps.y()) &&
563  isApproxEqual(a.z(), b.z(), eps.z());
564 }
565 
566 template<typename T>
567 inline bool
568 isFinite(const Vec3<T>& v)
569 {
570  return isFinite(v[0]) && isFinite(v[1]) && isFinite(v[2]);
571 }
572 
574 template<typename T>
575 inline bool
576 isZero(const Vec3<T>& v)
577 {
578  return isZero(v[0]) && isZero(v[1]) && isZero(v[2]);
579 }
580 
581 template<typename T>
582 inline Vec3<T>
583 Abs(const Vec3<T>& v)
584 {
585  return Vec3<T>(Abs(v[0]), Abs(v[1]), Abs(v[2]));
586 }
587 
590 template <typename T>
591 inline void orthonormalize(Vec3<T> &v1, Vec3<T> &v2, Vec3<T> &v3)
592 {
593  // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
594  // orthonormalization produces vectors u0, u1, and u2 as follows,
595  //
596  // u0 = v0/|v0|
597  // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
598  // u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
599  //
600  // where |A| indicates length of vector A and A*B indicates dot
601  // product of vectors A and B.
602 
603  // compute u0
604  v1.normalize();
605 
606  // compute u1
607  T d0 = v1.dot(v2);
608  v2 -= v1*d0;
609  v2.normalize();
610 
611  // compute u2
612  T d1 = v2.dot(v3);
613  d0 = v1.dot(v3);
614  v3 -= v1*d0 + v2*d1;
615  v3.normalize();
616 }
617 
622 
624 template <typename T>
625 inline Vec3<T> minComponent(const Vec3<T> &v1, const Vec3<T> &v2)
626 {
627  return Vec3<T>(
628  std::min(v1.x(), v2.x()),
629  std::min(v1.y(), v2.y()),
630  std::min(v1.z(), v2.z()));
631 }
632 
634 template <typename T>
635 inline Vec3<T> maxComponent(const Vec3<T> &v1, const Vec3<T> &v2)
636 {
637  return Vec3<T>(
638  std::max(v1.x(), v2.x()),
639  std::max(v1.y(), v2.y()),
640  std::max(v1.z(), v2.z()));
641 }
642 
645 template <typename T>
646 inline Vec3<T> Exp(Vec3<T> v) { return v.exp(); }
647 
652 
653 } // namespace math
654 } // namespace OPENVDB_VERSION_NAME
655 } // namespace openvdb
656 
657 #endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
658 
659 // Copyright (c) 2012-2016 DreamWorks Animation LLC
660 // All rights reserved. This software is distributed under the
661 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
const Vec3< T > & operator*=(S scalar)
Returns v, where for .
Definition: Vec3.h:253
Vec3< float > Vec3s
Definition: Vec3.h:650
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:203
bool isZero(const Vec3< T > &v)
Return true if all components are exactly equal to zero.
Definition: Vec3.h:576
T & z()
Definition: Vec3.h:99
static unsigned numElements()
Definition: Vec3.h:379
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:367
T angle(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Vec3.h:545
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:393
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:407
bool isFinite(const Vec3< T > &v)
Definition: Vec3.h:568
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
const Vec3< T > & operator+=(const Vec3< S > &v1)
Returns v0, where for .
Definition: Vec3.h:303
T value_type
Definition: Vec3.h:50
void orthonormalize(Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)
Definition: Vec3.h:591
Vec3< typename promote< T0, T1 >::type > operator*(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Returns V, where for .
Definition: Vec3.h:475
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:89
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:69
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:360
Definition: Mat.h:146
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:97
static unsigned numRows()
Definition: Vec3.h:377
Definition: Exceptions.h:78
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:171
Vec3< typename promote< S, T >::type > operator-(const Vec3< T > &v, S scalar)
Returns V, where for .
Definition: Vec3.h:535
const boost::disable_if_c< VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:132
Vec3< typename promote< S, T >::type > operator+(const Vec3< T > &v, S scalar)
Returns V, where for .
Definition: Vec3.h:517
bool isInfinite() const
True if an Inf is present in vector.
Definition: Vec3.h:432
bool isNan() const
True if a Nan is present in vector.
Definition: Vec3.h:429
T * asPointer()
Definition: Vec3.h:106
static unsigned numColumns()
Definition: Vec3.h:378
Vec3< int32_t > Vec3i
Definition: Vec3.h:648
Vec3< T > maxComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec3.h:635
bool isFinite() const
True if all no Nan or Inf values present.
Definition: Vec3.h:438
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:102
const Vec3< T > & operator/=(S scalar)
Returns v, where for .
Definition: Vec3.h:273
Definition: Tuple.h:50
#define OPENVDB_VERSION_NAME
Definition: version.h:43
Vec3< double > Vec3d
Definition: Vec3.h:651
T ValueType
Definition: Vec3.h:51
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:97
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:342
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:145
Definition: Exceptions.h:39
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:594
T length() const
Length of the vector.
Definition: Vec3.h:212
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:193
Vec3()
Trivial constructor, the vector is NOT initialized.
Definition: Vec3.h:54
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition: Vec3.h:79
const Vec3< T > & operator*=(const Vec3< S > &v1)
Returns v0, where for .
Definition: Vec3.h:263
bool isApproxEqual(const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)
Definition: Vec3.h:559
Vec3< T > minComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec3.h:625
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:154
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:348
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:444
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:241
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:134
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:113
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:232
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:383
const Vec3< T > & exp()
Definition: Vec3.h:333
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:110
T & y()
Definition: Vec3.h:98
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:450
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:117
Vec3< T > Abs(const Vec3< T > &v)
Definition: Vec3.h:583
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:404
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:125
T z() const
Definition: Vec3.h:104
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:417
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:458
const Vec3< T > & operator/=(const Vec3< S > &v1)
Returns v0, where for .
Definition: Vec3.h:283
T lengthSqr() const
Definition: Vec3.h:223
const T * asPointer() const
Definition: Vec3.h:107
Vec3< typename promote< T0, T1 >::type > operator/(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Returns V, where for .
Definition: Vec3.h:500
Vec3< uint32_t > Vec3ui
Definition: Vec3.h:649
const Vec3< T > & operator-=(S scalar)
Returns v, where for .
Definition: Vec3.h:313
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:646
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:71
const Vec3< T > & operator-=(const Vec3< S > &v1)
Returns v0, where for .
Definition: Vec3.h:323
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:159
Vec3(T val)
Constructor with one argument, e.g. Vec3f v(0);.
Definition: Vec3.h:57
const Vec3< T > & operator+=(S scalar)
Returns v, where for .
Definition: Vec3.h:293
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:627
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:183
T y() const
Definition: Vec3.h:103
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:60
const boost::disable_if_c< VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:128