OpenVDB  6.0.0
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 <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 {
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 
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 
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 
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>
505 {
507  result *= scalar;
508  return result;
509 }
510 
512 template <typename T0, typename T1>
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>
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>
530 {
532  result /= scalar;
533  return result;
534 }
535 
537 template <typename T0, typename T1>
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>
547 {
549  result += v1;
550  return result;
551 }
552 
554 template <typename S, typename T>
556 {
558  result += scalar;
559  return result;
560 }
561 
563 template <typename T0, typename T1>
565 {
567  result -= v1;
568  return result;
569 }
570 
572 template <typename S, typename T>
574 {
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 
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/ )
Vec3< T > Abs(const Vec3< T > &v)
Definition: Vec3.h:606
Real value_type
Definition: Vec3.h:53
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:216
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:377
static unsigned numElements()
Definition: Vec3.h:415
static unsigned numColumns()
Definition: Vec3.h:414
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:196
bool isApproxEqual(const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)
Definition: Vec3.h:597
Real ValueType
Definition: Vec3.h:54
T y() const
Definition: Vec3.h:116
Definition: Tuple.h:55
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:184
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
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
T z() const
Definition: Vec3.h:117
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:102
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:365
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:109
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:395
Definition: Mat.h:197
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition: Vec3.h:465
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition: Vec3.h:82
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:245
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:147
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
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:49
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:405
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
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:63
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:206
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:396
T * asPointer()
Definition: Vec3.h:119
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
const Vec3< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec3.h:286
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
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:126
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:440
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:488
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:136
T lengthSqr() const
Definition: Vec3.h:236
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:138
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
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
T & z()
Definition: Vec3.h:112
T & y()
Definition: Vec3.h:111
Definition: Exceptions.h:40
const Vec3< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec3.h:326
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:129
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:647
static Vec3< T > ones()
Definition: Vec3.h:482
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:429
T length() const
Length of the vector.
Definition: Vec3.h:225
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition: Vec3.h:60
Vec3< T > reversed() const
Return the vector (z, y, x)
Definition: Vec3.h:475
Vec3< T > minComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec3.h:648
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:72
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:133
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:130
const Vec3< T > & log()
Definition: Vec3.h:356
const T * asPointer() const
Definition: Vec3.h:120
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
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition: Vec3.h:406
T angle(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Vec3.h:583
static unsigned numRows()
Definition: Vec3.h:413
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
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:389
void orthonormalize(Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)
Definition: Vec3.h:614
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:115
T product() const
Return the product of all the vector components.
Definition: Vec3.h:371
const Vec3< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec3.h:306
Vec3()
Trivial constructor, the vector is NOT initialized.
Definition: Vec3.h:57
Vec3< T > maxComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec3.h:658
const Vec3< T > & exp()
Definition: Vec3.h:346
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:188
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
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
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:172
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:167
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:123
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:680
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:419
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
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:496
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:481
Definition: Exceptions.h:83
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:110