OpenVDB  7.0.0
Vec3.h
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1 // Copyright Contributors to the OpenVDB Project
2 // SPDX-License-Identifier: MPL-2.0
3 
4 #ifndef OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
5 #define OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
6 
7 #include <openvdb/Exceptions.h>
8 #include "Math.h"
9 #include "Tuple.h"
10 #include <algorithm>
11 #include <cmath>
12 #include <type_traits>
13 
14 
15 namespace openvdb {
17 namespace OPENVDB_VERSION_NAME {
18 namespace math {
19 
20 template<typename T> class Mat3;
21 
22 template<typename T>
23 class Vec3: public Tuple<3, T>
24 {
25 public:
26  using value_type = T;
27  using ValueType = T;
28 
30  Vec3() {}
31 
33  explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
34 
36  Vec3(T x, T y, T z)
37  {
38  this->mm[0] = x;
39  this->mm[1] = y;
40  this->mm[2] = z;
41  }
42 
44  template <typename Source>
45  Vec3(Source *a)
46  {
47  this->mm[0] = static_cast<T>(a[0]);
48  this->mm[1] = static_cast<T>(a[1]);
49  this->mm[2] = static_cast<T>(a[2]);
50  }
51 
54  template<typename Source>
55  explicit Vec3(const Tuple<3, Source> &v)
56  {
57  this->mm[0] = static_cast<T>(v[0]);
58  this->mm[1] = static_cast<T>(v[1]);
59  this->mm[2] = static_cast<T>(v[2]);
60  }
61 
65  template<typename Other>
66  explicit Vec3(Other val,
67  typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
68  {
69  this->mm[0] = this->mm[1] = this->mm[2] = static_cast<T>(val);
70  }
71 
74  template<typename Other>
75  Vec3(const Vec3<Other>& v)
76  {
77  this->mm[0] = static_cast<T>(v[0]);
78  this->mm[1] = static_cast<T>(v[1]);
79  this->mm[2] = static_cast<T>(v[2]);
80  }
81 
83  T& x() { return this->mm[0]; }
84  T& y() { return this->mm[1]; }
85  T& z() { return this->mm[2]; }
86 
88  T x() const { return this->mm[0]; }
89  T y() const { return this->mm[1]; }
90  T z() const { return this->mm[2]; }
91 
92  T* asPointer() { return this->mm; }
93  const T* asPointer() const { return this->mm; }
94 
96  T& operator()(int i) { return this->mm[i]; }
97 
99  T operator()(int i) const { return this->mm[i]; }
100 
103  const Vec3<T>& init(T x=0, T y=0, T z=0)
104  {
105  this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
106  return *this;
107  }
108 
109 
111  const Vec3<T>& setZero()
112  {
113  this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
114  return *this;
115  }
116 
119  template<typename Source>
120  const Vec3<T>& operator=(const Vec3<Source> &v)
121  {
122  // note: don't static_cast because that suppresses warnings
123  this->mm[0] = v[0];
124  this->mm[1] = v[1];
125  this->mm[2] = v[2];
126 
127  return *this;
128  }
129 
131  bool eq(const Vec3<T> &v, T eps = static_cast<T>(1.0e-7)) const
132  {
133  return isRelOrApproxEqual(this->mm[0], v.mm[0], eps, eps) &&
134  isRelOrApproxEqual(this->mm[1], v.mm[1], eps, eps) &&
135  isRelOrApproxEqual(this->mm[2], v.mm[2], eps, eps);
136  }
137 
138 
140  Vec3<T> operator-() const { return Vec3<T>(-this->mm[0], -this->mm[1], -this->mm[2]); }
141 
144  template <typename T0, typename T1>
145  const Vec3<T>& add(const Vec3<T0> &v1, const Vec3<T1> &v2)
146  {
147  this->mm[0] = v1[0] + v2[0];
148  this->mm[1] = v1[1] + v2[1];
149  this->mm[2] = v1[2] + v2[2];
150 
151  return *this;
152  }
153 
156  template <typename T0, typename T1>
157  const Vec3<T>& sub(const Vec3<T0> &v1, const Vec3<T1> &v2)
158  {
159  this->mm[0] = v1[0] - v2[0];
160  this->mm[1] = v1[1] - v2[1];
161  this->mm[2] = v1[2] - v2[2];
162 
163  return *this;
164  }
165 
168  template <typename T0, typename T1>
169  const Vec3<T>& scale(T0 scale, const Vec3<T1> &v)
170  {
171  this->mm[0] = scale * v[0];
172  this->mm[1] = scale * v[1];
173  this->mm[2] = scale * v[2];
174 
175  return *this;
176  }
177 
178  template <typename T0, typename T1>
179  const Vec3<T> &div(T0 scale, const Vec3<T1> &v)
180  {
181  this->mm[0] = v[0] / scale;
182  this->mm[1] = v[1] / scale;
183  this->mm[2] = v[2] / scale;
184 
185  return *this;
186  }
187 
189  T dot(const Vec3<T> &v) const
190  {
191  return
192  this->mm[0]*v.mm[0] +
193  this->mm[1]*v.mm[1] +
194  this->mm[2]*v.mm[2];
195  }
196 
198  T length() const
199  {
200  return static_cast<T>(sqrt(double(
201  this->mm[0]*this->mm[0] +
202  this->mm[1]*this->mm[1] +
203  this->mm[2]*this->mm[2])));
204  }
205 
206 
209  T lengthSqr() const
210  {
211  return
212  this->mm[0]*this->mm[0] +
213  this->mm[1]*this->mm[1] +
214  this->mm[2]*this->mm[2];
215  }
216 
218  Vec3<T> cross(const Vec3<T> &v) const
219  {
220  return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1],
221  this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2],
222  this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]);
223  }
224 
225 
227  const Vec3<T>& cross(const Vec3<T> &v1, const Vec3<T> &v2)
228  {
229  // assert(this!=&v1);
230  // assert(this!=&v2);
231  this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1];
232  this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2];
233  this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0];
234  return *this;
235  }
236 
238  template <typename S>
239  const Vec3<T> &operator*=(S scalar)
240  {
242  const auto value0 = this->mm[0] * scalar;
243  const auto value1 = this->mm[1] * scalar;
244  const auto value2 = this->mm[2] * scalar;
246  this->mm[0] = static_cast<T>(value0);
247  this->mm[1] = static_cast<T>(value1);
248  this->mm[2] = static_cast<T>(value2);
249  return *this;
250  }
251 
253  template <typename S>
254  const Vec3<T> &operator*=(const Vec3<S> &v1)
255  {
256  this->mm[0] *= v1[0];
257  this->mm[1] *= v1[1];
258  this->mm[2] *= v1[2];
259  return *this;
260  }
261 
263  template <typename S>
264  const Vec3<T> &operator/=(S scalar)
265  {
266  this->mm[0] /= scalar;
267  this->mm[1] /= scalar;
268  this->mm[2] /= scalar;
269  return *this;
270  }
271 
273  template <typename S>
274  const Vec3<T> &operator/=(const Vec3<S> &v1)
275  {
276  this->mm[0] /= v1[0];
277  this->mm[1] /= v1[1];
278  this->mm[2] /= v1[2];
279  return *this;
280  }
281 
283  template <typename S>
284  const Vec3<T> &operator+=(S scalar)
285  {
287  const auto value0 = this->mm[0] + scalar;
288  const auto value1 = this->mm[1] + scalar;
289  const auto value2 = this->mm[2] + scalar;
291  this->mm[0] = static_cast<T>(value0);
292  this->mm[1] = static_cast<T>(value1);
293  this->mm[2] = static_cast<T>(value2);
294  return *this;
295  }
296 
298  template <typename S>
299  const Vec3<T> &operator+=(const Vec3<S> &v1)
300  {
301  this->mm[0] += v1[0];
302  this->mm[1] += v1[1];
303  this->mm[2] += v1[2];
304  return *this;
305  }
306 
308  template <typename S>
309  const Vec3<T> &operator-=(S scalar)
310  {
311  this->mm[0] -= scalar;
312  this->mm[1] -= scalar;
313  this->mm[2] -= scalar;
314  return *this;
315  }
316 
318  template <typename S>
319  const Vec3<T> &operator-=(const Vec3<S> &v1)
320  {
321  this->mm[0] -= v1[0];
322  this->mm[1] -= v1[1];
323  this->mm[2] -= v1[2];
324  return *this;
325  }
326 
329  inline const Vec3<T>& exp()
330  {
331  this->mm[0] = std::exp(this->mm[0]);
332  this->mm[1] = std::exp(this->mm[1]);
333  this->mm[2] = std::exp(this->mm[2]);
334  return *this;
335  }
336 
339  inline const Vec3<T>& log()
340  {
341  this->mm[0] = std::log(this->mm[0]);
342  this->mm[1] = std::log(this->mm[1]);
343  this->mm[2] = std::log(this->mm[2]);
344  return *this;
345  }
346 
348  inline T sum() const
349  {
350  return this->mm[0] + this->mm[1] + this->mm[2];
351  }
352 
354  inline T product() const
355  {
356  return this->mm[0] * this->mm[1] * this->mm[2];
357  }
358 
360  bool normalize(T eps = T(1.0e-7))
361  {
362  T d = length();
363  if (isApproxEqual(d, T(0), eps)) {
364  return false;
365  }
366  *this *= (T(1) / d);
367  return true;
368  }
369 
370 
372  Vec3<T> unit(T eps=0) const
373  {
374  T d;
375  return unit(eps, d);
376  }
377 
379  Vec3<T> unit(T eps, T& len) const
380  {
381  len = length();
382  if (isApproxEqual(len, T(0), eps)) {
383  OPENVDB_THROW(ArithmeticError, "Normalizing null 3-vector");
384  }
385  return *this / len;
386  }
387 
390  {
391  T l2 = lengthSqr();
392  return l2 ? *this / static_cast<T>(sqrt(l2)) : Vec3<T>(1, 0 ,0);
393  }
394 
395  // Number of cols, rows, elements
396  static unsigned numRows() { return 1; }
397  static unsigned numColumns() { return 3; }
398  static unsigned numElements() { return 3; }
399 
402  T component(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
403  {
404  T l = onto.length();
405  if (isApproxEqual(l, T(0), eps)) return 0;
406 
407  return dot(onto)*(T(1)/l);
408  }
409 
412  Vec3<T> projection(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
413  {
414  T l = onto.lengthSqr();
415  if (isApproxEqual(l, T(0), eps)) return Vec3::zero();
416 
417  return onto*(dot(onto)*(T(1)/l));
418  }
419 
424  {
425  Vec3<T> u;
426  T l;
427 
428  if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
429  // v.x or v.z is the largest magnitude component, swap them
430  l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
431  l = static_cast<T>(T(1)/sqrt(double(l)));
432  u.mm[0] = -this->mm[2]*l;
433  u.mm[1] = T(0);
434  u.mm[2] = +this->mm[0]*l;
435  } else {
436  // W.y or W.z is the largest magnitude component, swap them
437  l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
438  l = static_cast<T>(T(1)/sqrt(double(l)));
439  u.mm[0] = T(0);
440  u.mm[1] = +this->mm[2]*l;
441  u.mm[2] = -this->mm[1]*l;
442  }
443 
444  return u;
445  }
446 
448  Vec3<T> sorted() const
449  {
450  Vec3<T> r(*this);
451  if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
452  if( r.mm[1] > r.mm[2] ) std::swap(r.mm[1], r.mm[2]);
453  if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
454  return r;
455  }
456 
459  {
460  return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]);
461  }
462 
464  static Vec3<T> zero() { return Vec3<T>(0, 0, 0); }
465  static Vec3<T> ones() { return Vec3<T>(1, 1, 1); }
466 };
467 
468 
470 template <typename T0, typename T1>
471 inline bool operator==(const Vec3<T0> &v0, const Vec3<T1> &v1)
472 {
473  return isExactlyEqual(v0[0], v1[0]) && isExactlyEqual(v0[1], v1[1])
474  && isExactlyEqual(v0[2], v1[2]);
475 }
476 
478 template <typename T0, typename T1>
479 inline bool operator!=(const Vec3<T0> &v0, const Vec3<T1> &v1) { return !(v0==v1); }
480 
482 template <typename S, typename T>
483 inline Vec3<typename promote<S, T>::type> operator*(S scalar, const Vec3<T> &v) { return v*scalar; }
484 
486 template <typename S, typename T>
488 {
490  result *= scalar;
491  return result;
492 }
493 
495 template <typename T0, typename T1>
497 {
498  Vec3<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1], v0[2] * v1[2]);
499  return result;
500 }
501 
502 
504 template <typename S, typename T>
506 {
507  return Vec3<typename promote<S, T>::type>(scalar/v[0], scalar/v[1], scalar/v[2]);
508 }
509 
511 template <typename S, typename T>
513 {
515  result /= scalar;
516  return result;
517 }
518 
520 template <typename T0, typename T1>
522 {
523  Vec3<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1], v0[2] / v1[2]);
524  return result;
525 }
526 
528 template <typename T0, typename T1>
530 {
532  result += v1;
533  return result;
534 }
535 
537 template <typename S, typename T>
539 {
541  result += scalar;
542  return result;
543 }
544 
546 template <typename T0, typename T1>
548 {
550  result -= v1;
551  return result;
552 }
553 
555 template <typename S, typename T>
557 {
559  result -= scalar;
560  return result;
561 }
562 
565 template <typename T>
566 inline T angle(const Vec3<T> &v1, const Vec3<T> &v2)
567 {
568  Vec3<T> c = v1.cross(v2);
569  return static_cast<T>(atan2(c.length(), v1.dot(v2)));
570 }
571 
572 template <typename T>
573 inline bool
574 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b)
575 {
576  return a.eq(b);
577 }
578 template <typename T>
579 inline bool
580 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b, const Vec3<T>& eps)
581 {
582  return isApproxEqual(a.x(), b.x(), eps.x()) &&
583  isApproxEqual(a.y(), b.y(), eps.y()) &&
584  isApproxEqual(a.z(), b.z(), eps.z());
585 }
586 
587 template<typename T>
588 inline Vec3<T>
589 Abs(const Vec3<T>& v)
590 {
591  return Vec3<T>(Abs(v[0]), Abs(v[1]), Abs(v[2]));
592 }
593 
596 template <typename T>
597 inline void orthonormalize(Vec3<T> &v1, Vec3<T> &v2, Vec3<T> &v3)
598 {
599  // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
600  // orthonormalization produces vectors u0, u1, and u2 as follows,
601  //
602  // u0 = v0/|v0|
603  // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
604  // u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
605  //
606  // where |A| indicates length of vector A and A*B indicates dot
607  // product of vectors A and B.
608 
609  // compute u0
610  v1.normalize();
611 
612  // compute u1
613  T d0 = v1.dot(v2);
614  v2 -= v1*d0;
615  v2.normalize();
616 
617  // compute u2
618  T d1 = v2.dot(v3);
619  d0 = v1.dot(v3);
620  v3 -= v1*d0 + v2*d1;
621  v3.normalize();
622 }
623 
628 
630 template <typename T>
631 inline Vec3<T> minComponent(const Vec3<T> &v1, const Vec3<T> &v2)
632 {
633  return Vec3<T>(
634  std::min(v1.x(), v2.x()),
635  std::min(v1.y(), v2.y()),
636  std::min(v1.z(), v2.z()));
637 }
638 
640 template <typename T>
641 inline Vec3<T> maxComponent(const Vec3<T> &v1, const Vec3<T> &v2)
642 {
643  return Vec3<T>(
644  std::max(v1.x(), v2.x()),
645  std::max(v1.y(), v2.y()),
646  std::max(v1.z(), v2.z()));
647 }
648 
651 template <typename T>
652 inline Vec3<T> Exp(Vec3<T> v) { return v.exp(); }
653 
656 template <typename T>
657 inline Vec3<T> Log(Vec3<T> v) { return v.log(); }
658 
663 
664 } // namespace math
665 } // namespace OPENVDB_VERSION_NAME
666 } // namespace openvdb
667 
668 #endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
Bracket code with OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN/_END, to inhibit warnings about type conve...
Definition: Platform.h:196
static Vec3< T > ones()
Definition: Vec3.h:465
T product() const
Return the product of all the vector components.
Definition: Vec3.h:354
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition: Vec3.h:33
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:652
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:218
Definition: Tuple.h:28
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:45
T & z()
Definition: Vec3.h:85
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:402
const Vec3< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition: Vec3.h:239
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition: Vec3.h:448
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
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:131
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:479
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:423
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:372
Real value_type
Definition: Vec3.h:26
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:82
const Vec3< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec3.h:284
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:111
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:254
T length() const
Length of the vector.
Definition: Vec3.h:198
static unsigned numElements()
Definition: Vec3.h:398
Vec3()
Trivial constructor, the vector is NOT initialized.
Definition: Vec3.h:30
T & y()
Definition: Vec3.h:84
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:412
const Vec3< T > & log()
Definition: Vec3.h:339
Vec3< T > Log(Vec3< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec3.h:657
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:140
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_END
Definition: Platform.h:197
T y() const
Definition: Vec3.h:89
static unsigned numColumns()
Definition: Vec3.h:397
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:538
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:169
Real ValueType
Definition: Vec3.h:27
const Vec3< T > & exp()
Definition: Vec3.h:329
Vec3< T > minComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec3.h:631
static unsigned numRows()
Definition: Vec3.h:396
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition: Vec3.h:389
Vec3< T > reversed() const
Return the vector (z, y, x)
Definition: Vec3.h:458
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:120
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:189
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:102
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:22
T * asPointer()
Definition: Vec3.h:92
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:398
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:145
Vec3< T > maxComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec3.h:641
Definition: Exceptions.h:13
Definition: Exceptions.h:56
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:379
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:103
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:75
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:274
T angle(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Vec3.h:566
Vec3< T > Abs(const Vec3< T > &v)
Definition: Vec3.h:589
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:83
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:521
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:227
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:653
bool isApproxEqual(const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)
Definition: Vec3.h:580
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:36
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:471
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:157
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:464
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:319
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:556
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:88
const Vec3< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec3.h:309
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:348
Definition: Mat.h:170
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:496
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:96
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:66
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:179
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:102
const Vec3< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec3.h:264
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:388
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:154
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:360
T lengthSqr() const
Definition: Vec3.h:209
const T * asPointer() const
Definition: Vec3.h:93
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:99
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:299
void orthonormalize(Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)
Definition: Vec3.h:597
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:620
T z() const
Definition: Vec3.h:90
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:106
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition: Vec3.h:55