OpenVDB  10.0.0
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 
29  /// Trivial constructor, the vector is NOT initialized
30  /// @note destructor, copy constructor, assignment operator and
31  /// move constructor are left to be defined by the compiler (default)
32  Vec3() = default;
33 
34  /// @brief Construct a vector all of whose components have the given value.
35  explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
36 
37  /// Constructor with three arguments, e.g. Vec3d v(1,2,3);
38  Vec3(T x, T y, T z)
39  {
40  this->mm[0] = x;
41  this->mm[1] = y;
42  this->mm[2] = z;
43  }
44 
45  /// Constructor with array argument, e.g. double a[3]; Vec3d v(a);
46  template <typename Source>
47  Vec3(Source *a)
48  {
49  this->mm[0] = static_cast<T>(a[0]);
50  this->mm[1] = static_cast<T>(a[1]);
51  this->mm[2] = static_cast<T>(a[2]);
52  }
53 
54  /// @brief Construct a Vec3 from a 3-Tuple with a possibly different value type.
55  /// @details Type conversion warnings are suppressed.
56  template<typename Source>
57  explicit Vec3(const Tuple<3, Source> &v)
58  {
59  this->mm[0] = static_cast<T>(v[0]);
60  this->mm[1] = static_cast<T>(v[1]);
61  this->mm[2] = static_cast<T>(v[2]);
62  }
63 
64  /// @brief Construct a vector all of whose components have the given value,
65  /// which may be of an arithmetic type different from this vector's value type.
66  /// @details Type conversion warnings are suppressed.
67  template<typename Other>
68  explicit Vec3(Other val,
69  typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
70  {
71  this->mm[0] = this->mm[1] = this->mm[2] = static_cast<T>(val);
72  }
73 
74  /// @brief Construct a Vec3 from another Vec3 with a possibly different value type.
75  /// @details Type conversion warnings are suppressed.
76  template<typename Other>
77  Vec3(const Vec3<Other>& v)
78  {
79  this->mm[0] = static_cast<T>(v[0]);
80  this->mm[1] = static_cast<T>(v[1]);
81  this->mm[2] = static_cast<T>(v[2]);
82  }
83 
84  /// Reference to the component, e.g. v.x() = 4.5f;
85  T& x() { return this->mm[0]; }
86  T& y() { return this->mm[1]; }
87  T& z() { return this->mm[2]; }
88 
89  /// Get the component, e.g. float f = v.y();
90  T x() const { return this->mm[0]; }
91  T y() const { return this->mm[1]; }
92  T z() const { return this->mm[2]; }
93 
94  T* asPointer() { return this->mm; }
95  const T* asPointer() const { return this->mm; }
96 
97  /// Alternative indexed reference to the elements
98  T& operator()(int i) { return this->mm[i]; }
99 
100  /// Alternative indexed constant reference to the elements,
101  T operator()(int i) const { return this->mm[i]; }
102 
103  /// "this" vector gets initialized to [x, y, z],
104  /// calling v.init(); has same effect as calling v = Vec3::zero();
105  const Vec3<T>& init(T x=0, T y=0, T z=0)
106  {
107  this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
108  return *this;
109  }
110 
111 
112  /// Set "this" vector to zero
113  const Vec3<T>& setZero()
114  {
115  this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
116  return *this;
117  }
118 
119  /// @brief Assignment operator
120  /// @details Type conversion warnings are not suppressed.
121  template<typename Source>
122  const Vec3<T>& operator=(const Vec3<Source> &v)
123  {
124  // note: don't static_cast because that suppresses warnings
125  this->mm[0] = v[0];
126  this->mm[1] = v[1];
127  this->mm[2] = v[2];
128 
129  return *this;
130  }
131 
132  /// Test if "this" vector is equivalent to vector v with tolerance of eps
133  bool eq(const Vec3<T> &v, T eps = static_cast<T>(1.0e-7)) const
134  {
135  return isRelOrApproxEqual(this->mm[0], v.mm[0], eps, eps) &&
136  isRelOrApproxEqual(this->mm[1], v.mm[1], eps, eps) &&
137  isRelOrApproxEqual(this->mm[2], v.mm[2], eps, eps);
138  }
139 
140 
141  /// Negation operator, for e.g. v1 = -v2;
142  Vec3<T> operator-() const { return Vec3<T>(-this->mm[0], -this->mm[1], -this->mm[2]); }
143 
144  /// this = v1 + v2
145  /// "this", v1 and v2 need not be distinct objects, e.g. v.add(v1,v);
146  template <typename T0, typename T1>
147  const Vec3<T>& add(const Vec3<T0> &v1, const Vec3<T1> &v2)
148  {
149  this->mm[0] = v1[0] + v2[0];
150  this->mm[1] = v1[1] + v2[1];
151  this->mm[2] = v1[2] + v2[2];
152 
153  return *this;
154  }
155 
156  /// this = v1 - v2
157  /// "this", v1 and v2 need not be distinct objects, e.g. v.sub(v1,v);
158  template <typename T0, typename T1>
159  const Vec3<T>& sub(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 
168  /// this = scalar*v, v need not be a distinct object from "this",
169  /// e.g. v.scale(1.5,v1);
170  template <typename T0, typename T1>
171  const Vec3<T>& scale(T0 scale, const Vec3<T1> &v)
172  {
173  this->mm[0] = scale * v[0];
174  this->mm[1] = scale * v[1];
175  this->mm[2] = scale * v[2];
176 
177  return *this;
178  }
179 
180  template <typename T0, typename T1>
181  const Vec3<T> &div(T0 scale, const Vec3<T1> &v)
182  {
183  this->mm[0] = v[0] / scale;
184  this->mm[1] = v[1] / scale;
185  this->mm[2] = v[2] / scale;
186 
187  return *this;
188  }
189 
190  /// Dot product
191  T dot(const Vec3<T> &v) const
192  {
193  return
194  this->mm[0]*v.mm[0] +
195  this->mm[1]*v.mm[1] +
196  this->mm[2]*v.mm[2];
197  }
198 
199  /// Length of the vector
200  T length() const
201  {
202  return static_cast<T>(sqrt(double(
203  this->mm[0]*this->mm[0] +
204  this->mm[1]*this->mm[1] +
205  this->mm[2]*this->mm[2])));
206  }
207 
208 
209  /// Squared length of the vector, much faster than length() as it
210  /// does not involve square root
211  T lengthSqr() const
212  {
213  return
214  this->mm[0]*this->mm[0] +
215  this->mm[1]*this->mm[1] +
216  this->mm[2]*this->mm[2];
217  }
218 
219  /// Return the cross product of "this" vector and v;
220  Vec3<T> cross(const Vec3<T> &v) const
221  {
222  return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1],
223  this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2],
224  this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]);
225  }
226 
227 
228  /// this = v1 cross v2, v1 and v2 must be distinct objects than "this"
229  const Vec3<T>& cross(const Vec3<T> &v1, const Vec3<T> &v2)
230  {
231  // assert(this!=&v1);
232  // assert(this!=&v2);
233  this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1];
234  this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2];
235  this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0];
236  return *this;
237  }
238 
239  /// Multiply each element of this vector by @a scalar.
240  template <typename S>
241  const Vec3<T> &operator*=(S scalar)
242  {
244  const auto value0 = this->mm[0] * scalar;
245  const auto value1 = this->mm[1] * scalar;
246  const auto value2 = this->mm[2] * scalar;
248  this->mm[0] = static_cast<T>(value0);
249  this->mm[1] = static_cast<T>(value1);
250  this->mm[2] = static_cast<T>(value2);
251  return *this;
252  }
253 
254  /// Multiply each element of this vector by the corresponding element of the given vector.
255  template <typename S>
256  const Vec3<T> &operator*=(const Vec3<S> &v1)
257  {
258  this->mm[0] *= v1[0];
259  this->mm[1] *= v1[1];
260  this->mm[2] *= v1[2];
261  return *this;
262  }
263 
264  /// Divide each element of this vector by @a scalar.
265  template <typename S>
266  const Vec3<T> &operator/=(S scalar)
267  {
268  this->mm[0] /= scalar;
269  this->mm[1] /= scalar;
270  this->mm[2] /= scalar;
271  return *this;
272  }
273 
274  /// Divide each element of this vector by the corresponding element of the given vector.
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 
284  /// Add @a scalar to each element of this vector.
285  template <typename S>
286  const Vec3<T> &operator+=(S scalar)
287  {
289  const auto value0 = this->mm[0] + scalar;
290  const auto value1 = this->mm[1] + scalar;
291  const auto value2 = this->mm[2] + scalar;
293  this->mm[0] = static_cast<T>(value0);
294  this->mm[1] = static_cast<T>(value1);
295  this->mm[2] = static_cast<T>(value2);
296  return *this;
297  }
298 
299  /// Add each element of the given vector to the corresponding element of this vector.
300  template <typename S>
301  const Vec3<T> &operator+=(const Vec3<S> &v1)
302  {
303  this->mm[0] += v1[0];
304  this->mm[1] += v1[1];
305  this->mm[2] += v1[2];
306  return *this;
307  }
308 
309  /// Subtract @a scalar from each element of this vector.
310  template <typename S>
311  const Vec3<T> &operator-=(S scalar)
312  {
313  this->mm[0] -= scalar;
314  this->mm[1] -= scalar;
315  this->mm[2] -= scalar;
316  return *this;
317  }
318 
319  /// Subtract each element of the given vector from the corresponding element of this vector.
320  template <typename S>
321  const Vec3<T> &operator-=(const Vec3<S> &v1)
322  {
323  this->mm[0] -= v1[0];
324  this->mm[1] -= v1[1];
325  this->mm[2] -= v1[2];
326  return *this;
327  }
328 
329  /// Return a reference to itself after the exponent has been
330  /// applied to all the vector components.
331  inline const Vec3<T>& exp()
332  {
333  this->mm[0] = std::exp(this->mm[0]);
334  this->mm[1] = std::exp(this->mm[1]);
335  this->mm[2] = std::exp(this->mm[2]);
336  return *this;
337  }
338 
339  /// Return a reference to itself after log has been
340  /// applied to all the vector components.
341  inline const Vec3<T>& log()
342  {
343  this->mm[0] = std::log(this->mm[0]);
344  this->mm[1] = std::log(this->mm[1]);
345  this->mm[2] = std::log(this->mm[2]);
346  return *this;
347  }
348 
349  /// Return the sum of all the vector components.
350  inline T sum() const
351  {
352  return this->mm[0] + this->mm[1] + this->mm[2];
353  }
354 
355  /// Return the product of all the vector components.
356  inline T product() const
357  {
358  return this->mm[0] * this->mm[1] * this->mm[2];
359  }
360 
361  /// this = normalized this
362  bool normalize(T eps = T(1.0e-7))
363  {
364  T d = length();
365  if (isApproxEqual(d, T(0), eps)) {
366  return false;
367  }
368  *this *= (T(1) / d);
369  return true;
370  }
371 
372 
373  /// return normalized this, throws if null vector
374  Vec3<T> unit(T eps=0) const
375  {
376  T d;
377  return unit(eps, d);
378  }
379 
380  /// return normalized this and length, throws if null vector
381  Vec3<T> unit(T eps, T& len) const
382  {
383  len = length();
384  if (isApproxEqual(len, T(0), eps)) {
385  OPENVDB_THROW(ArithmeticError, "Normalizing null 3-vector");
386  }
387  return *this / len;
388  }
389 
390  /// return normalized this, or (1, 0, 0) if this is null vector
392  {
393  T l2 = lengthSqr();
394  return l2 ? *this / static_cast<T>(sqrt(l2)) : Vec3<T>(1, 0 ,0);
395  }
396 
397  // Number of cols, rows, elements
398  static unsigned numRows() { return 1; }
399  static unsigned numColumns() { return 3; }
400  static unsigned numElements() { return 3; }
401 
402  /// Returns the scalar component of v in the direction of onto, onto need
403  /// not be unit. e.g double c = Vec3d::component(v1,v2);
404  T component(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
405  {
406  T l = onto.length();
407  if (isApproxEqual(l, T(0), eps)) return 0;
408 
409  return dot(onto)*(T(1)/l);
410  }
411 
412  /// Return the projection of v onto the vector, onto need not be unit
413  /// e.g. Vec3d a = vprojection(n);
414  Vec3<T> projection(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
415  {
416  T l = onto.lengthSqr();
417  if (isApproxEqual(l, T(0), eps)) return Vec3::zero();
418 
419  return onto*(dot(onto)*(T(1)/l));
420  }
421 
422  /// Return an arbitrary unit vector perpendicular to v
423  /// Vector this must be a unit vector
424  /// e.g. v = v.normalize(); Vec3d n = v.getArbPerpendicular();
426  {
427  Vec3<T> u;
428  T l;
429 
430  if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
431  // v.x or v.z is the largest magnitude component, swap them
432  l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
433  l = static_cast<T>(T(1)/sqrt(double(l)));
434  u.mm[0] = -this->mm[2]*l;
435  u.mm[1] = T(0);
436  u.mm[2] = +this->mm[0]*l;
437  } else {
438  // W.y or W.z is the largest magnitude component, swap them
439  l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
440  l = static_cast<T>(T(1)/sqrt(double(l)));
441  u.mm[0] = T(0);
442  u.mm[1] = +this->mm[2]*l;
443  u.mm[2] = -this->mm[1]*l;
444  }
445 
446  return u;
447  }
448 
449  /// Return a vector with the components of this in ascending order
450  Vec3<T> sorted() const
451  {
452  Vec3<T> r(*this);
453  if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
454  if( r.mm[1] > r.mm[2] ) std::swap(r.mm[1], r.mm[2]);
455  if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
456  return r;
457  }
458 
459  /// Return the vector (z, y, x)
461  {
462  return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]);
463  }
464 
465  /// Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();
466  static Vec3<T> zero() { return Vec3<T>(0, 0, 0); }
467  static Vec3<T> ones() { return Vec3<T>(1, 1, 1); }
468 };
469 
470 
471 /// Equality operator, does exact floating point comparisons
472 template <typename T0, typename T1>
473 inline bool operator==(const Vec3<T0> &v0, const Vec3<T1> &v1)
474 {
475  return isExactlyEqual(v0[0], v1[0]) && isExactlyEqual(v0[1], v1[1])
476  && isExactlyEqual(v0[2], v1[2]);
477 }
478 
479 /// Inequality operator, does exact floating point comparisons
480 template <typename T0, typename T1>
481 inline bool operator!=(const Vec3<T0> &v0, const Vec3<T1> &v1) { return !(v0==v1); }
482 
483 /// Multiply each element of the given vector by @a scalar and return the result.
484 template <typename S, typename T>
485 inline Vec3<typename promote<S, T>::type> operator*(S scalar, const Vec3<T> &v) { return v*scalar; }
486 
487 /// Multiply each element of the given vector by @a scalar and return the result.
488 template <typename S, typename T>
490 {
492  result *= scalar;
493  return result;
494 }
495 
496 /// Multiply corresponding elements of @a v0 and @a v1 and return the result.
497 template <typename T0, typename T1>
499 {
500  Vec3<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1], v0[2] * v1[2]);
501  return result;
502 }
503 
504 
505 /// Divide @a scalar by each element of the given vector and return the result.
506 template <typename S, typename T>
508 {
509  return Vec3<typename promote<S, T>::type>(scalar/v[0], scalar/v[1], scalar/v[2]);
510 }
511 
512 /// Divide each element of the given vector by @a scalar and return the result.
513 template <typename S, typename T>
515 {
517  result /= scalar;
518  return result;
519 }
520 
521 /// Divide corresponding elements of @a v0 and @a v1 and return the result.
522 template <typename T0, typename T1>
524 {
525  Vec3<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1], v0[2] / v1[2]);
526  return result;
527 }
528 
529 /// Add corresponding elements of @a v0 and @a v1 and return the result.
530 template <typename T0, typename T1>
532 {
534  result += v1;
535  return result;
536 }
537 
538 /// Add @a scalar to each element of the given vector and return the result.
539 template <typename S, typename T>
541 {
543  result += scalar;
544  return result;
545 }
546 
547 /// Subtract corresponding elements of @a v0 and @a v1 and return the result.
548 template <typename T0, typename T1>
550 {
552  result -= v1;
553  return result;
554 }
555 
556 /// Subtract @a scalar from each element of the given vector and return the result.
557 template <typename S, typename T>
559 {
561  result -= scalar;
562  return result;
563 }
564 
565 /// Angle between two vectors, the result is between [0, pi],
566 /// e.g. double a = Vec3d::angle(v1,v2);
567 template <typename T>
568 inline T angle(const Vec3<T> &v1, const Vec3<T> &v2)
569 {
570  Vec3<T> c = v1.cross(v2);
571  return static_cast<T>(atan2(c.length(), v1.dot(v2)));
572 }
573 
574 template <typename T>
575 inline bool
576 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b)
577 {
578  return a.eq(b);
579 }
580 template <typename T>
581 inline bool
582 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b, const Vec3<T>& eps)
583 {
584  return isApproxEqual(a.x(), b.x(), eps.x()) &&
585  isApproxEqual(a.y(), b.y(), eps.y()) &&
586  isApproxEqual(a.z(), b.z(), eps.z());
587 }
588 
589 template<typename T>
590 inline Vec3<T>
591 Abs(const Vec3<T>& v)
592 {
593  return Vec3<T>(Abs(v[0]), Abs(v[1]), Abs(v[2]));
594 }
595 
596 /// Orthonormalize vectors v1, v2 and v3 and store back the resulting
597 /// basis e.g. Vec3d::orthonormalize(v1,v2,v3);
598 template <typename T>
599 inline void orthonormalize(Vec3<T> &v1, Vec3<T> &v2, Vec3<T> &v3)
600 {
601  // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
602  // orthonormalization produces vectors u0, u1, and u2 as follows,
603  //
604  // u0 = v0/|v0|
605  // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
606  // u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
607  //
608  // where |A| indicates length of vector A and A*B indicates dot
609  // product of vectors A and B.
610 
611  // compute u0
612  v1.normalize();
613 
614  // compute u1
615  T d0 = v1.dot(v2);
616  v2 -= v1*d0;
617  v2.normalize();
618 
619  // compute u2
620  T d1 = v2.dot(v3);
621  d0 = v1.dot(v3);
622  v3 -= v1*d0 + v2*d1;
623  v3.normalize();
624 }
625 
626 /// @remark We are switching to a more explicit name because the semantics
627 /// are different from std::min/max. In that case, the function returns a
628 /// reference to one of the objects based on a comparator. Here, we must
629 /// fabricate a new object which might not match either of the inputs.
630 
631 /// Return component-wise minimum of the two vectors.
632 template <typename T>
633 inline Vec3<T> minComponent(const Vec3<T> &v1, const Vec3<T> &v2)
634 {
635  return Vec3<T>(
636  std::min(v1.x(), v2.x()),
637  std::min(v1.y(), v2.y()),
638  std::min(v1.z(), v2.z()));
639 }
640 
641 /// Return component-wise maximum of the two vectors.
642 template <typename T>
643 inline Vec3<T> maxComponent(const Vec3<T> &v1, const Vec3<T> &v2)
644 {
645  return Vec3<T>(
646  std::max(v1.x(), v2.x()),
647  std::max(v1.y(), v2.y()),
648  std::max(v1.z(), v2.z()));
649 }
650 
651 /// @brief Return a vector with the exponent applied to each of
652 /// the components of the input vector.
653 template <typename T>
654 inline Vec3<T> Exp(Vec3<T> v) { return v.exp(); }
655 
656 /// @brief Return a vector with log applied to each of
657 /// the components of the input vector.
658 template <typename T>
659 inline Vec3<T> Log(Vec3<T> v) { return v.log(); }
660 
665 
670 
671 } // namespace math
672 } // namespace OPENVDB_VERSION_NAME
673 } // namespace openvdb
674 
675 #endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
Vec3< T > Log(Vec3< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec3.h:659
#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:204
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:191
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:77
static unsigned numColumns()
Definition: Vec3.h:399
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:106
void orthonormalize(Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)
Definition: Vec3.h:599
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:38
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:74
static unsigned numRows()
Definition: Vec3.h:398
Real value_type
Definition: Vec3.h:26
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:540
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:374
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:466
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:276
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:110
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:523
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:615
const Vec3< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition: Vec3.h:241
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:381
T * asPointer()
Definition: Vec3.h:94
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:47
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:171
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:443
const Vec3< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec3.h:266
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:113
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:362
const Vec3< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec3.h:311
const Vec3< T > & exp()
Definition: Vec3.h:331
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:159
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_END
Definition: Platform.h:205
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:142
T & z()
Definition: Vec3.h:87
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:68
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:122
const T * asPointer() const
Definition: Vec3.h:95
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:101
Vec3< T > reversed() const
Return the vector (z, y, x)
Definition: Vec3.h:460
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:648
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:256
Real ValueType
Definition: Vec3.h:27
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:498
Definition: Tuple.h:29
Vec3< T > minComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec3.h:633
Vec3< T > Abs(const Vec3< T > &v)
Definition: Vec3.h:591
const Vec3< T > & log()
Definition: Vec3.h:341
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:85
static unsigned numElements()
Definition: Vec3.h:400
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:229
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:453
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:350
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:147
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:133
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:481
Definition: Mat.h:165
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:23
T y() const
Definition: Vec3.h:91
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:220
Definition: Exceptions.h:13
const Vec3< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec3.h:286
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:181
ValueT value
Definition: GridBuilder.h:1290
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:414
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:404
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:473
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:105
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition: Vec3.h:391
Vec3< T > maxComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec3.h:643
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:321
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition: Vec3.h:35
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition: Vec3.h:450
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition: Vec3.h:57
static Vec3< T > ones()
Definition: Vec3.h:467
bool isApproxEqual(const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)
Definition: Vec3.h:582
T lengthSqr() const
Definition: Vec3.h:211
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:654
T product() const
Return the product of all the vector components.
Definition: Vec3.h:356
T z() const
Definition: Vec3.h:92
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h.in:121
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:98
T & y()
Definition: Vec3.h:86
Definition: Exceptions.h:56
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:558
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:90
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:301
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:425
T length() const
Length of the vector.
Definition: Vec3.h:200
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h.in:212
T angle(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Vec3.h:568
#define OPENVDB_IS_POD(Type)
Definition: Math.h:56