OpenVDB  8.1.1
Vec2.h
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1 // Copyright Contributors to the OpenVDB Project
2 // SPDX-License-Identifier: MPL-2.0
3 
4 #ifndef OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED
5 #define OPENVDB_MATH_VEC2_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 Mat2;
21 
22 template<typename T>
23 class Vec2: public Tuple<2, T>
24 {
25 public:
26  using value_type = T;
27  using ValueType = T;
28 
30 #if OPENVDB_ABI_VERSION_NUMBER >= 8
31  Vec2() = default;
34 #else
35  Vec2() {}
36 #endif
37 
39  explicit Vec2(T val) { this->mm[0] = this->mm[1] = val; }
40 
42  Vec2(T x, T y)
43  {
44  this->mm[0] = x;
45  this->mm[1] = y;
46  }
47 
49  template <typename Source>
50  Vec2(Source *a)
51  {
52  this->mm[0] = static_cast<T>(a[0]);
53  this->mm[1] = static_cast<T>(a[1]);
54  } // trivial
55 
57  template<typename Source>
58  explicit Vec2(const Tuple<2, Source> &t)
59  {
60  this->mm[0] = static_cast<T>(t[0]);
61  this->mm[1] = static_cast<T>(t[1]);
62  }
63 
67  template<typename Other>
68  explicit Vec2(Other val,
69  typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
70  {
71  this->mm[0] = this->mm[1] = static_cast<T>(val);
72  }
73 
75  T& x() {return this->mm[0];}
76  T& y() {return this->mm[1];}
77 
79  T x() const {return this->mm[0];}
80  T y() const {return this->mm[1];}
81 
83  T& operator()(int i) {return this->mm[i];}
84 
86  T operator()(int i) const {return this->mm[i];}
87 
88  T* asPointer() {return this->mm;}
89  const T* asPointer() const {return this->mm;}
90 
93  const Vec2<T>& init(T x=0, T y=0)
94  {
95  this->mm[0] = x; this->mm[1] = y;
96  return *this;
97  }
98 
100  const Vec2<T>& setZero()
101  {
102  this->mm[0] = 0; this->mm[1] = 0;
103  return *this;
104  }
105 
107  template<typename Source>
108  const Vec2<T>& operator=(const Vec2<Source> &v)
109  {
110  // note: don't static_cast because that suppresses warnings
111  this->mm[0] = v[0];
112  this->mm[1] = v[1];
113 
114  return *this;
115  }
116 
118  bool operator==(const Vec2<T> &v) const
119  {
120  return (isExactlyEqual(this->mm[0], v.mm[0]) && isExactlyEqual(this->mm[1], v.mm[1]));
121  }
122 
124  bool operator!=(const Vec2<T> &v) const { return !(*this==v); }
125 
127  bool eq(const Vec2<T> &v, T eps = static_cast<T>(1.0e-7)) const
128  {
129  return isApproxEqual(this->mm[0], v.mm[0], eps) &&
130  isApproxEqual(this->mm[1], v.mm[1], eps);
131  } // trivial
132 
134  Vec2<T> operator-() const {return Vec2<T>(-this->mm[0], -this->mm[1]);}
135 
138  template <typename T0, typename T1>
139  const Vec2<T>& add(const Vec2<T0> &v1, const Vec2<T1> &v2)
140  {
141  this->mm[0] = v1[0] + v2[0];
142  this->mm[1] = v1[1] + v2[1];
143 
144  return *this;
145  }
146 
149  template <typename T0, typename T1>
150  const Vec2<T>& sub(const Vec2<T0> &v1, const Vec2<T1> &v2)
151  {
152  this->mm[0] = v1[0] - v2[0];
153  this->mm[1] = v1[1] - v2[1];
154 
155  return *this;
156  }
157 
160  template <typename T0, typename T1>
161  const Vec2<T>& scale(T0 scalar, const Vec2<T1> &v)
162  {
163  this->mm[0] = scalar * v[0];
164  this->mm[1] = scalar * v[1];
165 
166  return *this;
167  }
168 
169  template <typename T0, typename T1>
170  const Vec2<T> &div(T0 scalar, const Vec2<T1> &v)
171  {
172  this->mm[0] = v[0] / scalar;
173  this->mm[1] = v[1] / scalar;
174 
175  return *this;
176  }
177 
179  T dot(const Vec2<T> &v) const { return this->mm[0]*v[0] + this->mm[1]*v[1]; } // trivial
180 
182  T length() const
183  {
184  return static_cast<T>(sqrt(double(this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1])));
185  }
186 
189  T lengthSqr() const { return (this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1]); }
190 
193  inline const Vec2<T>& exp()
194  {
195  this->mm[0] = std::exp(this->mm[0]);
196  this->mm[1] = std::exp(this->mm[1]);
197  return *this;
198  }
199 
202  inline const Vec2<T>& log()
203  {
204  this->mm[0] = std::log(this->mm[0]);
205  this->mm[1] = std::log(this->mm[1]);
206  return *this;
207  }
208 
210  inline T sum() const
211  {
212  return this->mm[0] + this->mm[1];
213  }
214 
216  inline T product() const
217  {
218  return this->mm[0] * this->mm[1];
219  }
220 
222  bool normalize(T eps = static_cast<T>(1.0e-8))
223  {
224  T d = length();
225  if (isApproxEqual(d, T(0), eps)) {
226  return false;
227  }
228  *this *= (T(1) / d);
229  return true;
230  }
231 
233  Vec2<T> unit(T eps=0) const
234  {
235  T d;
236  return unit(eps, d);
237  }
238 
240  Vec2<T> unit(T eps, T& len) const
241  {
242  len = length();
243  if (isApproxEqual(len, T(0), eps)) {
244  OPENVDB_THROW(ArithmeticError, "Normalizing null 2-vector");
245  }
246  return *this / len;
247  }
248 
251  {
252  T l2 = lengthSqr();
253  return l2 ? *this/static_cast<T>(sqrt(l2)) : Vec2<T>(1,0);
254  }
255 
257  template <typename S>
258  const Vec2<T> &operator*=(S scalar)
259  {
260  this->mm[0] *= scalar;
261  this->mm[1] *= scalar;
262  return *this;
263  }
264 
266  template <typename S>
267  const Vec2<T> &operator*=(const Vec2<S> &v1)
268  {
269  this->mm[0] *= v1[0];
270  this->mm[1] *= v1[1];
271  return *this;
272  }
273 
275  template <typename S>
276  const Vec2<T> &operator/=(S scalar)
277  {
278  this->mm[0] /= scalar;
279  this->mm[1] /= scalar;
280  return *this;
281  }
282 
284  template <typename S>
285  const Vec2<T> &operator/=(const Vec2<S> &v1)
286  {
287  this->mm[0] /= v1[0];
288  this->mm[1] /= v1[1];
289  return *this;
290  }
291 
293  template <typename S>
294  const Vec2<T> &operator+=(S scalar)
295  {
296  this->mm[0] += scalar;
297  this->mm[1] += scalar;
298  return *this;
299  }
300 
302  template <typename S>
303  const Vec2<T> &operator+=(const Vec2<S> &v1)
304  {
305  this->mm[0] += v1[0];
306  this->mm[1] += v1[1];
307  return *this;
308  }
309 
311  template <typename S>
312  const Vec2<T> &operator-=(S scalar)
313  {
314  this->mm[0] -= scalar;
315  this->mm[1] -= scalar;
316  return *this;
317  }
318 
320  template <typename S>
321  const Vec2<T> &operator-=(const Vec2<S> &v1)
322  {
323  this->mm[0] -= v1[0];
324  this->mm[1] -= v1[1];
325  return *this;
326  }
327 
328  // Number of cols, rows, elements
329  static unsigned numRows() { return 1; }
330  static unsigned numColumns() { return 2; }
331  static unsigned numElements() { return 2; }
332 
335  T component(const Vec2<T> &onto, T eps = static_cast<T>(1.0e-8)) const
336  {
337  T l = onto.length();
338  if (isApproxEqual(l, T(0), eps)) return 0;
339 
340  return dot(onto)*(T(1)/l);
341  }
342 
345  Vec2<T> projection(const Vec2<T> &onto, T eps = static_cast<T>(1.0e-8)) const
346  {
347  T l = onto.lengthSqr();
348  if (isApproxEqual(l, T(0), eps)) return Vec2::zero();
349 
350  return onto*(dot(onto)*(T(1)/l));
351  }
352 
356  Vec2<T> getArbPerpendicular() const { return Vec2<T>(-this->mm[1], this->mm[0]); }
357 
359  static Vec2<T> zero() { return Vec2<T>(0, 0); }
360  static Vec2<T> ones() { return Vec2<T>(1, 1); }
361 };
362 
364 template <typename S, typename T>
366 {
367  return v * scalar;
368 }
369 
371 template <typename S, typename T>
373 {
375  result *= scalar;
376  return result;
377 }
378 
380 template <typename T0, typename T1>
382 {
383  Vec2<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1]);
384  return result;
385 }
386 
388 template <typename S, typename T>
390 {
391  return Vec2<typename promote<S, T>::type>(scalar/v[0], scalar/v[1]);
392 }
393 
395 template <typename S, typename T>
397 {
399  result /= scalar;
400  return result;
401 }
402 
404 template <typename T0, typename T1>
406 {
407  Vec2<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1]);
408  return result;
409 }
410 
412 template <typename T0, typename T1>
414 {
416  result += v1;
417  return result;
418 }
419 
421 template <typename S, typename T>
423 {
425  result += scalar;
426  return result;
427 }
428 
430 template <typename T0, typename T1>
432 {
434  result -= v1;
435  return result;
436 }
437 
439 template <typename S, typename T>
441 {
443  result -= scalar;
444  return result;
445 }
446 
449 template <typename T>
450 inline T angle(const Vec2<T> &v1, const Vec2<T> &v2)
451 {
452  T c = v1.dot(v2);
453  return acos(c);
454 }
455 
456 template <typename T>
457 inline bool
458 isApproxEqual(const Vec2<T>& a, const Vec2<T>& b)
459 {
460  return a.eq(b);
461 }
462 template <typename T>
463 inline bool
464 isApproxEqual(const Vec2<T>& a, const Vec2<T>& b, const Vec2<T>& eps)
465 {
466  return isApproxEqual(a.x(), b.x(), eps.x()) &&
467  isApproxEqual(a.y(), b.y(), eps.y());
468 }
469 
470 template<typename T>
471 inline Vec2<T>
472 Abs(const Vec2<T>& v)
473 {
474  return Vec2<T>(Abs(v[0]), Abs(v[1]));
475 }
476 
479 template <typename T>
480 inline void orthonormalize(Vec2<T> &v1, Vec2<T> &v2)
481 {
482  // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
483  // orthonormalization produces vectors u0, u1, and u2 as follows,
484  //
485  // u0 = v0/|v0|
486  // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
487  //
488  // where |A| indicates length of vector A and A*B indicates dot
489  // product of vectors A and B.
490 
491  // compute u0
492  v1.normalize();
493 
494  // compute u1
495  T d0 = v1.dot(v2);
496  v2 -= v1*d0;
497  v2.normalize();
498 }
499 
500 
505 
507 template <typename T>
508 inline Vec2<T> minComponent(const Vec2<T> &v1, const Vec2<T> &v2)
509 {
510  return Vec2<T>(
511  std::min(v1.x(), v2.x()),
512  std::min(v1.y(), v2.y()));
513 }
514 
516 template <typename T>
517 inline Vec2<T> maxComponent(const Vec2<T> &v1, const Vec2<T> &v2)
518 {
519  return Vec2<T>(
520  std::max(v1.x(), v2.x()),
521  std::max(v1.y(), v2.y()));
522 }
523 
526 template <typename T>
527 inline Vec2<T> Exp(Vec2<T> v) { return v.exp(); }
528 
531 template <typename T>
532 inline Vec2<T> Log(Vec2<T> v) { return v.log(); }
533 
538 
539 #if OPENVDB_ABI_VERSION_NUMBER >= 8
544 #endif
545 
546 } // namespace math
547 } // namespace OPENVDB_VERSION_NAME
548 } // namespace openvdb
549 
550 #endif // OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED
Vec2< T > projection(const Vec2< T > &onto, T eps=static_cast< T >(1.0e-8)) const
Definition: Vec2.h:345
Vec2< T > getArbPerpendicular() const
Definition: Vec2.h:356
Definition: Vec2.h:23
Vec2< typename promote< T0, T1 >::type > operator/(const Vec2< T0 > &v0, const Vec2< T1 > &v1)
Divide corresponding elements of v0 and v1 and return the result.
Definition: Vec2.h:405
static unsigned numElements()
Definition: Vec2.h:331
static unsigned numColumns()
Definition: Vec2.h:330
T mm[SIZE]
Definition: Tuple.h:179
#define OPENVDB_THROW(exception, message)
Definition: openvdb/Exceptions.h:74
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:670
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
const Vec2< T > & init(T x=0, T y=0)
Definition: Vec2.h:93
T length() const
Length of the vector.
Definition: Vec2.h:182
T & y()
Definition: Vec2.h:76
const Vec2< T > & exp()
Definition: Vec2.h:193
T component(const Vec2< T > &onto, T eps=static_cast< T >(1.0e-8)) const
Definition: Vec2.h:335
static Vec2< T > zero()
Predefined constants, e.g. Vec2f v = Vec2f::xNegAxis();.
Definition: Vec2.h:359
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec2.h:86
Vec2< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec2.h:233
Vec2< T > minComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec2.h:508
Definition: Vec2.h:20
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:444
T ValueType
Definition: Vec2.h:27
bool operator!=(const Vec2< T > &v) const
Inequality operator, does exact floating point comparisons.
Definition: Vec2.h:124
const Vec2< T > & scale(T0 scalar, const Vec2< T1 > &v)
Definition: Vec2.h:161
const Vec2< T > & operator/=(const Vec2< S > &v1)
Divide each element of this vector by the corresponding element of the given vector.
Definition: Vec2.h:285
Vec2< T > unitSafe() const
return normalized this, or (1, 0) if this is null vector
Definition: Vec2.h:250
Vec2< typename promote< S, T >::type > operator+(const Vec2< T > &v, S scalar)
Add scalar to each element of the given vector and return the result.
Definition: Vec2.h:422
static Vec2< T > ones()
Definition: Vec2.h:360
bool operator==(const Vec2< T > &v) const
Equality operator, does exact floating point comparisons.
Definition: Vec2.h:118
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:107
Vec2(T x, T y)
Constructor with two arguments, e.g. Vec2f v(1,2,3);.
Definition: Vec2.h:42
const T * asPointer() const
Definition: Vec2.h:89
const Vec2< T > & setZero()
Set "this" vector to zero.
Definition: Vec2.h:100
Vec2< T > maxComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec2.h:517
Vec2< typename promote< S, T >::type > operator-(const Vec2< T > &v, S scalar)
Subtract scalar from each element of the given vector and return the result.
Definition: Vec2.h:440
T y() const
Definition: Vec2.h:80
const Vec2< T > & operator-=(const Vec2< S > &v1)
Subtract each element of the given vector from the corresponding element of this vector.
Definition: Vec2.h:321
Vec2< T > Log(Vec2< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec2.h:532
const Vec2< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec2.h:276
Vec2(Source *a)
Constructor with array argument, e.g. float a[2]; Vec2f v(a);.
Definition: Vec2.h:50
Definition: openvdb/Exceptions.h:13
T lengthSqr() const
Definition: Vec2.h:189
static unsigned numRows()
Definition: Vec2.h:329
T value_type
Definition: Vec2.h:26
Definition: Tuple.h:29
bool normalize(T eps=static_cast< T >(1.0e-8))
this = normalized this
Definition: Vec2.h:222
T product() const
Return the product of all the vector components.
Definition: Vec2.h:216
const Vec2< T > & operator+=(const Vec2< S > &v1)
Add each element of the given vector to the corresponding element of this vector. ...
Definition: Vec2.h:303
Vec2(const Tuple< 2, Source > &t)
Conversion constructor.
Definition: Vec2.h:58
const Vec2< T > & add(const Vec2< T0 > &v1, const Vec2< T1 > &v2)
Definition: Vec2.h:139
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:23
const Vec2< T > & operator*=(const Vec2< S > &v1)
Multiply each element of this vector by the corresponding element of the given vector.
Definition: Vec2.h:267
const Vec2< T > & operator=(const Vec2< Source > &v)
Assignment operator.
Definition: Vec2.h:108
Vec2< typename promote< T0, T1 >::type > operator*(const Vec2< T0 > &v0, const Vec2< T1 > &v1)
Multiply corresponding elements of v0 and v1 and return the result.
Definition: Vec2.h:381
T * asPointer()
Definition: Vec2.h:88
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:450
bool eq(const Vec2< 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: Vec2.h:127
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec2.h:75
bool isApproxEqual(const Vec2< T > &a, const Vec2< T > &b, const Vec2< T > &eps)
Definition: Vec2.h:464
Vec2(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: Vec2.h:68
const Vec2< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec2.h:312
Vec2< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec2.h:134
Vec2< T > Abs(const Vec2< T > &v)
Definition: Vec2.h:472
void orthonormalize(Vec2< T > &v1, Vec2< T > &v2)
Definition: Vec2.h:480
Vec2< T > Exp(Vec2< T > v)
Return a vector with the exponent applied to each of the components of the input vector.
Definition: Vec2.h:527
const Vec2< T > & div(T0 scalar, const Vec2< T1 > &v)
Definition: Vec2.h:170
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:103
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h.in:116
const Vec2< T > & sub(const Vec2< T0 > &v1, const Vec2< T1 > &v2)
Definition: Vec2.h:150
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec2.h:83
T dot(const Vec2< T > &v) const
Dot product.
Definition: Vec2.h:179
const Vec2< T > & log()
Definition: Vec2.h:202
const Vec2< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec2.h:294
Vec2< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec2.h:240
Vec2(T val)
Construct a vector all of whose components have the given value.
Definition: Vec2.h:39
const Vec2< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition: Vec2.h:258
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec2.h:79
T sum() const
Return the sum of all the vector components.
Definition: Vec2.h:210
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h.in:178
Definition: openvdb/Exceptions.h:56
#define OPENVDB_IS_POD(Type)
Definition: Math.h:55