OpenVDB  7.0.0
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  Vec2() {}
31 
33  explicit Vec2(T val) { this->mm[0] = this->mm[1] = val; }
34 
36  Vec2(T x, T y)
37  {
38  this->mm[0] = x;
39  this->mm[1] = y;
40  }
41 
43  template <typename Source>
44  Vec2(Source *a)
45  {
46  this->mm[0] = static_cast<T>(a[0]);
47  this->mm[1] = static_cast<T>(a[1]);
48  } // trivial
49 
51  template<typename Source>
52  explicit Vec2(const Tuple<2, Source> &t)
53  {
54  this->mm[0] = static_cast<T>(t[0]);
55  this->mm[1] = static_cast<T>(t[1]);
56  }
57 
61  template<typename Other>
62  explicit Vec2(Other val,
63  typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
64  {
65  this->mm[0] = this->mm[1] = static_cast<T>(val);
66  }
67 
69  T& x() {return this->mm[0];}
70  T& y() {return this->mm[1];}
71 
73  T x() const {return this->mm[0];}
74  T y() const {return this->mm[1];}
75 
77  T& operator()(int i) {return this->mm[i];}
78 
80  T operator()(int i) const {return this->mm[i];}
81 
82  T* asPointer() {return this->mm;}
83  const T* asPointer() const {return this->mm;}
84 
87  const Vec2<T>& init(T x=0, T y=0)
88  {
89  this->mm[0] = x; this->mm[1] = y;
90  return *this;
91  }
92 
94  const Vec2<T>& setZero()
95  {
96  this->mm[0] = 0; this->mm[1] = 0;
97  return *this;
98  }
99 
101  template<typename Source>
102  const Vec2<T>& operator=(const Vec2<Source> &v)
103  {
104  // note: don't static_cast because that suppresses warnings
105  this->mm[0] = v[0];
106  this->mm[1] = v[1];
107 
108  return *this;
109  }
110 
112  bool operator==(const Vec2<T> &v) const
113  {
114  return (isExactlyEqual(this->mm[0], v.mm[0]) && isExactlyEqual(this->mm[1], v.mm[1]));
115  }
116 
118  bool operator!=(const Vec2<T> &v) const { return !(*this==v); }
119 
121  bool eq(const Vec2<T> &v, T eps = static_cast<T>(1.0e-7)) const
122  {
123  return isApproxEqual(this->mm[0], v.mm[0], eps) &&
124  isApproxEqual(this->mm[1], v.mm[1], eps);
125  } // trivial
126 
128  Vec2<T> operator-() const {return Vec2<T>(-this->mm[0], -this->mm[1]);}
129 
132  template <typename T0, typename T1>
133  const Vec2<T>& add(const Vec2<T0> &v1, const Vec2<T1> &v2)
134  {
135  this->mm[0] = v1[0] + v2[0];
136  this->mm[1] = v1[1] + v2[1];
137 
138  return *this;
139  }
140 
143  template <typename T0, typename T1>
144  const Vec2<T>& sub(const Vec2<T0> &v1, const Vec2<T1> &v2)
145  {
146  this->mm[0] = v1[0] - v2[0];
147  this->mm[1] = v1[1] - v2[1];
148 
149  return *this;
150  }
151 
154  template <typename T0, typename T1>
155  const Vec2<T>& scale(T0 scalar, const Vec2<T1> &v)
156  {
157  this->mm[0] = scalar * v[0];
158  this->mm[1] = scalar * v[1];
159 
160  return *this;
161  }
162 
163  template <typename T0, typename T1>
164  const Vec2<T> &div(T0 scalar, const Vec2<T1> &v)
165  {
166  this->mm[0] = v[0] / scalar;
167  this->mm[1] = v[1] / scalar;
168 
169  return *this;
170  }
171 
173  T dot(const Vec2<T> &v) const { return this->mm[0]*v[0] + this->mm[1]*v[1]; } // trivial
174 
176  T length() const
177  {
178  return static_cast<T>(sqrt(double(this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1])));
179  }
180 
183  T lengthSqr() const { return (this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1]); }
184 
187  inline const Vec2<T>& exp()
188  {
189  this->mm[0] = std::exp(this->mm[0]);
190  this->mm[1] = std::exp(this->mm[1]);
191  return *this;
192  }
193 
196  inline const Vec2<T>& log()
197  {
198  this->mm[0] = std::log(this->mm[0]);
199  this->mm[1] = std::log(this->mm[1]);
200  return *this;
201  }
202 
204  inline T sum() const
205  {
206  return this->mm[0] + this->mm[1];
207  }
208 
210  inline T product() const
211  {
212  return this->mm[0] * this->mm[1];
213  }
214 
216  bool normalize(T eps = static_cast<T>(1.0e-8))
217  {
218  T d = length();
219  if (isApproxEqual(d, T(0), eps)) {
220  return false;
221  }
222  *this *= (T(1) / d);
223  return true;
224  }
225 
227  Vec2<T> unit(T eps=0) const
228  {
229  T d;
230  return unit(eps, d);
231  }
232 
234  Vec2<T> unit(T eps, T& len) const
235  {
236  len = length();
237  if (isApproxEqual(len, T(0), eps)) {
238  OPENVDB_THROW(ArithmeticError, "Normalizing null 2-vector");
239  }
240  return *this / len;
241  }
242 
245  {
246  T l2 = lengthSqr();
247  return l2 ? *this/static_cast<T>(sqrt(l2)) : Vec2<T>(1,0);
248  }
249 
251  template <typename S>
252  const Vec2<T> &operator*=(S scalar)
253  {
254  this->mm[0] *= scalar;
255  this->mm[1] *= scalar;
256  return *this;
257  }
258 
260  template <typename S>
261  const Vec2<T> &operator*=(const Vec2<S> &v1)
262  {
263  this->mm[0] *= v1[0];
264  this->mm[1] *= v1[1];
265  return *this;
266  }
267 
269  template <typename S>
270  const Vec2<T> &operator/=(S scalar)
271  {
272  this->mm[0] /= scalar;
273  this->mm[1] /= scalar;
274  return *this;
275  }
276 
278  template <typename S>
279  const Vec2<T> &operator/=(const Vec2<S> &v1)
280  {
281  this->mm[0] /= v1[0];
282  this->mm[1] /= v1[1];
283  return *this;
284  }
285 
287  template <typename S>
288  const Vec2<T> &operator+=(S scalar)
289  {
290  this->mm[0] += scalar;
291  this->mm[1] += scalar;
292  return *this;
293  }
294 
296  template <typename S>
297  const Vec2<T> &operator+=(const Vec2<S> &v1)
298  {
299  this->mm[0] += v1[0];
300  this->mm[1] += v1[1];
301  return *this;
302  }
303 
305  template <typename S>
306  const Vec2<T> &operator-=(S scalar)
307  {
308  this->mm[0] -= scalar;
309  this->mm[1] -= scalar;
310  return *this;
311  }
312 
314  template <typename S>
315  const Vec2<T> &operator-=(const Vec2<S> &v1)
316  {
317  this->mm[0] -= v1[0];
318  this->mm[1] -= v1[1];
319  return *this;
320  }
321 
322  // Number of cols, rows, elements
323  static unsigned numRows() { return 1; }
324  static unsigned numColumns() { return 2; }
325  static unsigned numElements() { return 2; }
326 
329  T component(const Vec2<T> &onto, T eps = static_cast<T>(1.0e-8)) const
330  {
331  T l = onto.length();
332  if (isApproxEqual(l, T(0), eps)) return 0;
333 
334  return dot(onto)*(T(1)/l);
335  }
336 
339  Vec2<T> projection(const Vec2<T> &onto, T eps = static_cast<T>(1.0e-8)) const
340  {
341  T l = onto.lengthSqr();
342  if (isApproxEqual(l, T(0), eps)) return Vec2::zero();
343 
344  return onto*(dot(onto)*(T(1)/l));
345  }
346 
350  Vec2<T> getArbPerpendicular() const { return Vec2<T>(-this->mm[1], this->mm[0]); }
351 
353  static Vec2<T> zero() { return Vec2<T>(0, 0); }
354  static Vec2<T> ones() { return Vec2<T>(1, 1); }
355 };
356 
357 
359 template <typename S, typename T>
361 {
362  return v * scalar;
363 }
364 
366 template <typename S, typename T>
368 {
370  result *= scalar;
371  return result;
372 }
373 
375 template <typename T0, typename T1>
377 {
378  Vec2<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1]);
379  return result;
380 }
381 
383 template <typename S, typename T>
385 {
386  return Vec2<typename promote<S, T>::type>(scalar/v[0], scalar/v[1]);
387 }
388 
390 template <typename S, typename T>
392 {
394  result /= scalar;
395  return result;
396 }
397 
399 template <typename T0, typename T1>
401 {
402  Vec2<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1]);
403  return result;
404 }
405 
407 template <typename T0, typename T1>
409 {
411  result += v1;
412  return result;
413 }
414 
416 template <typename S, typename T>
418 {
420  result += scalar;
421  return result;
422 }
423 
425 template <typename T0, typename T1>
427 {
429  result -= v1;
430  return result;
431 }
432 
434 template <typename S, typename T>
436 {
438  result -= scalar;
439  return result;
440 }
441 
444 template <typename T>
445 inline T angle(const Vec2<T> &v1, const Vec2<T> &v2)
446 {
447  T c = v1.dot(v2);
448  return acos(c);
449 }
450 
451 template <typename T>
452 inline bool
453 isApproxEqual(const Vec2<T>& a, const Vec2<T>& b)
454 {
455  return a.eq(b);
456 }
457 template <typename T>
458 inline bool
459 isApproxEqual(const Vec2<T>& a, const Vec2<T>& b, const Vec2<T>& eps)
460 {
461  return isApproxEqual(a.x(), b.x(), eps.x()) &&
462  isApproxEqual(a.y(), b.y(), eps.y());
463 }
464 
465 template<typename T>
466 inline Vec2<T>
467 Abs(const Vec2<T>& v)
468 {
469  return Vec2<T>(Abs(v[0]), Abs(v[1]));
470 }
471 
474 template <typename T>
475 inline void orthonormalize(Vec2<T> &v1, Vec2<T> &v2)
476 {
477  // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
478  // orthonormalization produces vectors u0, u1, and u2 as follows,
479  //
480  // u0 = v0/|v0|
481  // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
482  //
483  // where |A| indicates length of vector A and A*B indicates dot
484  // product of vectors A and B.
485 
486  // compute u0
487  v1.normalize();
488 
489  // compute u1
490  T d0 = v1.dot(v2);
491  v2 -= v1*d0;
492  v2.normalize();
493 }
494 
495 
500 
502 template <typename T>
503 inline Vec2<T> minComponent(const Vec2<T> &v1, const Vec2<T> &v2)
504 {
505  return Vec2<T>(
506  std::min(v1.x(), v2.x()),
507  std::min(v1.y(), v2.y()));
508 }
509 
511 template <typename T>
512 inline Vec2<T> maxComponent(const Vec2<T> &v1, const Vec2<T> &v2)
513 {
514  return Vec2<T>(
515  std::max(v1.x(), v2.x()),
516  std::max(v1.y(), v2.y()));
517 }
518 
521 template <typename T>
522 inline Vec2<T> Exp(Vec2<T> v) { return v.exp(); }
523 
526 template <typename T>
527 inline Vec2<T> Log(Vec2<T> v) { return v.log(); }
528 
533 
534 } // namespace math
535 } // namespace OPENVDB_VERSION_NAME
536 } // namespace openvdb
537 
538 #endif // OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED
T lengthSqr() const
Definition: Vec2.h:183
Vec2(T x, T y)
Constructor with two arguments, e.g. Vec2f v(1,2,3);.
Definition: Vec2.h:36
const T * asPointer() const
Definition: Vec2.h:83
T value_type
Definition: Vec2.h:26
T y() const
Definition: Vec2.h:74
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:315
Definition: Tuple.h:28
Vec2(Source *a)
Constructor with array argument, e.g. float a[2]; Vec2f v(a);.
Definition: Vec2.h:44
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:297
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
static unsigned numRows()
Definition: Vec2.h:323
const Vec2< T > & add(const Vec2< T0 > &v1, const Vec2< T1 > &v2)
Definition: Vec2.h:133
Vec2< T > maxComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec2.h:512
T product() const
Return the product of all the vector components.
Definition: Vec2.h:210
bool normalize(T eps=static_cast< T >(1.0e-8))
this = normalized this
Definition: Vec2.h:216
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:400
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:82
T * asPointer()
Definition: Vec2.h:82
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:121
Definition: Vec2.h:20
Vec2(const Tuple< 2, Source > &t)
Conversion constructor.
Definition: Vec2.h:52
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:62
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:261
const Vec2< T > & operator=(const Vec2< Source > &v)
Assignment operator.
Definition: Vec2.h:102
const Vec2< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec2.h:306
Definition: Vec2.h:23
bool isApproxEqual(const Vec2< T > &a, const Vec2< T > &b, const Vec2< T > &eps)
Definition: Vec2.h:459
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec2.h:69
const Vec2< T > & div(T0 scalar, const Vec2< T1 > &v)
Definition: Vec2.h:164
Vec2< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec2.h:128
const Vec2< T > & log()
Definition: Vec2.h:196
Vec2(T val)
Construct a vector all of whose components have the given value.
Definition: Vec2.h:33
T mm[SIZE]
Definition: Tuple.h:170
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec2.h:73
T sum() const
Return the sum of all the vector components.
Definition: Vec2.h:204
const Vec2< T > & sub(const Vec2< T0 > &v1, const Vec2< T1 > &v2)
Definition: Vec2.h:144
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:102
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec2.h:77
T dot(const Vec2< T > &v) const
Dot product.
Definition: Vec2.h:173
Vec2< T > projection(const Vec2< T > &onto, T eps=static_cast< T >(1.0e-8)) const
Definition: Vec2.h:339
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:22
Vec2< T > getArbPerpendicular() const
Definition: Vec2.h:350
const Vec2< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec2.h:288
Vec2< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec2.h:234
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:376
const Vec2< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition: Vec2.h:252
Vec2< T > Log(Vec2< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec2.h:527
static unsigned numColumns()
Definition: Vec2.h:324
Definition: Exceptions.h:13
Definition: Exceptions.h:56
T length() const
Length of the vector.
Definition: Vec2.h:176
static unsigned numElements()
Definition: Vec2.h:325
T & y()
Definition: Vec2.h:70
T component(const Vec2< T > &onto, T eps=static_cast< T >(1.0e-8)) const
Definition: Vec2.h:329
void orthonormalize(Vec2< T > &v1, Vec2< T > &v2)
Definition: Vec2.h:475
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
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:435
const Vec2< T > & init(T x=0, T y=0)
Definition: Vec2.h:87
T ValueType
Definition: Vec2.h:27
const Vec2< T > & exp()
Definition: Vec2.h:187
static Vec2< T > zero()
Predefined constants, e.g. Vec2f v = Vec2f::xNegAxis();.
Definition: Vec2.h:353
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:522
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec2.h:80
Vec2< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec2.h:227
bool operator!=(const Vec2< T > &v) const
Inequality operator, does exact floating point comparisons.
Definition: Vec2.h:118
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:102
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:445
Vec2< T > Abs(const Vec2< T > &v)
Definition: Vec2.h:467
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:279
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
static Vec2< T > ones()
Definition: Vec2.h:354
bool operator==(const Vec2< T > &v) const
Equality operator, does exact floating point comparisons.
Definition: Vec2.h:112
const Vec2< T > & scale(T0 scalar, const Vec2< T1 > &v)
Definition: Vec2.h:155
Vec2()
Trivial constructor, the vector is NOT initialized.
Definition: Vec2.h:30
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:417
const Vec2< T > & setZero()
Set "this" vector to zero.
Definition: Vec2.h:94
Vec2< T > minComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec2.h:503
Vec2< T > unitSafe() const
return normalized this, or (1, 0) if this is null vector
Definition: Vec2.h:244
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:106
const Vec2< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec2.h:270