OpenVDB: Vec2.h Source File

OpenVDB 4.0.2

Vec2.h
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1 //
3 // Copyright (c) 2012-2017 DreamWorks Animation LLC
4 //
5 // All rights reserved. This software is distributed under the
6 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
7 //
8 // Redistributions of source code must retain the above copyright
9 // and license notice and the following restrictions and disclaimer.
10 //
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14 //
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28 //
30
31 #ifndef OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED
32 #define OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED
33
34 #include <openvdb/Exceptions.h>
35 #include "Math.h"
36 #include "Tuple.h"
37 #include <cmath>
38 #include <type_traits>
39
40
41 namespace openvdb {
42 OPENVDB_USE_VERSION_NAMESPACE
43 namespace OPENVDB_VERSION_NAME {
44 namespace math {
45
46 template<typename T> class Mat2;
47
48 template<typename T>
49 class Vec2: public Tuple<2, T>
50 {
51 public:
52 typedef T value_type;
53 typedef T ValueType;
54
56 Vec2() {}
57
59 explicit Vec2(T val) { this->mm[0] = this->mm[1] = val; }
60
62 Vec2(T x, T y)
63 {
64 this->mm[0] = x;
65 this->mm[1] = y;
66 }
67
69 template <typename Source>
70 Vec2(Source *a)
71 {
72 this->mm[0] = a[0];
73 this->mm[1] = a[1];
74 } // trivial
75
77 template<typename Source>
78 explicit Vec2(const Tuple<2, Source> &t)
79 {
80 this->mm[0] = static_cast<T>(t[0]);
81 this->mm[1] = static_cast<T>(t[1]);
82 }
83
87 template<typename Other>
88 explicit Vec2(Other val,
89 typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
90 {
91 this->mm[0] = this->mm[1] = static_cast<T>(val);
92 }
93
95 T& x() {return this->mm[0];}
96 T& y() {return this->mm[1];}
97
99 T x() const {return this->mm[0];}
100 T y() const {return this->mm[1];}
101
103 T& operator()(int i) {return this->mm[i];}
104
106 T operator()(int i) const {return this->mm[i];}
107
108 T* asPointer() {return this->mm;}
109 const T* asPointer() const {return this->mm;}
110
113 const Vec2<T>& init(T x=0, T y=0)
114 {
115 this->mm[0] = x; this->mm[1] = y;
116 return *this;
117 }
118
120 const Vec2<T>& setZero()
121 {
122 this->mm[0] = 0; this->mm[1] = 0;
123 return *this;
124 }
125
127 template<typename Source>
128 const Vec2<T>& operator=(const Vec2<Source> &v)
129 {
130 // note: don't static_cast because that suppresses warnings
131 this->mm[0] = v[0];
132 this->mm[1] = v[1];
133
134 return *this;
135 }
136
138 bool operator==(const Vec2<T> &v) const
139 {
140 return (isExactlyEqual(this->mm[0], v.mm[0]) && isExactlyEqual(this->mm[1], v.mm[1]));
141 }
142
144 bool operator!=(const Vec2<T> &v) const { return !(*this==v); }
145
147 bool eq(const Vec2<T> &v, T eps = static_cast<T>(1.0e-7)) const
148 {
149 return isApproxEqual(this->mm[0], v.mm[0], eps) &&
150 isApproxEqual(this->mm[1], v.mm[1], eps);
151 } // trivial
152
154 Vec2<T> operator-() const {return Vec2<T>(-this->mm[0], -this->mm[1]);}
155
158 template <typename T0, typename T1>
159 const Vec2<T>& add(const Vec2<T0> &v1, const Vec2<T1> &v2)
160 {
161 this->mm[0] = v1[0] + v2[0];
162 this->mm[1] = v1[1] + v2[1];
163
164 return *this;
165 }
166
169 template <typename T0, typename T1>
170 const Vec2<T>& sub(const Vec2<T0> &v1, const Vec2<T1> &v2)
171 {
172 this->mm[0] = v1[0] - v2[0];
173 this->mm[1] = v1[1] - v2[1];
174
175 return *this;
176 }
177
180 template <typename T0, typename T1>
181 const Vec2<T>& scale(T0 scalar, const Vec2<T1> &v)
182 {
183 this->mm[0] = scalar * v[0];
184 this->mm[1] = scalar * v[1];
185
186 return *this;
187 }
188
189 template <typename T0, typename T1>
190 const Vec2<T> &div(T0 scalar, const Vec2<T1> &v)
191 {
192 this->mm[0] = v[0] / scalar;
193 this->mm[1] = v[1] / scalar;
194
195 return *this;
196 }
197
199 T dot(const Vec2<T> &v) const { return this->mm[0]*v[0] + this->mm[1]*v[1]; } // trivial
200
202 T length() const
203 {
204 return static_cast<T>(sqrt(double(this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1])));
205 }
206
209 T lengthSqr() const { return (this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1]); }
210
213 inline const Vec2<T>& exp()
214 {
215 this->mm[0] = std::exp(this->mm[0]);
216 this->mm[1] = std::exp(this->mm[1]);
217 return *this;
218 }
219
222 inline const Vec2<T>& log()
223 {
224 this->mm[0] = std::log(this->mm[0]);
225 this->mm[1] = std::log(this->mm[1]);
226 return *this;
227 }
228
230 inline T sum() const
231 {
232 return this->mm[0] + this->mm[1];
233 }
234
236 inline T product() const
237 {
238 return this->mm[0] * this->mm[1];
239 }
240
242 bool normalize(T eps=1.0e-8)
243 {
244 T d = length();
245 if (isApproxEqual(d, T(0), eps)) {
246 return false;
247 }
248 *this *= (T(1) / d);
249 return true;
250 }
251
253 Vec2<T> unit(T eps=0) const
254 {
255 T d;
256 return unit(eps, d);
257 }
258
260 Vec2<T> unit(T eps, T& len) const
261 {
262 len = length();
263 if (isApproxEqual(len, T(0), eps)) {
264 OPENVDB_THROW(ArithmeticError, "Normalizing null 2-vector");
265 }
266 return *this / len;
267 }
268
270 Vec2<T> unitSafe() const
271 {
272 T l2 = lengthSqr();
273 return l2 ? *this/static_cast<T>(sqrt(l2)) : Vec2<T>(1,0);
274 }
275
277 template <typename S>
278 const Vec2<T> &operator*=(S scalar)
279 {
280 this->mm[0] *= scalar;
281 this->mm[1] *= scalar;
282 return *this;
283 }
284
286 template <typename S>
287 const Vec2<T> &operator*=(const Vec2<S> &v1)
288 {
289 this->mm[0] *= v1[0];
290 this->mm[1] *= v1[1];
291 return *this;
292 }
293
295 template <typename S>
296 const Vec2<T> &operator/=(S scalar)
297 {
298 this->mm[0] /= scalar;
299 this->mm[1] /= scalar;
300 return *this;
301 }
302
304 template <typename S>
305 const Vec2<T> &operator/=(const Vec2<S> &v1)
306 {
307 this->mm[0] /= v1[0];
308 this->mm[1] /= v1[1];
309 return *this;
310 }
311
313 template <typename S>
314 const Vec2<T> &operator+=(S scalar)
315 {
316 this->mm[0] += scalar;
317 this->mm[1] += scalar;
318 return *this;
319 }
320
322 template <typename S>
323 const Vec2<T> &operator+=(const Vec2<S> &v1)
324 {
325 this->mm[0] += v1[0];
326 this->mm[1] += v1[1];
327 return *this;
328 }
329
331 template <typename S>
332 const Vec2<T> &operator-=(S scalar)
333 {
334 this->mm[0] -= scalar;
335 this->mm[1] -= scalar;
336 return *this;
337 }
338
340 template <typename S>
341 const Vec2<T> &operator-=(const Vec2<S> &v1)
342 {
343 this->mm[0] -= v1[0];
344 this->mm[1] -= v1[1];
345 return *this;
346 }
347
348 // Number of cols, rows, elements
349 static unsigned numRows() { return 1; }
350 static unsigned numColumns() { return 2; }
351 static unsigned numElements() { return 2; }
352
355 T component(const Vec2<T> &onto, T eps=1.0e-8) const
356 {
357 T l = onto.length();
358 if (isApproxEqual(l, T(0), eps)) return 0;
359
360 return dot(onto)*(T(1)/l);
361 }
362
365 Vec2<T> projection(const Vec2<T> &onto, T eps=1.0e-8) const
366 {
367 T l = onto.lengthSqr();
368 if (isApproxEqual(l, T(0), eps)) return Vec2::zero();
369
370 return onto*(dot(onto)*(T(1)/l));
371 }
372
376 Vec2<T> getArbPerpendicular() const { return Vec2<T>(-this->mm[1], this->mm[0]); }
377
379 static Vec2<T> zero() { return Vec2<T>(0, 0); }
380 static Vec2<T> ones() { return Vec2<T>(1, 1); }
381 };
382
383
385 template <typename S, typename T>
386 inline Vec2<typename promote<S, T>::type> operator*(S scalar, const Vec2<T> &v)
387 {
388 return v * scalar;
389 }
390
392 template <typename S, typename T>
393 inline Vec2<typename promote<S, T>::type> operator*(const Vec2<T> &v, S scalar)
394 {
395 Vec2<typename promote<S, T>::type> result(v);
396 result *= scalar;
397 return result;
398 }
399
401 template <typename T0, typename T1>
402 inline Vec2<typename promote<T0, T1>::type> operator*(const Vec2<T0> &v0, const Vec2<T1> &v1)
403 {
404 Vec2<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1]);
405 return result;
406 }
407
409 template <typename S, typename T>
410 inline Vec2<typename promote<S, T>::type> operator/(S scalar, const Vec2<T> &v)
411 {
412 return Vec2<typename promote<S, T>::type>(scalar/v[0], scalar/v[1]);
413 }
414
416 template <typename S, typename T>
417 inline Vec2<typename promote<S, T>::type> operator/(const Vec2<T> &v, S scalar)
418 {
419 Vec2<typename promote<S, T>::type> result(v);
420 result /= scalar;
421 return result;
422 }
423
425 template <typename T0, typename T1>
426 inline Vec2<typename promote<T0, T1>::type> operator/(const Vec2<T0> &v0, const Vec2<T1> &v1)
427 {
428 Vec2<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1]);
429 return result;
430 }
431
433 template <typename T0, typename T1>
434 inline Vec2<typename promote<T0, T1>::type> operator+(const Vec2<T0> &v0, const Vec2<T1> &v1)
435 {
436 Vec2<typename promote<T0, T1>::type> result(v0);
437 result += v1;
438 return result;
439 }
440
442 template <typename S, typename T>
443 inline Vec2<typename promote<S, T>::type> operator+(const Vec2<T> &v, S scalar)
444 {
445 Vec2<typename promote<S, T>::type> result(v);
446 result += scalar;
447 return result;
448 }
449
451 template <typename T0, typename T1>
452 inline Vec2<typename promote<T0, T1>::type> operator-(const Vec2<T0> &v0, const Vec2<T1> &v1)
453 {
454 Vec2<typename promote<T0, T1>::type> result(v0);
455 result -= v1;
456 return result;
457 }
458
460 template <typename S, typename T>
461 inline Vec2<typename promote<S, T>::type> operator-(const Vec2<T> &v, S scalar)
462 {
463 Vec2<typename promote<S, T>::type> result(v);
464 result -= scalar;
465 return result;
466 }
467
470 template <typename T>
471 inline T angle(const Vec2<T> &v1, const Vec2<T> &v2)
472 {
473 T c = v1.dot(v2);
474 return acos(c);
475 }
476
477 template <typename T>
478 inline bool
479 isApproxEqual(const Vec2<T>& a, const Vec2<T>& b)
480 {
481 return a.eq(b);
482 }
483 template <typename T>
484 inline bool
485 isApproxEqual(const Vec2<T>& a, const Vec2<T>& b, const Vec2<T>& eps)
486 {
487 return isApproxEqual(a.x(), b.x(), eps.x()) &&
488 isApproxEqual(a.y(), b.y(), eps.y());
489 }
490
491 template<typename T>
492 inline Vec2<T>
493 Abs(const Vec2<T>& v)
494 {
495 return Vec2<T>(Abs(v[0]), Abs(v[1]));
496 }
497
500 template <typename T>
501 inline void orthonormalize(Vec2<T> &v1, Vec2<T> &v2)
502 {
503 // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
504 // orthonormalization produces vectors u0, u1, and u2 as follows,
505 //
506 // u0 = v0/|v0|
507 // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
508 //
509 // where |A| indicates length of vector A and A*B indicates dot
510 // product of vectors A and B.
511
512 // compute u0
513 v1.normalize();
514
515 // compute u1
516 T d0 = v1.dot(v2);
517 v2 -= v1*d0;
518 v2.normalize();
519 }
520
521
526
528 template <typename T>
529 inline Vec2<T> minComponent(const Vec2<T> &v1, const Vec2<T> &v2)
530 {
531 return Vec2<T>(
532 std::min(v1.x(), v2.x()),
533 std::min(v1.y(), v2.y()));
534 }
535
537 template <typename T>
538 inline Vec2<T> maxComponent(const Vec2<T> &v1, const Vec2<T> &v2)
539 {
540 return Vec2<T>(
541 std::max(v1.x(), v2.x()),
542 std::max(v1.y(), v2.y()));
543 }
544
547 template <typename T>
548 inline Vec2<T> Exp(Vec2<T> v) { return v.exp(); }
549
552 template <typename T>
553 inline Vec2<T> Log(Vec2<T> v) { return v.log(); }
554
555 typedef Vec2<int32_t> Vec2i;
556 typedef Vec2<uint32_t> Vec2ui;
557 typedef Vec2<float> Vec2s;
558 typedef Vec2<double> Vec2d;
559
560 } // namespace math
561 } // namespace OPENVDB_VERSION_NAME
562 } // namespace openvdb
563
564 #endif // OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED
565
566 // Copyright (c) 2012-2017 DreamWorks Animation LLC
567 // All rights reserved. This software is distributed under the
568 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v4_0_2::math::Vec2ui
Vec2< uint32_t > Vec2ui
Definition: Vec2.h:556
openvdb::v4_0_2::math::Vec2::operator-=
const Vec2< T > & operator-=(S scalar)
Returns v, where for .
Definition: Vec2.h:332
openvdb::v4_0_2::math::Vec2::div
const Vec2< T > & div(T0 scalar, const Vec2< T1 > &v)
Definition: Vec2.h:190
openvdb::v4_0_2::math::Conversion
Dummy class for tag dispatch of conversion constructors.
Definition: Tuple.h:48
openvdb::v4_0_2::math::Vec2::operator=
const Vec2< T > & operator=(const Vec2< Source > &v)
Assignment operator.
Definition: Vec2.h:128
openvdb::v4_0_2::math::Vec2::asPointer
T * asPointer()
Definition: Vec2.h:108
openvdb::v4_0_2::math::Vec2::zero
static Vec2< T > zero()
Predefined constants, e.g. Vec2f v = Vec2f::xNegAxis();.
Definition: Vec2.h:379
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v4_0_2::math::Vec2::Vec2
Vec2(const Tuple< 2, Source > &t)
Conversion constructor.
Definition: Vec2.h:78
openvdb::v4_0_2::math::angle
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:471
openvdb::v4_0_2::math::orthonormalize
void orthonormalize(Vec2< T > &v1, Vec2< T > &v2)
Definition: Vec2.h:501
openvdb::v4_0_2::math::Vec2::Vec2
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:88
openvdb::v4_0_2::math::operator-
Vec2< typename promote< S, T >::type > operator-(const Vec2< T > &v, S scalar)
Returns V, where for .
Definition: Vec2.h:461
openvdb::v4_0_2::math::Vec2::operator+=
const Vec2< T > & operator+=(const Vec2< S > &v1)
Returns v0, where for .
Definition: Vec2.h:323
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:101
openvdb::v4_0_2::math::operator*
Vec2< typename promote< T0, T1 >::type > operator*(const Vec2< T0 > &v0, const Vec2< T1 > &v1)
Returns V, where for .
Definition: Vec2.h:402
openvdb::v4_0_2::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:391
openvdb::v4_0_2::math::Vec2::projection
Vec2< T > projection(const Vec2< T > &onto, T eps=1.0e-8) const
Definition: Vec2.h:365
openvdb::v4_0_2::math::Vec2::eq
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:147
i
tbb::atomic< Index32 > i
Definition: LeafBuffer.h:71
openvdb::v4_0_2::ArithmeticError
Definition: Exceptions.h:82
openvdb::v4_0_2::math::Vec2::exp
const Vec2< T > & exp()
Definition: Vec2.h:213
openvdb::v4_0_2::math::Tuple< 2, T >::mm
T mm[SIZE]
Definition: Tuple.h:196
openvdb::v4_0_2::math::Vec2::getArbPerpendicular
Vec2< T > getArbPerpendicular() const
Definition: Vec2.h:376
openvdb::v4_0_2::math::Vec2::operator==
bool operator==(const Vec2< T > &v) const
Equality operator, does exact floating point comparisons.
Definition: Vec2.h:138
openvdb::v4_0_2::math::Vec2::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec2.h:95
openvdb::v4_0_2::math::Vec2::ones
static Vec2< T > ones()
Definition: Vec2.h:380
openvdb::v4_0_2::math::Vec2::operator()
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec2.h:103
openvdb::v4_0_2::math::Vec2::Vec2
Vec2(T val)
Construct a vector all of whose components have the given value.
Definition: Vec2.h:59
openvdb::v4_0_2::math::Vec2::sum
T sum() const
Return the sum of all the vector components.
Definition: Vec2.h:230
openvdb::v4_0_2::math::Vec2::init
const Vec2< T > & init(T x=0, T y=0)
Definition: Vec2.h:113
openvdb::v4_0_2::math::Log
Vec2< T > Log(Vec2< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec2.h:553
openvdb::v4_0_2::math::Vec2::numColumns
static unsigned numColumns()
Definition: Vec2.h:350
openvdb::v4_0_2::math::Vec2::x
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec2.h:99
openvdb::v4_0_2::math::Vec2::unit
Vec2< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec2.h:253
openvdb::v4_0_2::math::Vec2::operator+=
const Vec2< T > & operator+=(S scalar)
Returns v, where for .
Definition: Vec2.h:314
openvdb::v4_0_2::math::Vec2::length
T length() const
Length of the vector.
Definition: Vec2.h:202
openvdb::v4_0_2::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:133
openvdb::v4_0_2::math::Vec2s
Vec2< float > Vec2s
Definition: Vec2.h:557
openvdb::v4_0_2::tools::composite::min
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:129
openvdb::v4_0_2::math::minComponent
Vec2< T > minComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec2.h:529
openvdb::v4_0_2::math::Vec2::Vec2
Vec2()
Trivial constructor, the vector is NOT initialized.
Definition: Vec2.h:56
openvdb::v4_0_2::math::isApproxEqual
bool isApproxEqual(const Vec2< T > &a, const Vec2< T > &b, const Vec2< T > &eps)
Definition: Vec2.h:485
Exceptions.h
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
Definition: version.h:43
openvdb::v4_0_2::math::Vec2::dot
T dot(const Vec2< T > &v) const
Dot product.
Definition: Vec2.h:199
openvdb::v4_0_2::math::Vec2::setZero
const Vec2< T > & setZero()
Set "this" vector to zero.
Definition: Vec2.h:120
openvdb::v4_0_2::math::Vec2::numElements
static unsigned numElements()
Definition: Vec2.h:351
openvdb::v4_0_2::math::Vec2::Vec2
Vec2(T x, T y)
Constructor with two arguments, e.g. Vec2f v(1,2,3);.
Definition: Vec2.h:62
openvdb::v4_0_2::math::Vec2::operator!=
bool operator!=(const Vec2< T > &v) const
Inequality operator, does exact floating point comparisons.
Definition: Vec2.h:144
openvdb::v4_0_2::math::Vec2::unit
Vec2< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec2.h:260
openvdb::v4_0_2::math::Vec2::value_type
T value_type
Definition: Vec2.h:52
openvdb
Definition: Exceptions.h:39
openvdb::v4_0_2::math::Vec2::component
T component(const Vec2< T > &onto, T eps=1.0e-8) const
Definition: Vec2.h:355
openvdb::v4_0_2::math::Vec2::lengthSqr
T lengthSqr() const
Definition: Vec2.h:209
openvdb::v4_0_2::math::Vec2::operator/=
const Vec2< T > & operator/=(S scalar)
Returns v, where for .
Definition: Vec2.h:296
openvdb::v4_0_2::math::Vec2::log
const Vec2< T > & log()
Definition: Vec2.h:222
openvdb::v4_0_2::math::operator+
Vec2< typename promote< S, T >::type > operator+(const Vec2< T > &v, S scalar)
Returns V, where for .
Definition: Vec2.h:443
openvdb::v4_0_2::math::Vec2::product
T product() const
Return the product of all the vector components.
Definition: Vec2.h:236
openvdb::v4_0_2::math::Vec2::sub
const Vec2< T > & sub(const Vec2< T0 > &v1, const Vec2< T1 > &v2)
Definition: Vec2.h:170
openvdb::v4_0_2::math::operator/
Vec2< typename promote< T0, T1 >::type > operator/(const Vec2< T0 > &v0, const Vec2< T1 > &v1)
Returns V, where for .
Definition: Vec2.h:426
openvdb::v4_0_2::math::Vec2d
Vec2< double > Vec2d
Definition: Vec2.h:558
openvdb::v4_0_2::math::maxComponent
Vec2< T > maxComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec2.h:538
openvdb::v4_0_2::math::Vec2::ValueType
T ValueType
Definition: Vec2.h:53
openvdb::v4_0_2::math::Vec2::operator-
Vec2< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec2.h:154
openvdb::v4_0_2::math::Mat2
Definition: Vec2.h:46
openvdb::v4_0_2::math::Exp
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:548
openvdb::v4_0_2::math::Vec2::operator*=
const Vec2< T > & operator*=(const Vec2< S > &v1)
Returns v0, where for .
Definition: Vec2.h:287
openvdb::v4_0_2::math::unit
MatType unit(const MatType &mat, typename MatType::value_type eps=1.0e-8)
Return a copy of the given matrix with its upper 3x3 rows normalized.
Definition: Mat.h:676
openvdb::v4_0_2::math::Vec2::scale
const Vec2< T > & scale(T0 scalar, const Vec2< T1 > &v)
Definition: Vec2.h:181
openvdb::v4_0_2::math::Vec2::y
T y() const
Definition: Vec2.h:100
openvdb::v4_0_2::math::Abs
Vec2< T > Abs(const Vec2< T > &v)
Definition: Vec2.h:493
Tuple.h
openvdb::v4_0_2::math::Vec2
Definition: Vec2.h:49
openvdb::v4_0_2::math::Vec2::operator*=
const Vec2< T > & operator*=(S scalar)
Returns v, where for .
Definition: Vec2.h:278
openvdb::v4_0_2::math::Vec2::operator-=
const Vec2< T > & operator-=(const Vec2< S > &v1)
Returns v0, where for .
Definition: Vec2.h:341
openvdb::v4_0_2::math::Vec2::unitSafe
Vec2< T > unitSafe() const
return normalized this, or (1, 0) if this is null vector
Definition: Vec2.h:270
openvdb::v4_0_2::math::Vec2::asPointer
const T * asPointer() const
Definition: Vec2.h:109
openvdb::v4_0_2::math::Tuple
Definition: Tuple.h:54
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:71
openvdb::v4_0_2::math::Vec2::operator/=
const Vec2< T > & operator/=(const Vec2< S > &v1)
Returns v0, where for .
Definition: Vec2.h:305
openvdb::v4_0_2::math::Vec2::operator()
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec2.h:106
openvdb::v4_0_2::math::Vec2::y
T & y()
Definition: Vec2.h:96
openvdb::v4_0_2::math::Vec2i
Vec2< int32_t > Vec2i
Definition: Vec2.h:555
openvdb::v4_0_2::math::Vec2::normalize
bool normalize(T eps=1.0e-8)
this = normalized this
Definition: Vec2.h:242
openvdb::v4_0_2::math::Vec2::numRows
static unsigned numRows()
Definition: Vec2.h:349
openvdb::v4_0_2::math::Vec2::add
const Vec2< T > & add(const Vec2< T0 > &v1, const Vec2< T1 > &v2)
Definition: Vec2.h:159
openvdb::v4_0_2::math::Vec2::Vec2
Vec2(Source *a)
Constructor with array argument, e.g. float a[2]; Vec2f v(a);.
Definition: Vec2.h:70