OpenVDB 11.0.0

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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 {
16 OPENVDB_USE_VERSION_NAMESPACE
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
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 Vec2() = default;
33
34 /// @brief Construct a vector all of whose components have the given value.
35 explicit Vec2(T val) { this->mm[0] = this->mm[1] = val; }
36
37 /// Constructor with two arguments, e.g. Vec2f v(1,2,3);
38 Vec2(T x, T y)
39 {
40 this->mm[0] = x;
41 this->mm[1] = y;
42 }
43
44 /// Constructor with array argument, e.g. float a[2]; Vec2f v(a);
45 template <typename Source>
46 Vec2(Source *a)
47 {
48 this->mm[0] = static_cast<T>(a[0]);
49 this->mm[1] = static_cast<T>(a[1]);
50 } // trivial
51
52 /// Conversion constructor
53 template<typename Source>
54 explicit Vec2(const Tuple<2, Source> &t)
55 {
56 this->mm[0] = static_cast<T>(t[0]);
57 this->mm[1] = static_cast<T>(t[1]);
58 }
59
60 /// @brief Construct a vector all of whose components have the given value,
61 /// which may be of an arithmetic type different from this vector's value type.
62 /// @details Type conversion warnings are suppressed.
63 template<typename Other>
64 explicit Vec2(Other val,
65 typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
66 {
67 this->mm[0] = this->mm[1] = static_cast<T>(val);
68 }
69
70 /// Reference to the component, e.g. v.x() = 4.5f;
71 T& x() {return this->mm[0];}
72 T& y() {return this->mm[1];}
73
74 /// Get the component, e.g. float f = v.y();
75 T x() const {return this->mm[0];}
76 T y() const {return this->mm[1];}
77
78 /// Alternative indexed reference to the elements
79 T& operator()(int i) {return this->mm[i];}
80
81 /// Alternative indexed constant reference to the elements,
82 T operator()(int i) const {return this->mm[i];}
83
84 T* asPointer() {return this->mm;}
85 const T* asPointer() const {return this->mm;}
86
87 /// "this" vector gets initialized to [x, y, z],
88 /// calling v.init(); has same effect as calling v = Vec2::zero();
89 const Vec2<T>& init(T x=0, T y=0)
90 {
91 this->mm[0] = x; this->mm[1] = y;
92 return *this;
93 }
94
95 /// Set "this" vector to zero
96 const Vec2<T>& setZero()
97 {
98 this->mm[0] = 0; this->mm[1] = 0;
99 return *this;
100 }
101
102 /// Assignment operator
103 template<typename Source>
104 const Vec2<T>& operator=(const Vec2<Source> &v)
105 {
106 // note: don't static_cast because that suppresses warnings
107 this->mm[0] = v[0];
108 this->mm[1] = v[1];
109
110 return *this;
111 }
112
113 /// Equality operator, does exact floating point comparisons
114 bool operator==(const Vec2<T> &v) const
115 {
116 return (isExactlyEqual(this->mm[0], v.mm[0]) && isExactlyEqual(this->mm[1], v.mm[1]));
117 }
118
119 /// Inequality operator, does exact floating point comparisons
120 bool operator!=(const Vec2<T> &v) const { return !(*this==v); }
121
122 /// Test if "this" vector is equivalent to vector v with tolerance of eps
123 bool eq(const Vec2<T> &v, T eps = static_cast<T>(1.0e-7)) const
124 {
125 return isApproxEqual(this->mm[0], v.mm[0], eps) &&
126 isApproxEqual(this->mm[1], v.mm[1], eps);
127 } // trivial
128
129 /// Negation operator, for e.g. v1 = -v2;
130 Vec2<T> operator-() const {return Vec2<T>(-this->mm[0], -this->mm[1]);}
131
132 /// this = v1 + v2
133 /// "this", v1 and v2 need not be distinct objects, e.g. v.add(v1,v);
134 template <typename T0, typename T1>
135 const Vec2<T>& add(const Vec2<T0> &v1, const Vec2<T1> &v2)
136 {
137 this->mm[0] = v1[0] + v2[0];
138 this->mm[1] = v1[1] + v2[1];
139
140 return *this;
141 }
142
143 /// this = v1 - v2
144 /// "this", v1 and v2 need not be distinct objects, e.g. v.sub(v1,v);
145 template <typename T0, typename T1>
146 const Vec2<T>& sub(const Vec2<T0> &v1, const Vec2<T1> &v2)
147 {
148 this->mm[0] = v1[0] - v2[0];
149 this->mm[1] = v1[1] - v2[1];
150
151 return *this;
152 }
153
154 /// this = scalar*v, v need not be a distinct object from "this",
155 /// e.g. v.scale(1.5,v1);
156 template <typename T0, typename T1>
157 const Vec2<T>& scale(T0 scalar, const Vec2<T1> &v)
158 {
159 this->mm[0] = scalar * v[0];
160 this->mm[1] = scalar * v[1];
161
162 return *this;
163 }
164
165 template <typename T0, typename T1>
166 const Vec2<T> &div(T0 scalar, const Vec2<T1> &v)
167 {
168 this->mm[0] = v[0] / scalar;
169 this->mm[1] = v[1] / scalar;
170
171 return *this;
172 }
173
174 /// Dot product
175 T dot(const Vec2<T> &v) const { return this->mm[0]*v[0] + this->mm[1]*v[1]; } // trivial
176
177 /// Length of the vector
178 T length() const
179 {
180 return static_cast<T>(sqrt(double(this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1])));
181 }
182
183 /// Squared length of the vector, much faster than length() as it
184 /// does not involve square root
185 T lengthSqr() const { return (this->mm[0]*this->mm[0] + this->mm[1]*this->mm[1]); }
186
187 /// Return a reference to itsef after the exponent has been
188 /// applied to all the vector components.
189 inline const Vec2<T>& exp()
190 {
191 this->mm[0] = std::exp(this->mm[0]);
192 this->mm[1] = std::exp(this->mm[1]);
193 return *this;
194 }
195
196 /// Return a reference to itself after log has been
197 /// applied to all the vector components.
198 inline const Vec2<T>& log()
199 {
200 this->mm[0] = std::log(this->mm[0]);
201 this->mm[1] = std::log(this->mm[1]);
202 return *this;
203 }
204
205 /// Return the sum of all the vector components.
206 inline T sum() const
207 {
208 return this->mm[0] + this->mm[1];
209 }
210
211 /// Return the product of all the vector components.
212 inline T product() const
213 {
214 return this->mm[0] * this->mm[1];
215 }
216
217 /// this = normalized this
218 bool normalize(T eps = static_cast<T>(1.0e-8))
219 {
220 T d = length();
221 if (isApproxEqual(d, T(0), eps)) {
222 return false;
223 }
224 *this *= (T(1) / d);
225 return true;
226 }
227
228 /// return normalized this, throws if null vector
229 Vec2<T> unit(T eps=0) const
230 {
231 T d;
232 return unit(eps, d);
233 }
234
235 /// return normalized this and length, throws if null vector
236 Vec2<T> unit(T eps, T& len) const
237 {
238 len = length();
239 if (isApproxEqual(len, T(0), eps)) {
240 OPENVDB_THROW(ArithmeticError, "Normalizing null 2-vector");
241 }
242 return *this / len;
243 }
244
245 /// return normalized this, or (1, 0) if this is null vector
246 Vec2<T> unitSafe() const
247 {
248 T l2 = lengthSqr();
249 return l2 ? *this/static_cast<T>(sqrt(l2)) : Vec2<T>(1,0);
250 }
251
252 /// Multiply each element of this vector by @a scalar.
253 template <typename S>
254 const Vec2<T> &operator*=(S scalar)
255 {
256 this->mm[0] *= scalar;
257 this->mm[1] *= scalar;
258 return *this;
259 }
260
261 /// Multiply each element of this vector by the corresponding element of the given vector.
262 template <typename S>
263 const Vec2<T> &operator*=(const Vec2<S> &v1)
264 {
265 this->mm[0] *= v1[0];
266 this->mm[1] *= v1[1];
267 return *this;
268 }
269
270 /// Divide each element of this vector by @a scalar.
271 template <typename S>
272 const Vec2<T> &operator/=(S scalar)
273 {
274 this->mm[0] /= scalar;
275 this->mm[1] /= scalar;
276 return *this;
277 }
278
279 /// Divide each element of this vector by the corresponding element of the given vector.
280 template <typename S>
281 const Vec2<T> &operator/=(const Vec2<S> &v1)
282 {
283 this->mm[0] /= v1[0];
284 this->mm[1] /= v1[1];
285 return *this;
286 }
287
288 /// Add @a scalar to each element of this vector.
289 template <typename S>
290 const Vec2<T> &operator+=(S scalar)
291 {
292 this->mm[0] += scalar;
293 this->mm[1] += scalar;
294 return *this;
295 }
296
297 /// Add each element of the given vector to the corresponding element of this vector.
298 template <typename S>
299 const Vec2<T> &operator+=(const Vec2<S> &v1)
300 {
301 this->mm[0] += v1[0];
302 this->mm[1] += v1[1];
303 return *this;
304 }
305
306 /// Subtract @a scalar from each element of this vector.
307 template <typename S>
308 const Vec2<T> &operator-=(S scalar)
309 {
310 this->mm[0] -= scalar;
311 this->mm[1] -= scalar;
312 return *this;
313 }
314
315 /// Subtract each element of the given vector from the corresponding element of this vector.
316 template <typename S>
317 const Vec2<T> &operator-=(const Vec2<S> &v1)
318 {
319 this->mm[0] -= v1[0];
320 this->mm[1] -= v1[1];
321 return *this;
322 }
323
324 // Number of cols, rows, elements
325 static unsigned numRows() { return 1; }
326 static unsigned numColumns() { return 2; }
327 static unsigned numElements() { return 2; }
328
329 /// Returns the scalar component of v in the direction of onto, onto need
330 /// not be unit. e.g float c = Vec2f::component(v1,v2);
331 T component(const Vec2<T> &onto, T eps = static_cast<T>(1.0e-8)) const
332 {
333 T l = onto.length();
334 if (isApproxEqual(l, T(0), eps)) return 0;
335
336 return dot(onto)*(T(1)/l);
337 }
338
339 /// Return the projection of v onto the vector, onto need not be unit
340 /// e.g. Vec2f v = Vec2f::projection(v,n);
341 Vec2<T> projection(const Vec2<T> &onto, T eps = static_cast<T>(1.0e-8)) const
342 {
343 T l = onto.lengthSqr();
344 if (isApproxEqual(l, T(0), eps)) return Vec2::zero();
345
346 return onto*(dot(onto)*(T(1)/l));
347 }
348
349 /// Return an arbitrary unit vector perpendicular to v
350 /// Vector v must be a unit vector
351 /// e.g. v.normalize(); Vec2f n = Vec2f::getArbPerpendicular(v);
352 Vec2<T> getArbPerpendicular() const { return Vec2<T>(-this->mm[1], this->mm[0]); }
353
354 /// Predefined constants, e.g. Vec2f v = Vec2f::xNegAxis();
355 static Vec2<T> zero() { return Vec2<T>(0, 0); }
356 static Vec2<T> ones() { return Vec2<T>(1, 1); }
357};
358
359/// Multiply each element of the given vector by @a scalar and return the result.
360 template <typename S, typename T>
361 inline Vec2<typename promote<S, T>::type> operator*(S scalar, const Vec2<T> &v)
362{
363 return v * scalar;
364}
365
366/// Multiply each element of the given vector by @a scalar and return the result.
367 template <typename S, typename T>
368 inline Vec2<typename promote<S, T>::type> operator*(const Vec2<T> &v, S scalar)
369{
370 Vec2<typename promote<S, T>::type> result(v);
371 result *= scalar;
372 return result;
373}
374
375/// Multiply corresponding elements of @a v0 and @a v1 and return the result.
376 template <typename T0, typename T1>
377 inline Vec2<typename promote<T0, T1>::type> operator*(const Vec2<T0> &v0, const Vec2<T1> &v1)
378{
379 Vec2<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1]);
380 return result;
381}
382
383/// Divide @a scalar by each element of the given vector and return the result.
384 template <typename S, typename T>
385 inline Vec2<typename promote<S, T>::type> operator/(S scalar, const Vec2<T> &v)
386{
387 return Vec2<typename promote<S, T>::type>(scalar/v[0], scalar/v[1]);
388}
389
390/// Divide each element of the given vector by @a scalar and return the result.
391 template <typename S, typename T>
392 inline Vec2<typename promote<S, T>::type> operator/(const Vec2<T> &v, S scalar)
393{
394 Vec2<typename promote<S, T>::type> result(v);
395 result /= scalar;
396 return result;
397}
398
399/// Divide corresponding elements of @a v0 and @a v1 and return the result.
400 template <typename T0, typename T1>
401 inline Vec2<typename promote<T0, T1>::type> operator/(const Vec2<T0> &v0, const Vec2<T1> &v1)
402{
403 Vec2<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1]);
404 return result;
405}
406
407/// Add corresponding elements of @a v0 and @a v1 and return the result.
408 template <typename T0, typename T1>
409 inline Vec2<typename promote<T0, T1>::type> operator+(const Vec2<T0> &v0, const Vec2<T1> &v1)
410{
411 Vec2<typename promote<T0, T1>::type> result(v0);
412 result += v1;
413 return result;
414}
415
416/// Add @a scalar to each element of the given vector and return the result.
417 template <typename S, typename T>
418 inline Vec2<typename promote<S, T>::type> operator+(const Vec2<T> &v, S scalar)
419{
420 Vec2<typename promote<S, T>::type> result(v);
421 result += scalar;
422 return result;
423}
424
425/// Subtract corresponding elements of @a v0 and @a v1 and return the result.
426 template <typename T0, typename T1>
427 inline Vec2<typename promote<T0, T1>::type> operator-(const Vec2<T0> &v0, const Vec2<T1> &v1)
428{
429 Vec2<typename promote<T0, T1>::type> result(v0);
430 result -= v1;
431 return result;
432}
433
434/// Subtract @a scalar from each element of the given vector and return the result.
435 template <typename S, typename T>
436 inline Vec2<typename promote<S, T>::type> operator-(const Vec2<T> &v, S scalar)
437{
438 Vec2<typename promote<S, T>::type> result(v);
439 result -= scalar;
440 return result;
441}
442
443/// Angle between two vectors, the result is between [0, pi],
444/// e.g. float a = Vec2f::angle(v1,v2);
445 template <typename T>
446 inline T angle(const Vec2<T> &v1, const Vec2<T> &v2)
447{
448 T c = v1.dot(v2);
449 return acos(c);
450}
451
452 template <typename T>
453 inline bool
454 isApproxEqual(const Vec2<T>& a, const Vec2<T>& b)
455{
456 return a.eq(b);
457}
458 template <typename T>
459 inline bool
460 isApproxEqual(const Vec2<T>& a, const Vec2<T>& b, const Vec2<T>& eps)
461{
462 return isApproxEqual(a.x(), b.x(), eps.x()) &&
463 isApproxEqual(a.y(), b.y(), eps.y());
464}
465
466 template<typename T>
467 inline Vec2<T>
468 Abs(const Vec2<T>& v)
469{
470 return Vec2<T>(Abs(v[0]), Abs(v[1]));
471}
472
473/// Orthonormalize vectors v1 and v2 and store back the resulting basis
474/// e.g. Vec2f::orthonormalize(v1,v2);
475 template <typename T>
476 inline void orthonormalize(Vec2<T> &v1, Vec2<T> &v2)
477{
478 // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
479 // orthonormalization produces vectors u0, u1, and u2 as follows,
480 //
481 // u0 = v0/|v0|
482 // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
483 //
484 // where |A| indicates length of vector A and A*B indicates dot
485 // product of vectors A and B.
486
487 // compute u0
488 v1.normalize();
489
490 // compute u1
491 T d0 = v1.dot(v2);
492 v2 -= v1*d0;
493 v2.normalize();
494}
495
496
497/// \remark We are switching to a more explicit name because the semantics
498/// are different from std::min/max. In that case, the function returns a
499/// reference to one of the objects based on a comparator. Here, we must
500/// fabricate a new object which might not match either of the inputs.
501
502/// Return component-wise minimum of the two vectors.
503 template <typename T>
504 inline Vec2<T> minComponent(const Vec2<T> &v1, const Vec2<T> &v2)
505{
506 return Vec2<T>(
507 std::min(v1.x(), v2.x()),
508 std::min(v1.y(), v2.y()));
509}
510
511/// Return component-wise maximum of the two vectors.
512 template <typename T>
513 inline Vec2<T> maxComponent(const Vec2<T> &v1, const Vec2<T> &v2)
514{
515 return Vec2<T>(
516 std::max(v1.x(), v2.x()),
517 std::max(v1.y(), v2.y()));
518}
519
520/// @brief Return a vector with the exponent applied to each of
521/// the components of the input vector.
522 template <typename T>
523 inline Vec2<T> Exp(Vec2<T> v) { return v.exp(); }
524
525/// @brief Return a vector with log applied to each of
526/// the components of the input vector.
527 template <typename T>
528 inline Vec2<T> Log(Vec2<T> v) { return v.log(); }
529
530 using Vec2i = Vec2<int32_t>;
531 using Vec2ui = Vec2<uint32_t>;
532 using Vec2s = Vec2<float>;
533 using Vec2d = Vec2<double>;
534
535 OPENVDB_IS_POD(Vec2i)
536 OPENVDB_IS_POD(Vec2ui)
537 OPENVDB_IS_POD(Vec2s)
538 OPENVDB_IS_POD(Vec2d)
539
540} // namespace math
541} // namespace OPENVDB_VERSION_NAME
542} // namespace openvdb
543
544#endif // OPENVDB_MATH_VEC2_HAS_BEEN_INCLUDED
Exceptions.h
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition Exceptions.h:74
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
OPENVDB_IS_POD
#define OPENVDB_IS_POD(Type)
Definition Math.h:56
Tuple.h
openvdb::v11_0::ArithmeticError
Definition Exceptions.h:56
openvdb::v11_0::math::Mat2
Definition Vec2.h:20
openvdb::v11_0::math::Tuple
Definition Tuple.h:30
openvdb::v11_0::math::Tuple::mm
T mm[SIZE]
Copies this tuple into an array of a compatible type.
Definition Tuple.h:164
openvdb::v11_0::math::Vec2
Definition Vec2.h:24
openvdb::v11_0::math::Vec2::unit
Vec2< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition Vec2.h:236
openvdb::v11_0::math::Vec2::Vec2
Vec2(T x, T y)
Constructor with two arguments, e.g. Vec2f v(1,2,3);.
Definition Vec2.h:38
openvdb::v11_0::math::Vec2::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition Vec2.h:71
openvdb::v11_0::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:64
openvdb::v11_0::math::Vec2::normalize
bool normalize(T eps=static_cast< T >(1.0e-8))
this = normalized this
Definition Vec2.h:218
openvdb::v11_0::math::Vec2::operator=
const Vec2< T > & operator=(const Vec2< Source > &v)
Assignment operator.
Definition Vec2.h:104
openvdb::v11_0::math::Vec2::length
T length() const
Length of the vector.
Definition Vec2.h:178
openvdb::v11_0::math::Vec2::exp
const Vec2< T > & exp()
Definition Vec2.h:189
openvdb::v11_0::math::Vec2::sum
T sum() const
Return the sum of all the vector components.
Definition Vec2.h:206
openvdb::v11_0::math::Vec2::component
T component(const Vec2< T > &onto, T eps=static_cast< T >(1.0e-8)) const
Definition Vec2.h:331
openvdb::v11_0::math::Vec2::numColumns
static unsigned numColumns()
Definition Vec2.h:326
openvdb::v11_0::math::Vec2::sub
const Vec2< T > & sub(const Vec2< T0 > &v1, const Vec2< T1 > &v2)
Definition Vec2.h:146
openvdb::v11_0::math::Vec2::operator==
bool operator==(const Vec2< T > &v) const
Equality operator, does exact floating point comparisons.
Definition Vec2.h:114
openvdb::v11_0::math::Vec2::asPointer
T * asPointer()
Definition Vec2.h:84
openvdb::v11_0::math::Vec2::log
const Vec2< T > & log()
Definition Vec2.h:198
openvdb::v11_0::math::Vec2::numRows
static unsigned numRows()
Definition Vec2.h:325
openvdb::v11_0::math::Vec2::Vec2
Vec2(Source *a)
Constructor with array argument, e.g. float a[2]; Vec2f v(a);.
Definition Vec2.h:46
openvdb::v11_0::math::Vec2::operator/=
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:281
openvdb::v11_0::math::Vec2::operator+=
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:299
openvdb::v11_0::math::Vec2::operator*=
const Vec2< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition Vec2.h:254
openvdb::v11_0::math::Vec2::operator()
T & operator()(int i)
Alternative indexed reference to the elements.
Definition Vec2.h:79
openvdb::v11_0::math::Vec2::y
T & y()
Definition Vec2.h:72
openvdb::v11_0::math::Vec2::operator-=
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:317
openvdb::v11_0::math::Vec2::Vec2
Vec2(T val)
Construct a vector all of whose components have the given value.
Definition Vec2.h:35
openvdb::v11_0::math::Vec2::operator()
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition Vec2.h:82
openvdb::v11_0::math::Vec2::init
const Vec2< T > & init(T x=0, T y=0)
Definition Vec2.h:89
openvdb::v11_0::math::Vec2::product
T product() const
Return the product of all the vector components.
Definition Vec2.h:212
openvdb::v11_0::math::Vec2::add
const Vec2< T > & add(const Vec2< T0 > &v1, const Vec2< T1 > &v2)
Definition Vec2.h:135
openvdb::v11_0::math::Vec2::scale
const Vec2< T > & scale(T0 scalar, const Vec2< T1 > &v)
Definition Vec2.h:157
openvdb::v11_0::math::Vec2::dot
T dot(const Vec2< T > &v) const
Dot product.
Definition Vec2.h:175
openvdb::v11_0::math::Vec2::setZero
const Vec2< T > & setZero()
Set "this" vector to zero.
Definition Vec2.h:96
openvdb::v11_0::math::Vec2::asPointer
const T * asPointer() const
Definition Vec2.h:85
openvdb::v11_0::math::Vec2::lengthSqr
T lengthSqr() const
Definition Vec2.h:185
openvdb::v11_0::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:123
openvdb::v11_0::math::Vec2::projection
Vec2< T > projection(const Vec2< T > &onto, T eps=static_cast< T >(1.0e-8)) const
Definition Vec2.h:341
openvdb::v11_0::math::Vec2::ones
static Vec2< T > ones()
Definition Vec2.h:356
openvdb::v11_0::math::Vec2::x
T x() const
Get the component, e.g. float f = v.y();.
Definition Vec2.h:75
openvdb::v11_0::math::Vec2::Vec2
Vec2(const Tuple< 2, Source > &t)
Conversion constructor.
Definition Vec2.h:54
openvdb::v11_0::math::Vec2::operator/=
const Vec2< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition Vec2.h:272
openvdb::v11_0::math::Vec2::y
T y() const
Definition Vec2.h:76
openvdb::v11_0::math::Vec2::operator+=
const Vec2< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition Vec2.h:290
openvdb::v11_0::math::Vec2::operator*=
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:263
openvdb::v11_0::math::Vec2::numElements
static unsigned numElements()
Definition Vec2.h:327
openvdb::v11_0::math::Vec2::Vec2
Vec2()=default
openvdb::v11_0::math::Vec2::div
const Vec2< T > & div(T0 scalar, const Vec2< T1 > &v)
Definition Vec2.h:166
openvdb::v11_0::math::Vec2::operator!=
bool operator!=(const Vec2< T > &v) const
Inequality operator, does exact floating point comparisons.
Definition Vec2.h:120
openvdb::v11_0::math::Vec2::zero
static Vec2< T > zero()
Predefined constants, e.g. Vec2f v = Vec2f::xNegAxis();.
Definition Vec2.h:355
openvdb::v11_0::math::Vec2::unit
Vec2< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition Vec2.h:229
openvdb::v11_0::math::Vec2::operator-
Vec2< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition Vec2.h:130
openvdb::v11_0::math::Vec2::unitSafe
Vec2< T > unitSafe() const
return normalized this, or (1, 0) if this is null vector
Definition Vec2.h:246
openvdb::v11_0::math::Vec2::ValueType
T ValueType
Definition Vec2.h:27
openvdb::v11_0::math::Vec2::operator-=
const Vec2< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition Vec2.h:308
openvdb::v11_0::math::Vec2::getArbPerpendicular
Vec2< T > getArbPerpendicular() const
Definition Vec2.h:352
openvdb::v11_0::math::Vec2::value_type
T value_type
Definition Vec2.h:26
openvdb::v11_0::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:528
openvdb::v11_0::math::orthonormalize
void orthonormalize(Vec2< T > &v1, Vec2< T > &v2)
Definition Vec2.h:476
openvdb::v11_0::math::operator*
Mat3< typename promote< T0, T1 >::type > operator*(const Mat3< T0 > &m0, const Mat3< T1 > &m1)
Multiply m0 by m1 and return the resulting matrix.
Definition Mat3.h:597
openvdb::v11_0::math::isApproxEqual
bool isApproxEqual(const Type &a, const Type &b, const Type &tolerance)
Return true if a is equal to b to within the given tolerance.
Definition Math.h:406
openvdb::v11_0::math::operator-
Vec3< typename promote< T, Coord::ValueType >::type > operator-(const Vec3< T > &v0, const Coord &v1)
Allow a Coord to be subtracted from a Vec3.
Definition Coord.h:553
openvdb::v11_0::math::operator+
Vec3< typename promote< T, typename Coord::ValueType >::type > operator+(const Vec3< T > &v0, const Coord &v1)
Allow a Coord to be added to or subtracted from a Vec3.
Definition Coord.h:527
openvdb::v11_0::math::Exp
Type Exp(const Type &x)
Return ex.
Definition Math.h:710
openvdb::v11_0::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 3×3 rows normalized.
Definition Mat.h:648
openvdb::v11_0::math::Abs
Coord Abs(const Coord &xyz)
Definition Coord.h:517
openvdb::v11_0::math::angle
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition Vec2.h:446
openvdb::v11_0::math::operator/
Vec2< typename promote< S, T >::type > operator/(S scalar, const Vec2< T > &v)
Divide scalar by each element of the given vector and return the result.
Definition Vec2.h:385
openvdb::v11_0::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition Math.h:443
openvdb::v11_0::math::minComponent
Vec2< T > minComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise minimum of the two vectors.
Definition Vec2.h:504
openvdb::v11_0::math::maxComponent
Vec2< T > maxComponent(const Vec2< T > &v1, const Vec2< T > &v2)
Return component-wise maximum of the two vectors.
Definition Vec2.h:513
openvdb
Definition Exceptions.h:13
openvdb::v11_0::math::Conversion
Dummy class for tag dispatch of conversion constructors.
Definition Tuple.h:23
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition version.h.in:121
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition version.h.in:212