OpenVDB: openvdb/math/Vec3.h Source File

OpenVDB 9.0.0

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
15namespace openvdb {
16 OPENVDB_USE_VERSION_NAMESPACE
17namespace OPENVDB_VERSION_NAME {
18namespace math {
19
20template<typename T> class Mat3;
21
22template<typename T>
23 class Vec3: public Tuple<3, T>
24{
25public:
26 using value_type = T;
27 using ValueType = T;
28
29 /// Trivial constructor, the vector is NOT initialized
30#if OPENVDB_ABI_VERSION_NUMBER >= 8
31 /// @note destructor, copy constructor, assignment operator and
32 /// move constructor are left to be defined by the compiler (default)
33 Vec3() = default;
34#else
35 Vec3() {}
36#endif
37
38 /// @brief Construct a vector all of whose components have the given value.
39 explicit Vec3(T val) { this->mm[0] = this->mm[1] = this->mm[2] = val; }
40
41 /// Constructor with three arguments, e.g. Vec3d v(1,2,3);
42 Vec3(T x, T y, T z)
43 {
44 this->mm[0] = x;
45 this->mm[1] = y;
46 this->mm[2] = z;
47 }
48
49 /// Constructor with array argument, e.g. double a[3]; Vec3d v(a);
50 template <typename Source>
51 Vec3(Source *a)
52 {
53 this->mm[0] = static_cast<T>(a[0]);
54 this->mm[1] = static_cast<T>(a[1]);
55 this->mm[2] = static_cast<T>(a[2]);
56 }
57
58 /// @brief Construct a Vec3 from a 3-Tuple with a possibly different value type.
59 /// @details Type conversion warnings are suppressed.
60 template<typename Source>
61 explicit Vec3(const Tuple<3, Source> &v)
62 {
63 this->mm[0] = static_cast<T>(v[0]);
64 this->mm[1] = static_cast<T>(v[1]);
65 this->mm[2] = static_cast<T>(v[2]);
66 }
67
68 /// @brief Construct a vector all of whose components have the given value,
69 /// which may be of an arithmetic type different from this vector's value type.
70 /// @details Type conversion warnings are suppressed.
71 template<typename Other>
72 explicit Vec3(Other val,
73 typename std::enable_if<std::is_arithmetic<Other>::value, Conversion>::type = Conversion{})
74 {
75 this->mm[0] = this->mm[1] = this->mm[2] = static_cast<T>(val);
76 }
77
78 /// @brief Construct a Vec3 from another Vec3 with a possibly different value type.
79 /// @details Type conversion warnings are suppressed.
80 template<typename Other>
81 Vec3(const Vec3<Other>& v)
82 {
83 this->mm[0] = static_cast<T>(v[0]);
84 this->mm[1] = static_cast<T>(v[1]);
85 this->mm[2] = static_cast<T>(v[2]);
86 }
87
88 /// Reference to the component, e.g. v.x() = 4.5f;
89 T& x() { return this->mm[0]; }
90 T& y() { return this->mm[1]; }
91 T& z() { return this->mm[2]; }
92
93 /// Get the component, e.g. float f = v.y();
94 T x() const { return this->mm[0]; }
95 T y() const { return this->mm[1]; }
96 T z() const { return this->mm[2]; }
97
98 T* asPointer() { return this->mm; }
99 const T* asPointer() const { return this->mm; }
100
101 /// Alternative indexed reference to the elements
102 T& operator()(int i) { return this->mm[i]; }
103
104 /// Alternative indexed constant reference to the elements,
105 T operator()(int i) const { return this->mm[i]; }
106
107 /// "this" vector gets initialized to [x, y, z],
108 /// calling v.init(); has same effect as calling v = Vec3::zero();
109 const Vec3<T>& init(T x=0, T y=0, T z=0)
110 {
111 this->mm[0] = x; this->mm[1] = y; this->mm[2] = z;
112 return *this;
113 }
114
115
116 /// Set "this" vector to zero
117 const Vec3<T>& setZero()
118 {
119 this->mm[0] = 0; this->mm[1] = 0; this->mm[2] = 0;
120 return *this;
121 }
122
123 /// @brief Assignment operator
124 /// @details Type conversion warnings are not suppressed.
125 template<typename Source>
126 const Vec3<T>& operator=(const Vec3<Source> &v)
127 {
128 // note: don't static_cast because that suppresses warnings
129 this->mm[0] = v[0];
130 this->mm[1] = v[1];
131 this->mm[2] = v[2];
132
133 return *this;
134 }
135
136 /// Test if "this" vector is equivalent to vector v with tolerance of eps
137 bool eq(const Vec3<T> &v, T eps = static_cast<T>(1.0e-7)) const
138 {
139 return isRelOrApproxEqual(this->mm[0], v.mm[0], eps, eps) &&
140 isRelOrApproxEqual(this->mm[1], v.mm[1], eps, eps) &&
141 isRelOrApproxEqual(this->mm[2], v.mm[2], eps, eps);
142 }
143
144
145 /// Negation operator, for e.g. v1 = -v2;
146 Vec3<T> operator-() const { return Vec3<T>(-this->mm[0], -this->mm[1], -this->mm[2]); }
147
148 /// this = v1 + v2
149 /// "this", v1 and v2 need not be distinct objects, e.g. v.add(v1,v);
150 template <typename T0, typename T1>
151 const Vec3<T>& add(const Vec3<T0> &v1, const Vec3<T1> &v2)
152 {
153 this->mm[0] = v1[0] + v2[0];
154 this->mm[1] = v1[1] + v2[1];
155 this->mm[2] = v1[2] + v2[2];
156
157 return *this;
158 }
159
160 /// this = v1 - v2
161 /// "this", v1 and v2 need not be distinct objects, e.g. v.sub(v1,v);
162 template <typename T0, typename T1>
163 const Vec3<T>& sub(const Vec3<T0> &v1, const Vec3<T1> &v2)
164 {
165 this->mm[0] = v1[0] - v2[0];
166 this->mm[1] = v1[1] - v2[1];
167 this->mm[2] = v1[2] - v2[2];
168
169 return *this;
170 }
171
172 /// this = scalar*v, v need not be a distinct object from "this",
173 /// e.g. v.scale(1.5,v1);
174 template <typename T0, typename T1>
175 const Vec3<T>& scale(T0 scale, const Vec3<T1> &v)
176 {
177 this->mm[0] = scale * v[0];
178 this->mm[1] = scale * v[1];
179 this->mm[2] = scale * v[2];
180
181 return *this;
182 }
183
184 template <typename T0, typename T1>
185 const Vec3<T> &div(T0 scale, const Vec3<T1> &v)
186 {
187 this->mm[0] = v[0] / scale;
188 this->mm[1] = v[1] / scale;
189 this->mm[2] = v[2] / scale;
190
191 return *this;
192 }
193
194 /// Dot product
195 T dot(const Vec3<T> &v) const
196 {
197 return
198 this->mm[0]*v.mm[0] +
199 this->mm[1]*v.mm[1] +
200 this->mm[2]*v.mm[2];
201 }
202
203 /// Length of the vector
204 T length() const
205 {
206 return static_cast<T>(sqrt(double(
207 this->mm[0]*this->mm[0] +
208 this->mm[1]*this->mm[1] +
209 this->mm[2]*this->mm[2])));
210 }
211
212
213 /// Squared length of the vector, much faster than length() as it
214 /// does not involve square root
215 T lengthSqr() const
216 {
217 return
218 this->mm[0]*this->mm[0] +
219 this->mm[1]*this->mm[1] +
220 this->mm[2]*this->mm[2];
221 }
222
223 /// Return the cross product of "this" vector and v;
224 Vec3<T> cross(const Vec3<T> &v) const
225 {
226 return Vec3<T>(this->mm[1]*v.mm[2] - this->mm[2]*v.mm[1],
227 this->mm[2]*v.mm[0] - this->mm[0]*v.mm[2],
228 this->mm[0]*v.mm[1] - this->mm[1]*v.mm[0]);
229 }
230
231
232 /// this = v1 cross v2, v1 and v2 must be distinct objects than "this"
233 const Vec3<T>& cross(const Vec3<T> &v1, const Vec3<T> &v2)
234 {
235 // assert(this!=&v1);
236 // assert(this!=&v2);
237 this->mm[0] = v1.mm[1]*v2.mm[2] - v1.mm[2]*v2.mm[1];
238 this->mm[1] = v1.mm[2]*v2.mm[0] - v1.mm[0]*v2.mm[2];
239 this->mm[2] = v1.mm[0]*v2.mm[1] - v1.mm[1]*v2.mm[0];
240 return *this;
241 }
242
243 /// Multiply each element of this vector by @a scalar.
244 template <typename S>
245 const Vec3<T> &operator*=(S scalar)
246 {
247 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
248 const auto value0 = this->mm[0] * scalar;
249 const auto value1 = this->mm[1] * scalar;
250 const auto value2 = this->mm[2] * scalar;
251 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
252 this->mm[0] = static_cast<T>(value0);
253 this->mm[1] = static_cast<T>(value1);
254 this->mm[2] = static_cast<T>(value2);
255 return *this;
256 }
257
258 /// Multiply each element of this vector by the corresponding element of the given vector.
259 template <typename S>
260 const Vec3<T> &operator*=(const Vec3<S> &v1)
261 {
262 this->mm[0] *= v1[0];
263 this->mm[1] *= v1[1];
264 this->mm[2] *= v1[2];
265 return *this;
266 }
267
268 /// Divide each element of this vector by @a scalar.
269 template <typename S>
270 const Vec3<T> &operator/=(S scalar)
271 {
272 this->mm[0] /= scalar;
273 this->mm[1] /= scalar;
274 this->mm[2] /= scalar;
275 return *this;
276 }
277
278 /// Divide each element of this vector by the corresponding element of the given vector.
279 template <typename S>
280 const Vec3<T> &operator/=(const Vec3<S> &v1)
281 {
282 this->mm[0] /= v1[0];
283 this->mm[1] /= v1[1];
284 this->mm[2] /= v1[2];
285 return *this;
286 }
287
288 /// Add @a scalar to each element of this vector.
289 template <typename S>
290 const Vec3<T> &operator+=(S scalar)
291 {
292 OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
293 const auto value0 = this->mm[0] + scalar;
294 const auto value1 = this->mm[1] + scalar;
295 const auto value2 = this->mm[2] + scalar;
296 OPENVDB_NO_TYPE_CONVERSION_WARNING_END
297 this->mm[0] = static_cast<T>(value0);
298 this->mm[1] = static_cast<T>(value1);
299 this->mm[2] = static_cast<T>(value2);
300 return *this;
301 }
302
303 /// Add each element of the given vector to the corresponding element of this vector.
304 template <typename S>
305 const Vec3<T> &operator+=(const Vec3<S> &v1)
306 {
307 this->mm[0] += v1[0];
308 this->mm[1] += v1[1];
309 this->mm[2] += v1[2];
310 return *this;
311 }
312
313 /// Subtract @a scalar from each element of this vector.
314 template <typename S>
315 const Vec3<T> &operator-=(S scalar)
316 {
317 this->mm[0] -= scalar;
318 this->mm[1] -= scalar;
319 this->mm[2] -= scalar;
320 return *this;
321 }
322
323 /// Subtract each element of the given vector from the corresponding element of this vector.
324 template <typename S>
325 const Vec3<T> &operator-=(const Vec3<S> &v1)
326 {
327 this->mm[0] -= v1[0];
328 this->mm[1] -= v1[1];
329 this->mm[2] -= v1[2];
330 return *this;
331 }
332
333 /// Return a reference to itself after the exponent has been
334 /// applied to all the vector components.
335 inline const Vec3<T>& exp()
336 {
337 this->mm[0] = std::exp(this->mm[0]);
338 this->mm[1] = std::exp(this->mm[1]);
339 this->mm[2] = std::exp(this->mm[2]);
340 return *this;
341 }
342
343 /// Return a reference to itself after log has been
344 /// applied to all the vector components.
345 inline const Vec3<T>& log()
346 {
347 this->mm[0] = std::log(this->mm[0]);
348 this->mm[1] = std::log(this->mm[1]);
349 this->mm[2] = std::log(this->mm[2]);
350 return *this;
351 }
352
353 /// Return the sum of all the vector components.
354 inline T sum() const
355 {
356 return this->mm[0] + this->mm[1] + this->mm[2];
357 }
358
359 /// Return the product of all the vector components.
360 inline T product() const
361 {
362 return this->mm[0] * this->mm[1] * this->mm[2];
363 }
364
365 /// this = normalized this
366 bool normalize(T eps = T(1.0e-7))
367 {
368 T d = length();
369 if (isApproxEqual(d, T(0), eps)) {
370 return false;
371 }
372 *this *= (T(1) / d);
373 return true;
374 }
375
376
377 /// return normalized this, throws if null vector
378 Vec3<T> unit(T eps=0) const
379 {
380 T d;
381 return unit(eps, d);
382 }
383
384 /// return normalized this and length, throws if null vector
385 Vec3<T> unit(T eps, T& len) const
386 {
387 len = length();
388 if (isApproxEqual(len, T(0), eps)) {
389 OPENVDB_THROW(ArithmeticError, "Normalizing null 3-vector");
390 }
391 return *this / len;
392 }
393
394 /// return normalized this, or (1, 0, 0) if this is null vector
395 Vec3<T> unitSafe() const
396 {
397 T l2 = lengthSqr();
398 return l2 ? *this / static_cast<T>(sqrt(l2)) : Vec3<T>(1, 0 ,0);
399 }
400
401 // Number of cols, rows, elements
402 static unsigned numRows() { return 1; }
403 static unsigned numColumns() { return 3; }
404 static unsigned numElements() { return 3; }
405
406 /// Returns the scalar component of v in the direction of onto, onto need
407 /// not be unit. e.g double c = Vec3d::component(v1,v2);
408 T component(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
409 {
410 T l = onto.length();
411 if (isApproxEqual(l, T(0), eps)) return 0;
412
413 return dot(onto)*(T(1)/l);
414 }
415
416 /// Return the projection of v onto the vector, onto need not be unit
417 /// e.g. Vec3d a = vprojection(n);
418 Vec3<T> projection(const Vec3<T> &onto, T eps = static_cast<T>(1.0e-7)) const
419 {
420 T l = onto.lengthSqr();
421 if (isApproxEqual(l, T(0), eps)) return Vec3::zero();
422
423 return onto*(dot(onto)*(T(1)/l));
424 }
425
426 /// Return an arbitrary unit vector perpendicular to v
427 /// Vector this must be a unit vector
428 /// e.g. v = v.normalize(); Vec3d n = v.getArbPerpendicular();
429 Vec3<T> getArbPerpendicular() const
430 {
431 Vec3<T> u;
432 T l;
433
434 if ( fabs(this->mm[0]) >= fabs(this->mm[1]) ) {
435 // v.x or v.z is the largest magnitude component, swap them
436 l = this->mm[0]*this->mm[0] + this->mm[2]*this->mm[2];
437 l = static_cast<T>(T(1)/sqrt(double(l)));
438 u.mm[0] = -this->mm[2]*l;
439 u.mm[1] = T(0);
440 u.mm[2] = +this->mm[0]*l;
441 } else {
442 // W.y or W.z is the largest magnitude component, swap them
443 l = this->mm[1]*this->mm[1] + this->mm[2]*this->mm[2];
444 l = static_cast<T>(T(1)/sqrt(double(l)));
445 u.mm[0] = T(0);
446 u.mm[1] = +this->mm[2]*l;
447 u.mm[2] = -this->mm[1]*l;
448 }
449
450 return u;
451 }
452
453 /// Return a vector with the components of this in ascending order
454 Vec3<T> sorted() const
455 {
456 Vec3<T> r(*this);
457 if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
458 if( r.mm[1] > r.mm[2] ) std::swap(r.mm[1], r.mm[2]);
459 if( r.mm[0] > r.mm[1] ) std::swap(r.mm[0], r.mm[1]);
460 return r;
461 }
462
463 /// Return the vector (z, y, x)
464 Vec3<T> reversed() const
465 {
466 return Vec3<T>(this->mm[2], this->mm[1], this->mm[0]);
467 }
468
469 /// Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();
470 static Vec3<T> zero() { return Vec3<T>(0, 0, 0); }
471 static Vec3<T> ones() { return Vec3<T>(1, 1, 1); }
472};
473
474
475/// Equality operator, does exact floating point comparisons
476template <typename T0, typename T1>
477 inline bool operator==(const Vec3<T0> &v0, const Vec3<T1> &v1)
478{
479 return isExactlyEqual(v0[0], v1[0]) && isExactlyEqual(v0[1], v1[1])
480 && isExactlyEqual(v0[2], v1[2]);
481}
482
483/// Inequality operator, does exact floating point comparisons
484template <typename T0, typename T1>
485 inline bool operator!=(const Vec3<T0> &v0, const Vec3<T1> &v1) { return !(v0==v1); }
486
487/// Multiply each element of the given vector by @a scalar and return the result.
488template <typename S, typename T>
489 inline Vec3<typename promote<S, T>::type> operator*(S scalar, const Vec3<T> &v) { return v*scalar; }
490
491/// Multiply each element of the given vector by @a scalar and return the result.
492template <typename S, typename T>
493 inline Vec3<typename promote<S, T>::type> operator*(const Vec3<T> &v, S scalar)
494{
495 Vec3<typename promote<S, T>::type> result(v);
496 result *= scalar;
497 return result;
498}
499
500/// Multiply corresponding elements of @a v0 and @a v1 and return the result.
501template <typename T0, typename T1>
502 inline Vec3<typename promote<T0, T1>::type> operator*(const Vec3<T0> &v0, const Vec3<T1> &v1)
503{
504 Vec3<typename promote<T0, T1>::type> result(v0[0] * v1[0], v0[1] * v1[1], v0[2] * v1[2]);
505 return result;
506}
507
508
509/// Divide @a scalar by each element of the given vector and return the result.
510template <typename S, typename T>
511 inline Vec3<typename promote<S, T>::type> operator/(S scalar, const Vec3<T> &v)
512{
513 return Vec3<typename promote<S, T>::type>(scalar/v[0], scalar/v[1], scalar/v[2]);
514}
515
516/// Divide each element of the given vector by @a scalar and return the result.
517template <typename S, typename T>
518 inline Vec3<typename promote<S, T>::type> operator/(const Vec3<T> &v, S scalar)
519{
520 Vec3<typename promote<S, T>::type> result(v);
521 result /= scalar;
522 return result;
523}
524
525/// Divide corresponding elements of @a v0 and @a v1 and return the result.
526template <typename T0, typename T1>
527 inline Vec3<typename promote<T0, T1>::type> operator/(const Vec3<T0> &v0, const Vec3<T1> &v1)
528{
529 Vec3<typename promote<T0, T1>::type> result(v0[0] / v1[0], v0[1] / v1[1], v0[2] / v1[2]);
530 return result;
531}
532
533/// Add corresponding elements of @a v0 and @a v1 and return the result.
534template <typename T0, typename T1>
535 inline Vec3<typename promote<T0, T1>::type> operator+(const Vec3<T0> &v0, const Vec3<T1> &v1)
536{
537 Vec3<typename promote<T0, T1>::type> result(v0);
538 result += v1;
539 return result;
540}
541
542/// Add @a scalar to each element of the given vector and return the result.
543template <typename S, typename T>
544 inline Vec3<typename promote<S, T>::type> operator+(const Vec3<T> &v, S scalar)
545{
546 Vec3<typename promote<S, T>::type> result(v);
547 result += scalar;
548 return result;
549}
550
551/// Subtract corresponding elements of @a v0 and @a v1 and return the result.
552template <typename T0, typename T1>
553 inline Vec3<typename promote<T0, T1>::type> operator-(const Vec3<T0> &v0, const Vec3<T1> &v1)
554{
555 Vec3<typename promote<T0, T1>::type> result(v0);
556 result -= v1;
557 return result;
558}
559
560/// Subtract @a scalar from each element of the given vector and return the result.
561template <typename S, typename T>
562 inline Vec3<typename promote<S, T>::type> operator-(const Vec3<T> &v, S scalar)
563{
564 Vec3<typename promote<S, T>::type> result(v);
565 result -= scalar;
566 return result;
567}
568
569/// Angle between two vectors, the result is between [0, pi],
570/// e.g. double a = Vec3d::angle(v1,v2);
571template <typename T>
572 inline T angle(const Vec3<T> &v1, const Vec3<T> &v2)
573{
574 Vec3<T> c = v1.cross(v2);
575 return static_cast<T>(atan2(c.length(), v1.dot(v2)));
576}
577
578template <typename T>
579inline bool
580 isApproxEqual(const Vec3<T>& a, const Vec3<T>& b)
581{
582 return a.eq(b);
583}
584template <typename T>
585inline bool
586isApproxEqual(const Vec3<T>& a, const Vec3<T>& b, const Vec3<T>& eps)
587{
588 return isApproxEqual(a.x(), b.x(), eps.x()) &&
589 isApproxEqual(a.y(), b.y(), eps.y()) &&
590 isApproxEqual(a.z(), b.z(), eps.z());
591}
592
593template<typename T>
594inline Vec3<T>
595Abs(const Vec3<T>& v)
596{
597 return Vec3<T>(Abs(v[0]), Abs(v[1]), Abs(v[2]));
598}
599
600/// Orthonormalize vectors v1, v2 and v3 and store back the resulting
601/// basis e.g. Vec3d::orthonormalize(v1,v2,v3);
602template <typename T>
603 inline void orthonormalize(Vec3<T> &v1, Vec3<T> &v2, Vec3<T> &v3)
604{
605 // If the input vectors are v0, v1, and v2, then the Gram-Schmidt
606 // orthonormalization produces vectors u0, u1, and u2 as follows,
607 //
608 // u0 = v0/|v0|
609 // u1 = (v1-(u0*v1)u0)/|v1-(u0*v1)u0|
610 // u2 = (v2-(u0*v2)u0-(u1*v2)u1)/|v2-(u0*v2)u0-(u1*v2)u1|
611 //
612 // where |A| indicates length of vector A and A*B indicates dot
613 // product of vectors A and B.
614
615 // compute u0
616 v1.normalize();
617
618 // compute u1
619 T d0 = v1.dot(v2);
620 v2 -= v1*d0;
621 v2.normalize();
622
623 // compute u2
624 T d1 = v2.dot(v3);
625 d0 = v1.dot(v3);
626 v3 -= v1*d0 + v2*d1;
627 v3.normalize();
628}
629
630/// @remark We are switching to a more explicit name because the semantics
631/// are different from std::min/max. In that case, the function returns a
632/// reference to one of the objects based on a comparator. Here, we must
633/// fabricate a new object which might not match either of the inputs.
634
635/// Return component-wise minimum of the two vectors.
636template <typename T>
637 inline Vec3<T> minComponent(const Vec3<T> &v1, const Vec3<T> &v2)
638{
639 return Vec3<T>(
640 std::min(v1.x(), v2.x()),
641 std::min(v1.y(), v2.y()),
642 std::min(v1.z(), v2.z()));
643}
644
645/// Return component-wise maximum of the two vectors.
646template <typename T>
647 inline Vec3<T> maxComponent(const Vec3<T> &v1, const Vec3<T> &v2)
648{
649 return Vec3<T>(
650 std::max(v1.x(), v2.x()),
651 std::max(v1.y(), v2.y()),
652 std::max(v1.z(), v2.z()));
653}
654
655/// @brief Return a vector with the exponent applied to each of
656/// the components of the input vector.
657template <typename T>
658 inline Vec3<T> Exp(Vec3<T> v) { return v.exp(); }
659
660/// @brief Return a vector with log applied to each of
661/// the components of the input vector.
662template <typename T>
663 inline Vec3<T> Log(Vec3<T> v) { return v.log(); }
664
665 using Vec3i = Vec3<int32_t>;
666 using Vec3ui = Vec3<uint32_t>;
667 using Vec3s = Vec3<float>;
668 using Vec3d = Vec3<double>;
669
670#if OPENVDB_ABI_VERSION_NUMBER >= 8
671 OPENVDB_IS_POD(Vec3i)
672 OPENVDB_IS_POD(Vec3ui)
673 OPENVDB_IS_POD(Vec3s)
674 OPENVDB_IS_POD(Vec3d)
675#endif
676
677} // namespace math
678} // namespace OPENVDB_VERSION_NAME
679} // namespace openvdb
680
681#endif // OPENVDB_MATH_VEC3_HAS_BEEN_INCLUDED
value
ValueT value
Definition: GridBuilder.h:1287
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:55
OPENVDB_NO_TYPE_CONVERSION_WARNING_BEGIN
#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:206
OPENVDB_NO_TYPE_CONVERSION_WARNING_END
#define OPENVDB_NO_TYPE_CONVERSION_WARNING_END
Definition: Platform.h:207
Tuple.h
openvdb::v9_0::ArithmeticError
Definition: Exceptions.h:56
openvdb::v9_0::math::Tuple
Definition: Tuple.h:30
openvdb::v9_0::math::Tuple::mm
T mm[SIZE]
Copies this tuple into an array of a compatible type.
Definition: Tuple.h:179
openvdb::v9_0::math::Vec3
Definition: Vec3.h:24
openvdb::v9_0::math::Vec3::sorted
Vec3< T > sorted() const
Return a vector with the components of this in ascending order.
Definition: Vec3.h:454
openvdb::v9_0::math::Vec3::div
const Vec3< T > & div(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:185
openvdb::v9_0::math::Vec3::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:89
openvdb::v9_0::math::Vec3::sub
const Vec3< T > & sub(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:163
openvdb::v9_0::math::Vec3::setZero
const Vec3< T > & setZero()
Set "this" vector to zero.
Definition: Vec3.h:117
openvdb::v9_0::math::Vec3::operator/=
const Vec3< T > & operator/=(S scalar)
Divide each element of this vector by scalar.
Definition: Vec3.h:270
openvdb::v9_0::math::Vec3::reversed
Vec3< T > reversed() const
Return the vector (z, y, x)
Definition: Vec3.h:464
openvdb::v9_0::math::Vec3::add
const Vec3< T > & add(const Vec3< T0 > &v1, const Vec3< T1 > &v2)
Definition: Vec3.h:151
openvdb::v9_0::math::Vec3::length
T length() const
Length of the vector.
Definition: Vec3.h:204
openvdb::v9_0::math::Vec3::Vec3
Vec3(Source *a)
Constructor with array argument, e.g. double a[3]; Vec3d v(a);.
Definition: Vec3.h:51
openvdb::v9_0::math::Vec3::dot
T dot(const Vec3< T > &v) const
Dot product.
Definition: Vec3.h:195
openvdb::v9_0::math::Vec3::operator*=
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:260
openvdb::v9_0::math::Vec3::operator*=
const Vec3< T > & operator*=(S scalar)
Multiply each element of this vector by scalar.
Definition: Vec3.h:245
openvdb::v9_0::math::Vec3::sum
T sum() const
Return the sum of all the vector components.
Definition: Vec3.h:354
openvdb::v9_0::math::Vec3::numColumns
static unsigned numColumns()
Definition: Vec3.h:403
openvdb::v9_0::math::Vec3::operator/=
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:280
openvdb::v9_0::math::Vec3::init
const Vec3< T > & init(T x=0, T y=0, T z=0)
Definition: Vec3.h:109
openvdb::v9_0::math::Vec3::Vec3
Vec3(T x, T y, T z)
Constructor with three arguments, e.g. Vec3d v(1,2,3);.
Definition: Vec3.h:42
openvdb::v9_0::math::Vec3::unit
Vec3< T > unit(T eps, T &len) const
return normalized this and length, throws if null vector
Definition: Vec3.h:385
openvdb::v9_0::math::Vec3::asPointer
T * asPointer()
Definition: Vec3.h:98
openvdb::v9_0::math::Vec3::eq
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:137
openvdb::v9_0::math::Vec3::numRows
static unsigned numRows()
Definition: Vec3.h:402
openvdb::v9_0::math::Vec3::getArbPerpendicular
Vec3< T > getArbPerpendicular() const
Definition: Vec3.h:429
openvdb::v9_0::math::Vec3::log
const Vec3< T > & log()
Definition: Vec3.h:345
openvdb::v9_0::math::Vec3::operator()
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Vec3.h:102
openvdb::v9_0::math::Vec3::y
T & y()
Definition: Vec3.h:90
openvdb::v9_0::math::Vec3::component
T component(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:408
openvdb::v9_0::math::Vec3::Vec3
Vec3(T val)
Construct a vector all of whose components have the given value.
Definition: Vec3.h:39
openvdb::v9_0::math::Vec3::z
T & z()
Definition: Vec3.h:91
openvdb::v9_0::math::Vec3::operator()
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Vec3.h:105
openvdb::v9_0::math::Vec3::product
T product() const
Return the product of all the vector components.
Definition: Vec3.h:360
openvdb::v9_0::math::Vec3::cross
Vec3< T > cross(const Vec3< T > &v) const
Return the cross product of "this" vector and v;.
Definition: Vec3.h:224
openvdb::v9_0::math::Vec3::asPointer
const T * asPointer() const
Definition: Vec3.h:99
openvdb::v9_0::math::Vec3::lengthSqr
T lengthSqr() const
Definition: Vec3.h:215
openvdb::v9_0::math::Vec3::Vec3
Vec3(const Vec3< Other > &v)
Construct a Vec3 from another Vec3 with a possibly different value type.
Definition: Vec3.h:81
openvdb::v9_0::math::Vec3::zero
static Vec3< T > zero()
Predefined constants, e.g. Vec3d v = Vec3d::xNegAxis();.
Definition: Vec3.h:470
openvdb::v9_0::math::Vec3::Vec3
Vec3()=default
Trivial constructor, the vector is NOT initialized.
openvdb::v9_0::math::Vec3::cross
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:233
openvdb::v9_0::math::Vec3::Vec3
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:72
openvdb::v9_0::math::Vec3::x
T x() const
Get the component, e.g. float f = v.y();.
Definition: Vec3.h:94
openvdb::v9_0::math::Vec3::Vec3
Vec3(const Tuple< 3, Source > &v)
Construct a Vec3 from a 3-Tuple with a possibly different value type.
Definition: Vec3.h:61
openvdb::v9_0::math::Vec3::operator+=
const Vec3< T > & operator+=(S scalar)
Add scalar to each element of this vector.
Definition: Vec3.h:290
openvdb::v9_0::math::Vec3::operator=
const Vec3< T > & operator=(const Vec3< Source > &v)
Assignment operator.
Definition: Vec3.h:126
openvdb::v9_0::math::Vec3::z
T z() const
Definition: Vec3.h:96
openvdb::v9_0::math::Vec3::ones
static Vec3< T > ones()
Definition: Vec3.h:471
openvdb::v9_0::math::Vec3::unitSafe
Vec3< T > unitSafe() const
return normalized this, or (1, 0, 0) if this is null vector
Definition: Vec3.h:395
openvdb::v9_0::math::Vec3::y
T y() const
Definition: Vec3.h:95
openvdb::v9_0::math::Vec3::operator-
Vec3< T > operator-() const
Negation operator, for e.g. v1 = -v2;.
Definition: Vec3.h:146
openvdb::v9_0::math::Vec3::scale
const Vec3< T > & scale(T0 scale, const Vec3< T1 > &v)
Definition: Vec3.h:175
openvdb::v9_0::math::Vec3::projection
Vec3< T > projection(const Vec3< T > &onto, T eps=static_cast< T >(1.0e-7)) const
Definition: Vec3.h:418
openvdb::v9_0::math::Vec3::numElements
static unsigned numElements()
Definition: Vec3.h:404
openvdb::v9_0::math::Vec3::unit
Vec3< T > unit(T eps=0) const
return normalized this, throws if null vector
Definition: Vec3.h:378
openvdb::v9_0::math::Vec3::operator-=
const Vec3< T > & operator-=(S scalar)
Subtract scalar from each element of this vector.
Definition: Vec3.h:315
openvdb::v9_0::math::Vec3::normalize
bool normalize(T eps=T(1.0e-7))
this = normalized this
Definition: Vec3.h:366
openvdb::v9_0::math::Vec3::ValueType
T ValueType
Definition: Vec3.h:27
openvdb::v9_0::math::Vec3::operator-=
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:325
openvdb::v9_0::math::Vec3::exp
const Vec3< T > & exp()
Definition: Vec3.h:335
openvdb::v9_0::math::Vec3::operator+=
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:305
openvdb::v9_0::math::Vec3::value_type
T value_type
Definition: Vec3.h:26
openvdb::v9_0::math::Log
Vec3< T > Log(Vec3< T > v)
Return a vector with log applied to each of the components of the input vector.
Definition: Vec3.h:663
openvdb::v9_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:670
openvdb::v9_0::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:444
openvdb::v9_0::math::orthonormalize
void orthonormalize(Vec3< T > &v1, Vec3< T > &v2, Vec3< T > &v3)
Definition: Vec3.h:603
openvdb::v9_0::math::operator!=
bool operator!=(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Inequality operator, does exact floating point comparisons.
Definition: Vec3.h:485
openvdb::v9_0::math::maxComponent
Vec3< T > maxComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise maximum of the two vectors.
Definition: Vec3.h:647
openvdb::v9_0::math::isRelOrApproxEqual
bool isRelOrApproxEqual(const Type &a, const Type &b, const Type &absTol, const Type &relTol)
Definition: Math.h:454
openvdb::v9_0::math::operator-
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:562
openvdb::v9_0::math::Abs
Vec3< T > Abs(const Vec3< T > &v)
Definition: Vec3.h:595
openvdb::v9_0::math::Exp
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:658
openvdb::v9_0::math::minComponent
Vec3< T > minComponent(const Vec3< T > &v1, const Vec3< T > &v2)
Return component-wise minimum of the two vectors.
Definition: Vec3.h:637
openvdb::v9_0::math::operator*
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:502
openvdb::v9_0::math::operator/
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:527
openvdb::v9_0::math::scale
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:637
openvdb::v9_0::math::isApproxEqual
bool isApproxEqual(const Vec3< T > &a, const Vec3< T > &b, const Vec3< T > &eps)
Definition: Vec3.h:586
openvdb::v9_0::math::angle
T angle(const Vec3< T > &v1, const Vec3< T > &v2)
Definition: Vec3.h:572
openvdb::v9_0::math::operator+
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:544
openvdb::v9_0::math::operator==
bool operator==(const Vec3< T0 > &v0, const Vec3< T1 > &v1)
Equality operator, does exact floating point comparisons.
Definition: Vec3.h:477
openvdb::v9_0::tools::composite::max
const std::enable_if<!VecTraits< T >::IsVec, T >::type & max(const T &a, const T &b)
Definition: Composite.h:107
openvdb::v9_0::tools::composite::min
const std::enable_if<!VecTraits< T >::IsVec, T >::type & min(const T &a, const T &b)
Definition: Composite.h:103
openvdb
Definition: Exceptions.h:13
Exceptions.h
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:74
openvdb::v9_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:116
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h.in:202