OpenVDB 12.1.0

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Quat.h
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1// Copyright Contributors to the OpenVDB Project
2// SPDX-License-Identifier: Apache-2.0
3
4#ifndef OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
5#define OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
6
7#include "Mat.h"
8#include "Mat3.h"
9#include "Math.h"
10#include "Vec3.h"
11#include <openvdb/Exceptions.h>
12#include <openvdb/util/Assert.h>
13#include <cmath>
14#include <iostream>
15#include <sstream>
16#include <string>
17
18
19 namespace openvdb {
20 OPENVDB_USE_VERSION_NAMESPACE
21 namespace OPENVDB_VERSION_NAME {
22 namespace math {
23
24 template<typename T> class Quat;
25
26/// Linear interpolation between the two quaternions
27 template <typename T>
28 Quat<T> slerp(const Quat<T> &q1, const Quat<T> &q2, T t, T tolerance=0.00001)
29{
30 T qdot, angle, sineAngle;
31
32 qdot = q1.dot(q2);
33
34 if (fabs(qdot) >= 1.0) {
35 angle = 0; // not necessary but suppresses compiler warning
36 sineAngle = 0;
37 } else {
38 angle = acos(qdot);
39 sineAngle = sin(angle);
40 }
41
42 //
43 // Denominator close to 0 corresponds to the case where the
44 // two quaternions are close to the same rotation. In this
45 // case linear interpolation is used but we normalize to
46 // guarantee unit length
47 //
48 if (sineAngle <= tolerance) {
49 T s = 1.0 - t;
50
51 Quat<T> qtemp(s * q1[0] + t * q2[0], s * q1[1] + t * q2[1],
52 s * q1[2] + t * q2[2], s * q1[3] + t * q2[3]);
53 //
54 // Check the case where two close to antipodal quaternions were
55 // blended resulting in a nearly zero result which can happen,
56 // for example, if t is close to 0.5. In this case it is not safe
57 // to project back onto the sphere.
58 //
59 double lengthSquared = qtemp.dot(qtemp);
60
61 if (lengthSquared <= tolerance * tolerance) {
62 qtemp = (t < 0.5) ? q1 : q2;
63 } else {
64 qtemp *= 1.0 / sqrt(lengthSquared);
65 }
66 return qtemp;
67 } else {
68
69 T sine = 1.0 / sineAngle;
70 T a = sin((1.0 - t) * angle) * sine;
71 T b = sin(t * angle) * sine;
72 return Quat<T>(a * q1[0] + b * q2[0], a * q1[1] + b * q2[1],
73 a * q1[2] + b * q2[2], a * q1[3] + b * q2[3]);
74 }
75
76}
77
78 template<typename T>
79 class Quat
80{
81 public:
82 using value_type = T;
83 using ValueType = T;
84 static const int size = 4;
85
86 /// Trivial constructor, the quaternion is NOT initialized
87 /// @note destructor, copy constructor, assignment operator and
88 /// move constructor are left to be defined by the compiler (default)
89 Quat() = default;
90
91 /// Constructor with four arguments, e.g. Quatf q(1,2,3,4);
92 Quat(T x, T y, T z, T w)
93 {
94 mm[0] = x;
95 mm[1] = y;
96 mm[2] = z;
97 mm[3] = w;
98
99 }
100
101 /// Constructor with array argument, e.g. float a[4]; Quatf q(a);
102 Quat(T *a)
103 {
104 mm[0] = a[0];
105 mm[1] = a[1];
106 mm[2] = a[2];
107 mm[3] = a[3];
108
109 }
110
111 /// Constructor given rotation as axis and angle, the axis must be
112 /// unit vector
113 Quat(const Vec3<T> &axis, T angle)
114 {
115 OPENVDB_ASSERT(isApproxEqual(axis.length(), T(1)));
116
117 T s = T(sin(angle*T(0.5)));
118
119 mm[0] = axis.x() * s;
120 mm[1] = axis.y() * s;
121 mm[2] = axis.z() * s;
122
123 mm[3] = T(cos(angle*T(0.5)));
124
125 }
126
127 /// Constructor given rotation as axis and angle
128 Quat(math::Axis axis, T angle)
129 {
130 T s = T(sin(angle*T(0.5)));
131
132 mm[0] = (axis==math::X_AXIS) * s;
133 mm[1] = (axis==math::Y_AXIS) * s;
134 mm[2] = (axis==math::Z_AXIS) * s;
135
136 mm[3] = T(cos(angle*T(0.5)));
137 }
138
139 /// Constructor given a rotation matrix
140 template<typename T1>
141 Quat(const Mat3<T1> &rot) {
142
143 // verify that the matrix is really a rotation
144 if(!isUnitary(rot)) { // unitary is reflection or rotation
145 OPENVDB_THROW(ArithmeticError,
146 "A non-rotation matrix can not be used to construct a quaternion");
147 }
148 if (!isApproxEqual(rot.det(), T1(1))) { // rule out reflection
149 OPENVDB_THROW(ArithmeticError,
150 "A reflection matrix can not be used to construct a quaternion");
151 }
152
153 T trace(rot.trace());
154 if (trace > 0) {
155
156 T q_w = 0.5 * std::sqrt(trace+1);
157 T factor = 0.25 / q_w;
158
159 mm[0] = factor * (rot(1,2) - rot(2,1));
160 mm[1] = factor * (rot(2,0) - rot(0,2));
161 mm[2] = factor * (rot(0,1) - rot(1,0));
162 mm[3] = q_w;
163 } else if (rot(0,0) > rot(1,1) && rot(0,0) > rot(2,2)) {
164
165 T q_x = 0.5 * sqrt(rot(0,0)- rot(1,1)-rot(2,2)+1);
166 T factor = 0.25 / q_x;
167
168 mm[0] = q_x;
169 mm[1] = factor * (rot(0,1) + rot(1,0));
170 mm[2] = factor * (rot(2,0) + rot(0,2));
171 mm[3] = factor * (rot(1,2) - rot(2,1));
172 } else if (rot(1,1) > rot(2,2)) {
173
174 T q_y = 0.5 * sqrt(rot(1,1)-rot(0,0)-rot(2,2)+1);
175 T factor = 0.25 / q_y;
176
177 mm[0] = factor * (rot(0,1) + rot(1,0));
178 mm[1] = q_y;
179 mm[2] = factor * (rot(1,2) + rot(2,1));
180 mm[3] = factor * (rot(2,0) - rot(0,2));
181 } else {
182
183 T q_z = 0.5 * sqrt(rot(2,2)-rot(0,0)-rot(1,1)+1);
184 T factor = 0.25 / q_z;
185
186 mm[0] = factor * (rot(2,0) + rot(0,2));
187 mm[1] = factor * (rot(1,2) + rot(2,1));
188 mm[2] = q_z;
189 mm[3] = factor * (rot(0,1) - rot(1,0));
190 }
191 }
192
193 /// Reference to the component, e.g. q.x() = 4.5f;
194 T& x() { return mm[0]; }
195 T& y() { return mm[1]; }
196 T& z() { return mm[2]; }
197 T& w() { return mm[3]; }
198
199 /// Get the component, e.g. float f = q.w();
200 T x() const { return mm[0]; }
201 T y() const { return mm[1]; }
202 T z() const { return mm[2]; }
203 T w() const { return mm[3]; }
204
205 // Number of elements
206 static unsigned numElements() { return 4; }
207
208 /// Array style reference to the components, e.g. q[3] = 1.34f;
209 T& operator[](int i) { return mm[i]; }
210
211 /// Array style constant reference to the components, e.g. float f = q[1];
212 T operator[](int i) const { return mm[i]; }
213
214 /// Cast to T*
215 operator T*() { return mm; }
216 operator const T*() const { return mm; }
217
218 /// Alternative indexed reference to the elements
219 T& operator()(int i) { return mm[i]; }
220
221 /// Alternative indexed constant reference to the elements,
222 T operator()(int i) const { return mm[i]; }
223
224 /// Return angle of rotation
225 T angle() const
226 {
227 T sqrLength = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2];
228
229 if ( sqrLength > 1.0e-8 ) {
230
231 return T(T(2.0) * acos(mm[3]));
232
233 } else {
234
235 return T(0.0);
236 }
237 }
238
239 /// Return axis of rotation
240 Vec3<T> axis() const
241 {
242 T sqrLength = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2];
243
244 if ( sqrLength > 1.0e-8 ) {
245
246 T invLength = T(T(1)/sqrt(sqrLength));
247
248 return Vec3<T>( mm[0]*invLength, mm[1]*invLength, mm[2]*invLength );
249 } else {
250
251 return Vec3<T>(1,0,0);
252 }
253 }
254
255
256 /// "this" quaternion gets initialized to [x, y, z, w]
257 Quat& init(T x, T y, T z, T w)
258 {
259 mm[0] = x; mm[1] = y; mm[2] = z; mm[3] = w;
260 return *this;
261 }
262
263 /// "this" quaternion gets initialized to identity, same as setIdentity()
264 Quat& init() { return setIdentity(); }
265
266 /// Set "this" quaternion to rotation specified by axis and angle,
267 /// the axis must be unit vector
268 Quat& setAxisAngle(const Vec3<T>& axis, T angle)
269 {
270
271 T s = T(sin(angle*T(0.5)));
272
273 mm[0] = axis.x() * s;
274 mm[1] = axis.y() * s;
275 mm[2] = axis.z() * s;
276
277 mm[3] = T(cos(angle*T(0.5)));
278
279 return *this;
280 } // axisAngleTest
281
282 /// Set "this" vector to zero
283 Quat& setZero()
284 {
285 mm[0] = mm[1] = mm[2] = mm[3] = 0;
286 return *this;
287 }
288
289 /// Set "this" vector to identity
290 Quat& setIdentity()
291 {
292 mm[0] = mm[1] = mm[2] = 0;
293 mm[3] = 1;
294 return *this;
295 }
296
297 /// Returns vector of x,y,z rotational components
298 Vec3<T> eulerAngles(RotationOrder rotationOrder) const
299 { return math::eulerAngles(Mat3<T>(*this), rotationOrder); }
300
301 /// Equality operator, does exact floating point comparisons
302 bool operator==(const Quat &q) const
303 {
304 return (isExactlyEqual(mm[0],q.mm[0]) &&
305 isExactlyEqual(mm[1],q.mm[1]) &&
306 isExactlyEqual(mm[2],q.mm[2]) &&
307 isExactlyEqual(mm[3],q.mm[3]) );
308 }
309
310 /// Test if "this" is equivalent to q with tolerance of eps value
311 bool eq(const Quat &q, T eps=1.0e-7) const
312 {
313 return isApproxEqual(mm[0],q.mm[0],eps) && isApproxEqual(mm[1],q.mm[1],eps) &&
314 isApproxEqual(mm[2],q.mm[2],eps) && isApproxEqual(mm[3],q.mm[3],eps) ;
315 } // trivial
316
317 /// Add quaternion q to "this" quaternion, e.g. q += q1;
318 Quat& operator+=(const Quat &q)
319 {
320 mm[0] += q.mm[0];
321 mm[1] += q.mm[1];
322 mm[2] += q.mm[2];
323 mm[3] += q.mm[3];
324
325 return *this;
326 }
327
328 /// Subtract quaternion q from "this" quaternion, e.g. q -= q1;
329 Quat& operator-=(const Quat &q)
330 {
331 mm[0] -= q.mm[0];
332 mm[1] -= q.mm[1];
333 mm[2] -= q.mm[2];
334 mm[3] -= q.mm[3];
335
336 return *this;
337 }
338
339 /// Scale "this" quaternion by scalar, e.g. q *= scalar;
340 Quat& operator*=(T scalar)
341 {
342 mm[0] *= scalar;
343 mm[1] *= scalar;
344 mm[2] *= scalar;
345 mm[3] *= scalar;
346
347 return *this;
348 }
349
350 /// Return (this+q), e.g. q = q1 + q2;
351 Quat operator+(const Quat &q) const
352 {
353 return Quat<T>(mm[0]+q.mm[0], mm[1]+q.mm[1], mm[2]+q.mm[2], mm[3]+q.mm[3]);
354 }
355
356 /// Return (this-q), e.g. q = q1 - q2;
357 Quat operator-(const Quat &q) const
358 {
359 return Quat<T>(mm[0]-q.mm[0], mm[1]-q.mm[1], mm[2]-q.mm[2], mm[3]-q.mm[3]);
360 }
361
362 /// Return (this*q), e.g. q = q1 * q2;
363 Quat operator*(const Quat &q) const
364 {
365 Quat<T> prod;
366
367 prod.mm[0] = mm[3]*q.mm[0] + mm[0]*q.mm[3] + mm[1]*q.mm[2] - mm[2]*q.mm[1];
368 prod.mm[1] = mm[3]*q.mm[1] + mm[1]*q.mm[3] + mm[2]*q.mm[0] - mm[0]*q.mm[2];
369 prod.mm[2] = mm[3]*q.mm[2] + mm[2]*q.mm[3] + mm[0]*q.mm[1] - mm[1]*q.mm[0];
370 prod.mm[3] = mm[3]*q.mm[3] - mm[0]*q.mm[0] - mm[1]*q.mm[1] - mm[2]*q.mm[2];
371
372 return prod;
373
374 }
375
376 /// Assigns this to (this*q), e.g. q *= q1;
377 Quat operator*=(const Quat &q)
378 {
379 *this = *this * q;
380 return *this;
381 }
382
383 /// Return (this*scalar), e.g. q = q1 * scalar;
384 Quat operator*(T scalar) const
385 {
386 return Quat<T>(mm[0]*scalar, mm[1]*scalar, mm[2]*scalar, mm[3]*scalar);
387 }
388
389 /// Return (this/scalar), e.g. q = q1 / scalar;
390 Quat operator/(T scalar) const
391 {
392 return Quat<T>(mm[0]/scalar, mm[1]/scalar, mm[2]/scalar, mm[3]/scalar);
393 }
394
395 /// Negation operator, e.g. q = -q;
396 Quat operator-() const
397 { return Quat<T>(-mm[0], -mm[1], -mm[2], -mm[3]); }
398
399 /// this = q1 + q2
400 /// "this", q1 and q2 need not be distinct objects, e.g. q.add(q1,q);
401 Quat& add(const Quat &q1, const Quat &q2)
402 {
403 mm[0] = q1.mm[0] + q2.mm[0];
404 mm[1] = q1.mm[1] + q2.mm[1];
405 mm[2] = q1.mm[2] + q2.mm[2];
406 mm[3] = q1.mm[3] + q2.mm[3];
407
408 return *this;
409 }
410
411 /// this = q1 - q2
412 /// "this", q1 and q2 need not be distinct objects, e.g. q.sub(q1,q);
413 Quat& sub(const Quat &q1, const Quat &q2)
414 {
415 mm[0] = q1.mm[0] - q2.mm[0];
416 mm[1] = q1.mm[1] - q2.mm[1];
417 mm[2] = q1.mm[2] - q2.mm[2];
418 mm[3] = q1.mm[3] - q2.mm[3];
419
420 return *this;
421 }
422
423 /// this = q1 * q2
424 /// q1 and q2 must be distinct objects than "this", e.g. q.mult(q1,q2);
425 Quat& mult(const Quat &q1, const Quat &q2)
426 {
427 mm[0] = q1.mm[3]*q2.mm[0] + q1.mm[0]*q2.mm[3] +
428 q1.mm[1]*q2.mm[2] - q1.mm[2]*q2.mm[1];
429 mm[1] = q1.mm[3]*q2.mm[1] + q1.mm[1]*q2.mm[3] +
430 q1.mm[2]*q2.mm[0] - q1.mm[0]*q2.mm[2];
431 mm[2] = q1.mm[3]*q2.mm[2] + q1.mm[2]*q2.mm[3] +
432 q1.mm[0]*q2.mm[1] - q1.mm[1]*q2.mm[0];
433 mm[3] = q1.mm[3]*q2.mm[3] - q1.mm[0]*q2.mm[0] -
434 q1.mm[1]*q2.mm[1] - q1.mm[2]*q2.mm[2];
435
436 return *this;
437 }
438
439 /// this = scalar*q, q need not be distinct object than "this",
440 /// e.g. q.scale(1.5,q1);
441 Quat& scale(T scale, const Quat &q)
442 {
443 mm[0] = scale * q.mm[0];
444 mm[1] = scale * q.mm[1];
445 mm[2] = scale * q.mm[2];
446 mm[3] = scale * q.mm[3];
447
448 return *this;
449 }
450
451 /// Dot product
452 T dot(const Quat &q) const
453 {
454 return (mm[0]*q.mm[0] + mm[1]*q.mm[1] + mm[2]*q.mm[2] + mm[3]*q.mm[3]);
455 }
456
457 /// Return the quaternion rate corrsponding to the angular velocity omega
458 /// and "this" current rotation
459 Quat derivative(const Vec3<T>& omega) const
460 {
461 return Quat<T>( +w()*omega.x() -z()*omega.y() +y()*omega.z() ,
462 +z()*omega.x() +w()*omega.y() -x()*omega.z() ,
463 -y()*omega.x() +x()*omega.y() +w()*omega.z() ,
464 -x()*omega.x() -y()*omega.y() -z()*omega.z() );
465 }
466
467 /// this = normalized this
468 bool normalize(T eps = T(1.0e-8))
469 {
470 T d = T(sqrt(mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3]));
471 if( isApproxEqual(d, T(0.0), eps) ) return false;
472 *this *= ( T(1)/d );
473 return true;
474 }
475
476 /// this = normalized this
477 Quat unit() const
478 {
479 T d = sqrt(mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3]);
480 if( isExactlyEqual(d , T(0.0) ) )
481 OPENVDB_THROW(ArithmeticError,
482 "Normalizing degenerate quaternion");
483 return *this / d;
484 }
485
486 /// returns inverse of this
487 Quat inverse(T tolerance = T(0)) const
488 {
489 T d = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3];
490 if( isApproxEqual(d, T(0.0), tolerance) )
491 OPENVDB_THROW(ArithmeticError,
492 "Cannot invert degenerate quaternion");
493 Quat result = *this/-d;
494 result.mm[3] = -result.mm[3];
495 return result;
496 }
497
498
499 /// Return the conjugate of "this", same as invert without
500 /// unit quaternion test
501 Quat conjugate() const
502 {
503 return Quat<T>(-mm[0], -mm[1], -mm[2], mm[3]);
504 }
505
506 /// Return rotated vector by "this" quaternion
507 Vec3<T> rotateVector(const Vec3<T> &v) const
508 {
509 Mat3<T> m(*this);
510 return m.transform(v);
511 }
512
513 /// Predefined constants, e.g. Quat q = Quat::identity();
514 static Quat zero() { return Quat<T>(0,0,0,0); }
515 static Quat identity() { return Quat<T>(0,0,0,1); }
516
517 /// @return string representation of Classname
518 std::string str() const
519 {
520 std::ostringstream buffer;
521
522 buffer << "[";
523
524 // For each column
525 for (unsigned j(0); j < 4; j++) {
526 if (j) buffer << ", ";
527 buffer << mm[j];
528 }
529
530 buffer << "]";
531
532 return buffer.str();
533 }
534
535 /// Output to the stream, e.g. std::cout << q << std::endl;
536 friend std::ostream& operator<<(std::ostream &stream, const Quat &q)
537 {
538 stream << q.str();
539 return stream;
540 }
541
542 friend Quat slerp<>(const Quat &q1, const Quat &q2, T t, T tolerance);
543
544 void write(std::ostream& os) const { os.write(static_cast<char*>(&mm), sizeof(T) * 4); }
545 void read(std::istream& is) { is.read(static_cast<char*>(&mm), sizeof(T) * 4); }
546
547 protected:
548 T mm[4];
549};
550
551/// Multiply each element of the given quaternion by @a scalar and return the result.
552 template <typename S, typename T>
553 Quat<T> operator*(S scalar, const Quat<T> &q) { return q*scalar; }
554
555
556/// @brief Interpolate between m1 and m2.
557/// Converts to quaternion form and uses slerp
558/// m1 and m2 must be rotation matrices!
559 template <typename T, typename T0>
560 Mat3<T> slerp(const Mat3<T0> &m1, const Mat3<T0> &m2, T t)
561{
562 using MatType = Mat3<T>;
563
564 Quat<T> q1(m1);
565 Quat<T> q2(m2);
566
567 if (q1.dot(q2) < 0) q2 *= -1;
568
569 Quat<T> qslerp = slerp<T>(q1, q2, static_cast<T>(t));
570 MatType m = rotation<MatType>(qslerp);
571 return m;
572}
573
574
575
576/// Interpolate between m1 and m4 by converting m1 ... m4 into
577/// quaternions and treating them as control points of a Bezier
578/// curve using slerp in place of lerp in the De Castlejeau evaluation
579/// algorithm. Just like a cubic Bezier curve, this will interpolate
580/// m1 at t = 0 and m4 at t = 1 but in general will not pass through
581/// m2 and m3. Unlike a standard Bezier curve this curve will not have
582/// the convex hull property.
583/// m1 ... m4 must be rotation matrices!
584 template <typename T, typename T0>
585 Mat3<T> bezLerp(const Mat3<T0> &m1, const Mat3<T0> &m2,
586 const Mat3<T0> &m3, const Mat3<T0> &m4,
587 T t)
588{
589 Mat3<T> m00, m01, m02, m10, m11;
590
591 m00 = slerp(m1, m2, t);
592 m01 = slerp(m2, m3, t);
593 m02 = slerp(m3, m4, t);
594
595 m10 = slerp(m00, m01, t);
596 m11 = slerp(m01, m02, t);
597
598 return slerp(m10, m11, t);
599}
600
601 using Quats = Quat<float>;
602 using Quatd = Quat<double>;
603
604 OPENVDB_IS_POD(Quats)
605 OPENVDB_IS_POD(Quatd)
606
607} // namespace math
608
609
610 template<> inline math::Quats zeroVal<math::Quats >() { return math::Quats::zero(); }
611 template<> inline math::Quatd zeroVal<math::Quatd >() { return math::Quatd::zero(); }
612
613} // namespace OPENVDB_VERSION_NAME
614} // namespace openvdb
615
616#endif //OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
Assert.h
OPENVDB_ASSERT
#define OPENVDB_ASSERT(X)
Definition Assert.h:41
Mat3.h
Mat.h
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
Vec3.h
openvdb::v12_1::ArithmeticError
Definition Exceptions.h:56
openvdb::v12_1::math::Mat3
3x3 matrix class.
Definition Mat3.h:29
openvdb::v12_1::math::Mat3::trace
T trace() const
Trace of matrix.
Definition Mat3.h:488
openvdb::v12_1::math::Mat3::det
T det() const
Determinant of matrix.
Definition Mat3.h:479
openvdb::v12_1::math::Mat3::transform
Vec3< T0 > transform(const Vec3< T0 > &v) const
Definition Mat3.h:505
openvdb::v12_1::math::Quat
Definition Quat.h:80
openvdb::v12_1::math::Quat< Real >::angle
Real angle() const
Definition Quat.h:225
openvdb::v12_1::math::Quat< Real >::x
Real & x()
Definition Quat.h:194
openvdb::v12_1::math::Quat::sub
Quat & sub(const Quat &q1, const Quat &q2)
Definition Quat.h:413
openvdb::v12_1::math::Quat::conjugate
Quat conjugate() const
Definition Quat.h:501
openvdb::v12_1::math::Quat< Real >::axis
Vec3< Real > axis() const
Definition Quat.h:240
openvdb::v12_1::math::Quat::operator/
Quat operator/(T scalar) const
Return (this/scalar), e.g. q = q1 / scalar;.
Definition Quat.h:390
openvdb::v12_1::math::Quat::operator*=
Quat & operator*=(T scalar)
Scale "this" quaternion by scalar, e.g. q *= scalar;.
Definition Quat.h:340
openvdb::v12_1::math::Quat::setAxisAngle
Quat & setAxisAngle(const Vec3< T > &axis, T angle)
Definition Quat.h:268
openvdb::v12_1::math::Quat::unit
Quat unit() const
this = normalized this
Definition Quat.h:477
openvdb::v12_1::math::Quat::write
void write(std::ostream &os) const
Definition Quat.h:544
openvdb::v12_1::math::Quat::operator*
Quat operator*(const Quat &q) const
Return (this*q), e.g. q = q1 * q2;.
Definition Quat.h:363
openvdb::v12_1::math::Quat::operator==
bool operator==(const Quat &q) const
Equality operator, does exact floating point comparisons.
Definition Quat.h:302
openvdb::v12_1::math::Quat::Quat
Quat(T *a)
Constructor with array argument, e.g. float a[4]; Quatf q(a);.
Definition Quat.h:102
openvdb::v12_1::math::Quat::add
Quat & add(const Quat &q1, const Quat &q2)
Definition Quat.h:401
openvdb::v12_1::math::Quat::operator<<
friend std::ostream & operator<<(std::ostream &stream, const Quat &q)
Output to the stream, e.g. std::cout << q << std::endl;.
Definition Quat.h:536
openvdb::v12_1::math::Quat::w
T w() const
Definition Quat.h:203
openvdb::v12_1::math::Quat::Quat
Quat(math::Axis axis, T angle)
Constructor given rotation as axis and angle.
Definition Quat.h:128
openvdb::v12_1::math::Quat::operator+=
Quat & operator+=(const Quat &q)
Add quaternion q to "this" quaternion, e.g. q += q1;.
Definition Quat.h:318
openvdb::v12_1::math::Quat::Quat
Quat()=default
openvdb::v12_1::math::Quat::operator-
Quat operator-() const
Negation operator, e.g. q = -q;.
Definition Quat.h:396
openvdb::v12_1::math::Quat::operator()
T & operator()(int i)
Alternative indexed reference to the elements.
Definition Quat.h:219
openvdb::v12_1::math::Quat< Real >::y
Real & y()
Definition Quat.h:195
openvdb::v12_1::math::Quat< Real >::z
Real & z()
Definition Quat.h:196
openvdb::v12_1::math::Quat::Quat
Quat(const Vec3< T > &axis, T angle)
Definition Quat.h:113
openvdb::v12_1::math::Quat::scale
Quat & scale(T scale, const Quat &q)
Definition Quat.h:441
openvdb::v12_1::math::Quat::operator()
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition Quat.h:222
openvdb::v12_1::math::Quat::Quat
Quat(const Mat3< T1 > &rot)
Constructor given a rotation matrix.
Definition Quat.h:141
openvdb::v12_1::math::Quat< Real >::setIdentity
Quat & setIdentity()
Definition Quat.h:290
openvdb::v12_1::math::Quat::operator+
Quat operator+(const Quat &q) const
Return (this+q), e.g. q = q1 + q2;.
Definition Quat.h:351
openvdb::v12_1::math::Quat::init
Quat & init()
"this" quaternion gets initialized to identity, same as setIdentity()
Definition Quat.h:264
openvdb::v12_1::math::Quat::operator*=
Quat operator*=(const Quat &q)
Assigns this to (this*q), e.g. q *= q1;.
Definition Quat.h:377
openvdb::v12_1::math::Quat::Quat
Quat(T x, T y, T z, T w)
Constructor with four arguments, e.g. Quatf q(1,2,3,4);.
Definition Quat.h:92
openvdb::v12_1::math::Quat::rotateVector
Vec3< T > rotateVector(const Vec3< T > &v) const
Return rotated vector by "this" quaternion.
Definition Quat.h:507
openvdb::v12_1::math::Quat::x
T x() const
Get the component, e.g. float f = q.w();.
Definition Quat.h:200
openvdb::v12_1::math::Quat< Real >::size
static const int size
Definition Quat.h:84
openvdb::v12_1::math::Quat::normalize
bool normalize(T eps=T(1.0e-8))
this = normalized this
Definition Quat.h:468
openvdb::v12_1::math::Quat::identity
static Quat identity()
Definition Quat.h:515
openvdb::v12_1::math::Quat::init
Quat & init(T x, T y, T z, T w)
"this" quaternion gets initialized to [x, y, z, w]
Definition Quat.h:257
openvdb::v12_1::math::Quat::z
T z() const
Definition Quat.h:202
openvdb::v12_1::math::Quat::y
T y() const
Definition Quat.h:201
openvdb::v12_1::math::Quat::eulerAngles
Vec3< T > eulerAngles(RotationOrder rotationOrder) const
Returns vector of x,y,z rotational components.
Definition Quat.h:298
openvdb::v12_1::math::Quat::operator[]
T operator[](int i) const
Array style constant reference to the components, e.g. float f = q[1];.
Definition Quat.h:212
openvdb::v12_1::math::Quat::numElements
static unsigned numElements()
Definition Quat.h:206
openvdb::v12_1::math::Quat::derivative
Quat derivative(const Vec3< T > &omega) const
Definition Quat.h:459
openvdb::v12_1::math::Quat::operator[]
T & operator[](int i)
Array style reference to the components, e.g. q[3] = 1.34f;.
Definition Quat.h:209
openvdb::v12_1::math::Quat::operator*
Quat operator*(T scalar) const
Return (this*scalar), e.g. q = q1 * scalar;.
Definition Quat.h:384
openvdb::v12_1::math::Quat< Real >::mm
Real mm[4]
Definition Quat.h:548
openvdb::v12_1::math::Quat::str
std::string str() const
Definition Quat.h:518
openvdb::v12_1::math::Quat< Real >::slerp
friend Quat slerp(const Quat &q1, const Quat &q2, Real t, Real tolerance)
openvdb::v12_1::math::Quat::operator-=
Quat & operator-=(const Quat &q)
Subtract quaternion q from "this" quaternion, e.g. q -= q1;.
Definition Quat.h:329
openvdb::v12_1::math::Quat< Real >::ValueType
Real ValueType
Definition Quat.h:83
openvdb::v12_1::math::Quat::mult
Quat & mult(const Quat &q1, const Quat &q2)
Definition Quat.h:425
openvdb::v12_1::math::Quat::zero
static Quat zero()
Predefined constants, e.g. Quat q = Quat::identity();.
Definition Quat.h:514
openvdb::v12_1::math::Quat::inverse
Quat inverse(T tolerance=T(0)) const
returns inverse of this
Definition Quat.h:487
openvdb::v12_1::math::Quat::eq
bool eq(const Quat &q, T eps=1.0e-7) const
Test if "this" is equivalent to q with tolerance of eps value.
Definition Quat.h:311
openvdb::v12_1::math::Quat::setZero
Quat & setZero()
Set "this" vector to zero.
Definition Quat.h:283
openvdb::v12_1::math::Quat::operator-
Quat operator-(const Quat &q) const
Return (this-q), e.g. q = q1 - q2;.
Definition Quat.h:357
openvdb::v12_1::math::Quat< Real >::value_type
Real value_type
Definition Quat.h:82
openvdb::v12_1::math::Quat< Real >::w
Real & w()
Definition Quat.h:197
openvdb::v12_1::math::Quat::read
void read(std::istream &is)
Definition Quat.h:545
openvdb::v12_1::math::Quat::dot
T dot(const Quat &q) const
Dot product.
Definition Quat.h:452
openvdb::v12_1::math::Vec3
Definition Vec3.h:25
openvdb::v12_1::math::Vec3::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition Vec3.h:86
openvdb::v12_1::math::Vec3::y
T & y()
Definition Vec3.h:87
openvdb::v12_1::math::Vec3::z
T & z()
Definition Vec3.h:88
openvdb::v12_1::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::v12_1::math::eulerAngles
Vec3< typename MatType::value_type > eulerAngles(const MatType &mat, RotationOrder rotationOrder, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
Return the Euler angles composing the given rotation matrix.
Definition Mat.h:333
openvdb::v12_1::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::v12_1::math::isUnitary
bool isUnitary(const MatType &m)
Determine if a matrix is unitary (i.e., rotation or reflection).
Definition Mat.h:889
openvdb::v12_1::math::rotation
MatType rotation(const Quat< typename MatType::value_type > &q, typename MatType::value_type eps=static_cast< typename MatType::value_type >(1.0e-8))
Return the rotation matrix specified by the given quaternion.
Definition Mat.h:172
openvdb::v12_1::math::angle
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition Vec2.h:446
openvdb::v12_1::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition Math.h:443
openvdb::v12_1::math::Quatd
Quat< double > Quatd
Definition Quat.h:602
openvdb::v12_1::math::Axis
Axis
Definition Math.h:901
openvdb::v12_1::math::Z_AXIS
@ Z_AXIS
Definition Math.h:904
openvdb::v12_1::math::X_AXIS
@ X_AXIS
Definition Math.h:902
openvdb::v12_1::math::Y_AXIS
@ Y_AXIS
Definition Math.h:903
openvdb::v12_1::math::Quats
Quat< float > Quats
Definition Quat.h:601
openvdb::v12_1::math::bezLerp
Mat3< T > bezLerp(const Mat3< T0 > &m1, const Mat3< T0 > &m2, const Mat3< T0 > &m3, const Mat3< T0 > &m4, T t)
Definition Quat.h:585
openvdb::v12_1::math::RotationOrder
RotationOrder
Definition Math.h:908
openvdb::v12_1::math::slerp
Quat< T > slerp(const Quat< T > &q1, const Quat< T > &q2, T t, T tolerance=0.00001)
Linear interpolation between the two quaternions.
Definition Quat.h:28
openvdb::v12_1::zeroVal
constexpr T zeroVal()
Return the value of type T that corresponds to zero.
Definition Math.h:70
openvdb
Definition Exceptions.h:13
Exceptions.h
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition Exceptions.h:74
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:218