OpenVDB: Quat.h Source File

OpenVDB 6.1.0

Quat.h
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1 //
3 // Copyright (c) 2012-2019 DreamWorks Animation LLC
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30
31 #ifndef OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
32 #define OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
33
34 #include "Mat.h"
35 #include "Mat3.h"
36 #include "Math.h"
37 #include "Vec3.h"
38 #include <openvdb/Exceptions.h>
39 #include <cmath>
40 #include <iostream>
41 #include <sstream>
42 #include <string>
43
44
45 namespace openvdb {
46 OPENVDB_USE_VERSION_NAMESPACE
47 namespace OPENVDB_VERSION_NAME {
48 namespace math {
49
50 template<typename T> class Quat;
51
53 template <typename T>
54 Quat<T> slerp(const Quat<T> &q1, const Quat<T> &q2, T t, T tolerance=0.00001)
55 {
56 T qdot, angle, sineAngle;
57
58 qdot = q1.dot(q2);
59
60 if (fabs(qdot) >= 1.0) {
61 angle = 0; // not necessary but suppresses compiler warning
62 sineAngle = 0;
63 } else {
64 angle = acos(qdot);
65 sineAngle = sin(angle);
66 }
67
68 //
69 // Denominator close to 0 corresponds to the case where the
70 // two quaternions are close to the same rotation. In this
71 // case linear interpolation is used but we normalize to
72 // guarantee unit length
73 //
74 if (sineAngle <= tolerance) {
75 T s = 1.0 - t;
76
77 Quat<T> qtemp(s * q1[0] + t * q2[0], s * q1[1] + t * q2[1],
78 s * q1[2] + t * q2[2], s * q1[3] + t * q2[3]);
79 //
80 // Check the case where two close to antipodal quaternions were
81 // blended resulting in a nearly zero result which can happen,
82 // for example, if t is close to 0.5. In this case it is not safe
83 // to project back onto the sphere.
84 //
85 double lengthSquared = qtemp.dot(qtemp);
86
87 if (lengthSquared <= tolerance * tolerance) {
88 qtemp = (t < 0.5) ? q1 : q2;
89 } else {
90 qtemp *= 1.0 / sqrt(lengthSquared);
91 }
92 return qtemp;
93 } else {
94
95 T sine = 1.0 / sineAngle;
96 T a = sin((1.0 - t) * angle) * sine;
97 T b = sin(t * angle) * sine;
98 return Quat<T>(a * q1[0] + b * q2[0], a * q1[1] + b * q2[1],
99 a * q1[2] + b * q2[2], a * q1[3] + b * q2[3]);
100 }
101
102 }
103
104 template<typename T>
105 class Quat
106 {
107 public:
108 using value_type = T;
109 using ValueType = T;
110 static const int size = 4;
111
113 Quat() {}
114
116 Quat(T x, T y, T z, T w)
117 {
118 mm[0] = x;
119 mm[1] = y;
120 mm[2] = z;
121 mm[3] = w;
122
123 }
124
126 Quat(T *a)
127 {
128 mm[0] = a[0];
129 mm[1] = a[1];
130 mm[2] = a[2];
131 mm[3] = a[3];
132
133 }
134
137 Quat(const Vec3<T> &axis, T angle)
138 {
139 // assert( REL_EQ(axis.length(), 1.) );
140
141 T s = T(sin(angle*T(0.5)));
142
143 mm[0] = axis.x() * s;
144 mm[1] = axis.y() * s;
145 mm[2] = axis.z() * s;
146
147 mm[3] = T(cos(angle*T(0.5)));
148
149 }
150
152 Quat(math::Axis axis, T angle)
153 {
154 T s = T(sin(angle*T(0.5)));
155
156 mm[0] = (axis==math::X_AXIS) * s;
157 mm[1] = (axis==math::Y_AXIS) * s;
158 mm[2] = (axis==math::Z_AXIS) * s;
159
160 mm[3] = T(cos(angle*T(0.5)));
161 }
162
164 template<typename T1>
165 Quat(const Mat3<T1> &rot) {
166
167 // verify that the matrix is really a rotation
168 if(!isUnitary(rot)) { // unitary is reflection or rotation
169 OPENVDB_THROW(ArithmeticError,
170 "A non-rotation matrix can not be used to construct a quaternion");
171 }
172 if (!isApproxEqual(rot.det(), T1(1))) { // rule out reflection
173 OPENVDB_THROW(ArithmeticError,
174 "A reflection matrix can not be used to construct a quaternion");
175 }
176
177 T trace(rot.trace());
178 if (trace > 0) {
179
180 T q_w = 0.5 * std::sqrt(trace+1);
181 T factor = 0.25 / q_w;
182
183 mm[0] = factor * (rot(1,2) - rot(2,1));
184 mm[1] = factor * (rot(2,0) - rot(0,2));
185 mm[2] = factor * (rot(0,1) - rot(1,0));
186 mm[3] = q_w;
187 } else if (rot(0,0) > rot(1,1) && rot(0,0) > rot(2,2)) {
188
189 T q_x = 0.5 * sqrt(rot(0,0)- rot(1,1)-rot(2,2)+1);
190 T factor = 0.25 / q_x;
191
192 mm[0] = q_x;
193 mm[1] = factor * (rot(0,1) + rot(1,0));
194 mm[2] = factor * (rot(2,0) + rot(0,2));
195 mm[3] = factor * (rot(1,2) - rot(2,1));
196 } else if (rot(1,1) > rot(2,2)) {
197
198 T q_y = 0.5 * sqrt(rot(1,1)-rot(0,0)-rot(2,2)+1);
199 T factor = 0.25 / q_y;
200
201 mm[0] = factor * (rot(0,1) + rot(1,0));
202 mm[1] = q_y;
203 mm[2] = factor * (rot(1,2) + rot(2,1));
204 mm[3] = factor * (rot(2,0) - rot(0,2));
205 } else {
206
207 T q_z = 0.5 * sqrt(rot(2,2)-rot(0,0)-rot(1,1)+1);
208 T factor = 0.25 / q_z;
209
210 mm[0] = factor * (rot(2,0) + rot(0,2));
211 mm[1] = factor * (rot(1,2) + rot(2,1));
212 mm[2] = q_z;
213 mm[3] = factor * (rot(0,1) - rot(1,0));
214 }
215 }
216
218 Quat(const Quat &q)
219 {
220 mm[0] = q.mm[0];
221 mm[1] = q.mm[1];
222 mm[2] = q.mm[2];
223 mm[3] = q.mm[3];
224
225 }
226
228 T& x() { return mm[0]; }
229 T& y() { return mm[1]; }
230 T& z() { return mm[2]; }
231 T& w() { return mm[3]; }
232
234 T x() const { return mm[0]; }
235 T y() const { return mm[1]; }
236 T z() const { return mm[2]; }
237 T w() const { return mm[3]; }
238
239 // Number of elements
240 static unsigned numElements() { return 4; }
241
243 T& operator[](int i) { return mm[i]; }
244
246 T operator[](int i) const { return mm[i]; }
247
249 operator T*() { return mm; }
250 operator const T*() const { return mm; }
251
253 T& operator()(int i) { return mm[i]; }
254
256 T operator()(int i) const { return mm[i]; }
257
259 T angle() const
260 {
261 T sqrLength = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2];
262
263 if ( sqrLength > 1.0e-8 ) {
264
265 return T(T(2.0) * acos(mm[3]));
266
267 } else {
268
269 return T(0.0);
270 }
271 }
272
274 Vec3<T> axis() const
275 {
276 T sqrLength = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2];
277
278 if ( sqrLength > 1.0e-8 ) {
279
280 T invLength = T(T(1)/sqrt(sqrLength));
281
282 return Vec3<T>( mm[0]*invLength, mm[1]*invLength, mm[2]*invLength );
283 } else {
284
285 return Vec3<T>(1,0,0);
286 }
287 }
288
289
291 Quat& init(T x, T y, T z, T w)
292 {
293 mm[0] = x; mm[1] = y; mm[2] = z; mm[3] = w;
294 return *this;
295 }
296
298 Quat& init() { return setIdentity(); }
299
302 Quat& setAxisAngle(const Vec3<T>& axis, T angle)
303 {
304
305 T s = T(sin(angle*T(0.5)));
306
307 mm[0] = axis.x() * s;
308 mm[1] = axis.y() * s;
309 mm[2] = axis.z() * s;
310
311 mm[3] = T(cos(angle*T(0.5)));
312
313 return *this;
314 } // axisAngleTest
315
317 Quat& setZero()
318 {
319 mm[0] = mm[1] = mm[2] = mm[3] = 0;
320 return *this;
321 }
322
324 Quat& setIdentity()
325 {
326 mm[0] = mm[1] = mm[2] = 0;
327 mm[3] = 1;
328 return *this;
329 }
330
332 Vec3<T> eulerAngles(RotationOrder rotationOrder) const
333 { return math::eulerAngles(Mat3<T>(*this), rotationOrder); }
334
336 Quat& operator=(const Quat &q)
337 {
338 mm[0] = q.mm[0];
339 mm[1] = q.mm[1];
340 mm[2] = q.mm[2];
341 mm[3] = q.mm[3];
342
343 return *this;
344 }
345
347 bool operator==(const Quat &q) const
348 {
349 return (isExactlyEqual(mm[0],q.mm[0]) &&
350 isExactlyEqual(mm[1],q.mm[1]) &&
351 isExactlyEqual(mm[2],q.mm[2]) &&
352 isExactlyEqual(mm[3],q.mm[3]) );
353 }
354
356 bool eq(const Quat &q, T eps=1.0e-7) const
357 {
358 return isApproxEqual(mm[0],q.mm[0],eps) && isApproxEqual(mm[1],q.mm[1],eps) &&
359 isApproxEqual(mm[2],q.mm[2],eps) && isApproxEqual(mm[3],q.mm[3],eps) ;
360 } // trivial
361
363 Quat& operator+=(const Quat &q)
364 {
365 mm[0] += q.mm[0];
366 mm[1] += q.mm[1];
367 mm[2] += q.mm[2];
368 mm[3] += q.mm[3];
369
370 return *this;
371 }
372
374 Quat& operator-=(const Quat &q)
375 {
376 mm[0] -= q.mm[0];
377 mm[1] -= q.mm[1];
378 mm[2] -= q.mm[2];
379 mm[3] -= q.mm[3];
380
381 return *this;
382 }
383
385 Quat& operator*=(T scalar)
386 {
387 mm[0] *= scalar;
388 mm[1] *= scalar;
389 mm[2] *= scalar;
390 mm[3] *= scalar;
391
392 return *this;
393 }
394
396 Quat operator+(const Quat &q) const
397 {
398 return Quat<T>(mm[0]+q.mm[0], mm[1]+q.mm[1], mm[2]+q.mm[2], mm[3]+q.mm[3]);
399 }
400
402 Quat operator-(const Quat &q) const
403 {
404 return Quat<T>(mm[0]-q.mm[0], mm[1]-q.mm[1], mm[2]-q.mm[2], mm[3]-q.mm[3]);
405 }
406
408 Quat operator*(const Quat &q) const
409 {
410 Quat<T> prod;
411
412 prod.mm[0] = mm[3]*q.mm[0] + mm[0]*q.mm[3] + mm[1]*q.mm[2] - mm[2]*q.mm[1];
413 prod.mm[1] = mm[3]*q.mm[1] + mm[1]*q.mm[3] + mm[2]*q.mm[0] - mm[0]*q.mm[2];
414 prod.mm[2] = mm[3]*q.mm[2] + mm[2]*q.mm[3] + mm[0]*q.mm[1] - mm[1]*q.mm[0];
415 prod.mm[3] = mm[3]*q.mm[3] - mm[0]*q.mm[0] - mm[1]*q.mm[1] - mm[2]*q.mm[2];
416
417 return prod;
418
419 }
420
422 Quat operator*=(const Quat &q)
423 {
424 *this = *this * q;
425 return *this;
426 }
427
429 Quat operator*(T scalar) const
430 {
431 return Quat<T>(mm[0]*scalar, mm[1]*scalar, mm[2]*scalar, mm[3]*scalar);
432 }
433
435 Quat operator/(T scalar) const
436 {
437 return Quat<T>(mm[0]/scalar, mm[1]/scalar, mm[2]/scalar, mm[3]/scalar);
438 }
439
441 Quat operator-() const
442 { return Quat<T>(-mm[0], -mm[1], -mm[2], -mm[3]); }
443
446 Quat& add(const Quat &q1, const Quat &q2)
447 {
448 mm[0] = q1.mm[0] + q2.mm[0];
449 mm[1] = q1.mm[1] + q2.mm[1];
450 mm[2] = q1.mm[2] + q2.mm[2];
451 mm[3] = q1.mm[3] + q2.mm[3];
452
453 return *this;
454 }
455
458 Quat& sub(const Quat &q1, const Quat &q2)
459 {
460 mm[0] = q1.mm[0] - q2.mm[0];
461 mm[1] = q1.mm[1] - q2.mm[1];
462 mm[2] = q1.mm[2] - q2.mm[2];
463 mm[3] = q1.mm[3] - q2.mm[3];
464
465 return *this;
466 }
467
470 Quat& mult(const Quat &q1, const Quat &q2)
471 {
472 mm[0] = q1.mm[3]*q2.mm[0] + q1.mm[0]*q2.mm[3] +
473 q1.mm[1]*q2.mm[2] - q1.mm[2]*q2.mm[1];
474 mm[1] = q1.mm[3]*q2.mm[1] + q1.mm[1]*q2.mm[3] +
475 q1.mm[2]*q2.mm[0] - q1.mm[0]*q2.mm[2];
476 mm[2] = q1.mm[3]*q2.mm[2] + q1.mm[2]*q2.mm[3] +
477 q1.mm[0]*q2.mm[1] - q1.mm[1]*q2.mm[0];
478 mm[3] = q1.mm[3]*q2.mm[3] - q1.mm[0]*q2.mm[0] -
479 q1.mm[1]*q2.mm[1] - q1.mm[2]*q2.mm[2];
480
481 return *this;
482 }
483
486 Quat& scale(T scale, const Quat &q)
487 {
488 mm[0] = scale * q.mm[0];
489 mm[1] = scale * q.mm[1];
490 mm[2] = scale * q.mm[2];
491 mm[3] = scale * q.mm[3];
492
493 return *this;
494 }
495
497 T dot(const Quat &q) const
498 {
499 return (mm[0]*q.mm[0] + mm[1]*q.mm[1] + mm[2]*q.mm[2] + mm[3]*q.mm[3]);
500 }
501
504 Quat derivative(const Vec3<T>& omega) const
505 {
506 return Quat<T>( +w()*omega.x() -z()*omega.y() +y()*omega.z() ,
507 +z()*omega.x() +w()*omega.y() -x()*omega.z() ,
508 -y()*omega.x() +x()*omega.y() +w()*omega.z() ,
509 -x()*omega.x() -y()*omega.y() -z()*omega.z() );
510 }
511
513 bool normalize(T eps = T(1.0e-8))
514 {
515 T d = T(sqrt(mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3]));
516 if( isApproxEqual(d, T(0.0), eps) ) return false;
517 *this *= ( T(1)/d );
518 return true;
519 }
520
522 Quat unit() const
523 {
524 T d = sqrt(mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3]);
525 if( isExactlyEqual(d , T(0.0) ) )
526 OPENVDB_THROW(ArithmeticError,
527 "Normalizing degenerate quaternion");
528 return *this / d;
529 }
530
532 Quat inverse(T tolerance = T(0))
533 {
534 T d = mm[0]*mm[0] + mm[1]*mm[1] + mm[2]*mm[2] + mm[3]*mm[3];
535 if( isApproxEqual(d, T(0.0), tolerance) )
536 OPENVDB_THROW(ArithmeticError,
537 "Cannot invert degenerate quaternion");
538 Quat result = *this/-d;
539 result.mm[3] = -result.mm[3];
540 return result;
541 }
542
543
546 Quat conjugate() const
547 {
548 return Quat<T>(-mm[0], -mm[1], -mm[2], mm[3]);
549 }
550
552 Vec3<T> rotateVector(const Vec3<T> &v) const
553 {
554 Mat3<T> m(*this);
555 return m.transform(v);
556 }
557
559 static Quat zero() { return Quat<T>(0,0,0,0); }
560 static Quat identity() { return Quat<T>(0,0,0,1); }
561
563 std::string str() const
564 {
565 std::ostringstream buffer;
566
567 buffer << "[";
568
569 // For each column
570 for (unsigned j(0); j < 4; j++) {
571 if (j) buffer << ", ";
572 buffer << mm[j];
573 }
574
575 buffer << "]";
576
577 return buffer.str();
578 }
579
581 friend std::ostream& operator<<(std::ostream &stream, const Quat &q)
582 {
583 stream << q.str();
584 return stream;
585 }
586
587 friend Quat slerp<>(const Quat &q1, const Quat &q2, T t, T tolerance);
588
589 void write(std::ostream& os) const { os.write(static_cast<char*>(&mm), sizeof(T) * 4); }
590 void read(std::istream& is) { is.read(static_cast<char*>(&mm), sizeof(T) * 4); }
591
592 protected:
593 T mm[4];
594 };
595
597 template <typename S, typename T>
598 Quat<T> operator*(S scalar, const Quat<T> &q) { return q*scalar; }
599
600
604 template <typename T, typename T0>
605 Mat3<T> slerp(const Mat3<T0> &m1, const Mat3<T0> &m2, T t)
606 {
607 using MatType = Mat3<T>;
608
609 Quat<T> q1(m1);
610 Quat<T> q2(m2);
611
612 if (q1.dot(q2) < 0) q2 *= -1;
613
614 Quat<T> qslerp = slerp<T>(q1, q2, static_cast<T>(t));
615 MatType m = rotation<MatType>(qslerp);
616 return m;
617 }
618
619
620
629 template <typename T, typename T0>
630 Mat3<T> bezLerp(const Mat3<T0> &m1, const Mat3<T0> &m2,
631 const Mat3<T0> &m3, const Mat3<T0> &m4,
632 T t)
633 {
634 Mat3<T> m00, m01, m02, m10, m11;
635
636 m00 = slerp(m1, m2, t);
637 m01 = slerp(m2, m3, t);
638 m02 = slerp(m3, m4, t);
639
640 m10 = slerp(m00, m01, t);
641 m11 = slerp(m01, m02, t);
642
643 return slerp(m10, m11, t);
644 }
645
646 using Quats = Quat<float>;
647 using Quatd = Quat<double>;
648
649 } // namespace math
650
651
652 template<> inline math::Quats zeroVal<math::Quats >() { return math::Quats::zero(); }
653 template<> inline math::Quatd zeroVal<math::Quatd >() { return math::Quatd::zero(); }
654
655 } // namespace OPENVDB_VERSION_NAME
656 } // namespace openvdb
657
658 #endif //OPENVDB_MATH_QUAT_H_HAS_BEEN_INCLUDED
659
660 // Copyright (c) 2012-2019 DreamWorks Animation LLC
661 // All rights reserved. This software is distributed under the
662 // Mozilla Public License 2.0 ( http://www.mozilla.org/MPL/2.0/ )
openvdb::v6_1::math::Quat::dot
T dot(const Quat &q) const
Dot product.
Definition: Quat.h:497
openvdb::v6_1::math::Quat::z
T z() const
Definition: Quat.h:236
openvdb::v6_1::math::X_AXIS
Definition: Math.h:857
openvdb::v6_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:116
openvdb::v6_1::math::Quat::setZero
Quat & setZero()
Set "this" vector to zero.
Definition: Quat.h:317
openvdb::v6_1::math::Quat::operator[]
T & operator[](int i)
Array style reference to the components, e.g. q[3] = 1.34f;.
Definition: Quat.h:243
Vec3.h
openvdb::v6_1::math::Quat::x
T x() const
Get the component, e.g. float f = q.w();.
Definition: Quat.h:234
openvdb::v6_1::math::Axis
Axis
Definition: Math.h:856
openvdb::v6_1::math::Quat::mm
T mm[4]
Definition: Quat.h:593
Math.h
General-purpose arithmetic and comparison routines, most of which accept arbitrary value types (or at...
openvdb::v6_1::math::Quat::operator/
Quat operator/(T scalar) const
Return (this/scalar), e.g. q = q1 / scalar;.
Definition: Quat.h:435
openvdb::v6_1::math::Quat::identity
static Quat identity()
Definition: Quat.h:560
openvdb::v6_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:630
openvdb::v6_1::math::Quat::ValueType
T ValueType
Definition: Quat.h:109
openvdb::v6_1::math::Quat::add
Quat & add(const Quat &q1, const Quat &q2)
Definition: Quat.h:446
openvdb::v6_1::math::Quat::operator()
T operator()(int i) const
Alternative indexed constant reference to the elements,.
Definition: Quat.h:256
openvdb::v6_1::math::isUnitary
bool isUnitary(const MatType &m)
Determine if a matrix is unitary (i.e., rotation or reflection).
Definition: Mat.h:921
openvdb::v6_1::math::angle
T angle(const Vec2< T > &v1, const Vec2< T > &v2)
Definition: Vec2.h:472
openvdb::v6_1::math::Quat::eulerAngles
Vec3< T > eulerAngles(RotationOrder rotationOrder) const
Returns vector of x,y,z rotational components.
Definition: Quat.h:332
openvdb::v6_1::math::Quat::operator-
Quat operator-() const
Negation operator, e.g. q = -q;.
Definition: Quat.h:441
OPENVDB_THROW
#define OPENVDB_THROW(exception, message)
Definition: Exceptions.h:109
openvdb::v6_1::math::Quat::operator-=
Quat & operator-=(const Quat &q)
Subtract quaternion q from "this" quaternion, e.g. q -= q1;.
Definition: Quat.h:374
openvdb::v6_1::math::Quat::sub
Quat & sub(const Quat &q1, const Quat &q2)
Definition: Quat.h:458
openvdb::v6_1::math::isExactlyEqual
bool isExactlyEqual(const T0 &a, const T1 &b)
Return true if a is exactly equal to b.
Definition: Math.h:395
openvdb::v6_1::math::Quat::scale
Quat & scale(T scale, const Quat &q)
Definition: Quat.h:486
openvdb::v6_1::math::Quat::inverse
Quat inverse(T tolerance=T(0))
returns inverse of this
Definition: Quat.h:532
openvdb::v6_1::math::Quat::z
T & z()
Definition: Quat.h:230
openvdb::v6_1::math::Quat::y
T & y()
Definition: Quat.h:229
openvdb::v6_1::math::Quat::init
Quat & init()
"this" quaternion gets initialized to identity, same as setIdentity()
Definition: Quat.h:298
openvdb::v6_1::math::Y_AXIS
Definition: Math.h:858
Mat3.h
openvdb::v6_1::math::Quat::normalize
bool normalize(T eps=T(1.0e-8))
this = normalized this
Definition: Quat.h:513
openvdb::v6_1::math::Quat::read
void read(std::istream &is)
Definition: Quat.h:590
openvdb::v6_1::math::Quat::y
T y() const
Definition: Quat.h:235
openvdb::v6_1::math::Mat3::transform
Vec3< T0 > transform(const Vec3< T0 > &v) const
Definition: Mat3.h:553
openvdb::v6_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:291
openvdb::v6_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:581
openvdb::v6_1::math::Quat::operator-
Quat operator-(const Quat &q) const
Return (this-q), e.g. q = q1 - q2;.
Definition: Quat.h:402
openvdb::v6_1::math::isApproxEqual
bool isApproxEqual(const Type &a, const Type &b)
Return true if a is equal to b to within the default floating-point comparison tolerance.
Definition: Math.h:358
Exceptions.h
OPENVDB_VERSION_NAME
#define OPENVDB_VERSION_NAME
The version namespace name for this library version.
Definition: version.h:125
openvdb::v6_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:356
openvdb::v6_1::math::operator *
Quat< T > operator *(S scalar, const Quat< T > &q)
Multiply each element of the given quaternion by scalar and return the result.
Definition: Quat.h:598
openvdb::v6_1::math::Quat::x
T & x()
Reference to the component, e.g. q.x() = 4.5f;.
Definition: Quat.h:228
openvdb::v6_1::math::Vec3::z
T & z()
Definition: Vec3.h:112
openvdb::v6_1::math::Quat::derivative
Quat derivative(const Vec3< T > &omega) const
Definition: Quat.h:504
openvdb::v6_1::math::RotationOrder
RotationOrder
Definition: Math.h:863
openvdb::v6_1::math::Vec3::y
T & y()
Definition: Vec3.h:111
openvdb
Definition: Exceptions.h:40
openvdb::v6_1::math::Quat::operator+
Quat operator+(const Quat &q) const
Return (this+q), e.g. q = q1 + q2;.
Definition: Quat.h:396
openvdb::v6_1::math::Quat::conjugate
Quat conjugate() const
Definition: Quat.h:546
openvdb::v6_1::math::Mat3::trace
T trace() const
Trace of matrix.
Definition: Mat3.h:536
openvdb::v6_1::math::Vec3
Definition: Mat.h:197
openvdb::v6_1::math::Quat::w
T w() const
Definition: Quat.h:237
openvdb::v6_1::math::Quat::operator=
Quat & operator=(const Quat &q)
Assignment operator.
Definition: Quat.h:336
openvdb::v6_1::math::Quat::write
void write(std::ostream &os) const
Definition: Quat.h:589
openvdb::v6_1::math::Quat::Quat
Quat(math::Axis axis, T angle)
Constructor given rotation as axis and angle.
Definition: Quat.h:152
openvdb::v6_1::math::scale
MatType scale(const Vec3< typename MatType::value_type > &s)
Return a matrix that scales by s.
Definition: Mat.h:647
openvdb::v6_1::math::Quat::unit
Quat unit() const
this = normalized this
Definition: Quat.h:522
openvdb::v6_1::math::Quat::Quat
Quat()
Trivial constructor, the quaternion is NOT initialized.
Definition: Quat.h:113
openvdb::v6_1::math::Quat::Quat
Quat(const Vec3< T > &axis, T angle)
Definition: Quat.h:137
openvdb::v6_1::math::Quat::operator==
bool operator==(const Quat &q) const
Equality operator, does exact floating point comparisons.
Definition: Quat.h:347
openvdb::v6_1::math::Quat::rotateVector
Vec3< T > rotateVector(const Vec3< T > &v) const
Return rotated vector by "this" quaternion.
Definition: Quat.h:552
openvdb::v6_1::math::Quat::numElements
static unsigned numElements()
Definition: Quat.h:240
openvdb::v6_1::math::Z_AXIS
Definition: Math.h:859
openvdb::v6_1::math::slerp
Mat3< T > slerp(const Mat3< T0 > &m1, const Mat3< T0 > &m2, T t)
Interpolate between m1 and m2. Converts to quaternion form and uses slerp m1 and m2 must be rotation ...
Definition: Quat.h:605
openvdb::v6_1::math::Mat3::det
T det() const
Determinant of matrix.
Definition: Mat3.h:527
openvdb::v6_1::math::Quat::operator+=
Quat & operator+=(const Quat &q)
Add quaternion q to "this" quaternion, e.g. q += q1;.
Definition: Quat.h:363
openvdb::v6_1::math::Quat::Quat
Quat(T *a)
Constructor with array argument, e.g. float a[4]; Quatf q(a);.
Definition: Quat.h:126
openvdb::v6_1::ArithmeticError
Definition: Exceptions.h:83
openvdb::v6_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:365
openvdb::v6_1::math::Quat::mult
Quat & mult(const Quat &q1, const Quat &q2)
Definition: Quat.h:470
openvdb::v6_1::math::Quat::operator()
T & operator()(int i)
Alternative indexed reference to the elements.
Definition: Quat.h:253
openvdb::v6_1::math::Mat3
3x3 matrix class.
Definition: Mat3.h:55
OPENVDB_USE_VERSION_NAMESPACE
#define OPENVDB_USE_VERSION_NAMESPACE
Definition: version.h:177
openvdb::v6_1::math::Quat::Quat
Quat(const Mat3< T1 > &rot)
Constructor given a rotation matrix.
Definition: Quat.h:165
openvdb::v6_1::math::Quat::value_type
T value_type
Definition: Quat.h:108
openvdb::v6_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:246
openvdb::v6_1::math::Quat::zero
static Quat zero()
Predefined constants, e.g. Quat q = Quat::identity();.
Definition: Quat.h:559
openvdb::v6_1::math::Quat::str
std::string str() const
Definition: Quat.h:563
Mat.h
openvdb::v6_1::math::Quat::setAxisAngle
Quat & setAxisAngle(const Vec3< T > &axis, T angle)
Definition: Quat.h:302
openvdb::v6_1::math::Quat::axis
Vec3< T > axis() const
Return axis of rotation.
Definition: Quat.h:274
openvdb::v6_1::math::Quat::Quat
Quat(const Quat &q)
Copy constructor.
Definition: Quat.h:218
openvdb::v6_1::math::Quat::setIdentity
Quat & setIdentity()
Set "this" vector to identity.
Definition: Quat.h:324
openvdb::v6_1::math::Vec3::x
T & x()
Reference to the component, e.g. v.x() = 4.5f;.
Definition: Vec3.h:110
openvdb::v6_1::math::Quat::w
T & w()
Definition: Quat.h:231
openvdb::v6_1::math::Quat
Definition: Mat.h:196
openvdb::v6_1::math::Quat::angle
T angle() const
Return angle of rotation.
Definition: Quat.h:259