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Eigen  3.4.0
 
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Quaternion.h
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
5// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
6//
7// This Source Code Form is subject to the terms of the Mozilla
8// Public License v. 2.0. If a copy of the MPL was not distributed
9// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
10
11#ifndef EIGEN_QUATERNION_H
12#define EIGEN_QUATERNION_H
13namespace Eigen {
14
15
16/***************************************************************************
17* Definition of QuaternionBase<Derived>
18* The implementation is at the end of the file
19***************************************************************************/
20
21namespace internal {
22template<typename Other,
23 int OtherRows=Other::RowsAtCompileTime,
24 int OtherCols=Other::ColsAtCompileTime>
25struct quaternionbase_assign_impl;
26}
27
34template<class Derived>
35class QuaternionBase : public RotationBase<Derived, 3>
36{
37 public:
39
40 using Base::operator*;
41 using Base::derived;
42
43 typedef typename internal::traits<Derived>::Scalar Scalar;
44 typedef typename NumTraits<Scalar>::Real RealScalar;
45 typedef typename internal::traits<Derived>::Coefficients Coefficients;
46 typedef typename Coefficients::CoeffReturnType CoeffReturnType;
47 typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
48 Scalar&, CoeffReturnType>::type NonConstCoeffReturnType;
49
50
51 enum {
52 Flags = Eigen::internal::traits<Derived>::Flags
53 };
54
55 // typedef typename Matrix<Scalar,4,1> Coefficients;
62
63
64
66 EIGEN_DEVICE_FUNC inline CoeffReturnType x() const { return this->derived().coeffs().coeff(0); }
68 EIGEN_DEVICE_FUNC inline CoeffReturnType y() const { return this->derived().coeffs().coeff(1); }
70 EIGEN_DEVICE_FUNC inline CoeffReturnType z() const { return this->derived().coeffs().coeff(2); }
72 EIGEN_DEVICE_FUNC inline CoeffReturnType w() const { return this->derived().coeffs().coeff(3); }
73
75 EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType x() { return this->derived().coeffs().x(); }
77 EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType y() { return this->derived().coeffs().y(); }
79 EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType z() { return this->derived().coeffs().z(); }
81 EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType w() { return this->derived().coeffs().w(); }
82
84 EIGEN_DEVICE_FUNC inline const VectorBlock<const Coefficients,3> vec() const { return coeffs().template head<3>(); }
85
87 EIGEN_DEVICE_FUNC inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); }
88
90 EIGEN_DEVICE_FUNC inline const typename internal::traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }
91
93 EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); }
94
95 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& operator=(const QuaternionBase<Derived>& other);
96 template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const QuaternionBase<OtherDerived>& other);
97
98// disabled this copy operator as it is giving very strange compilation errors when compiling
99// test_stdvector with GCC 4.4.2. This looks like a GCC bug though, so feel free to re-enable it if it's
100// useful; however notice that we already have the templated operator= above and e.g. in MatrixBase
101// we didn't have to add, in addition to templated operator=, such a non-templated copy operator.
102// Derived& operator=(const QuaternionBase& other)
103// { return operator=<Derived>(other); }
104
105 EIGEN_DEVICE_FUNC Derived& operator=(const AngleAxisType& aa);
106 template<class OtherDerived> EIGEN_DEVICE_FUNC Derived& operator=(const MatrixBase<OtherDerived>& m);
107
111 EIGEN_DEVICE_FUNC static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); }
112
115 EIGEN_DEVICE_FUNC inline QuaternionBase& setIdentity() { coeffs() << Scalar(0), Scalar(0), Scalar(0), Scalar(1); return *this; }
116
120 EIGEN_DEVICE_FUNC inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
121
125 EIGEN_DEVICE_FUNC inline Scalar norm() const { return coeffs().norm(); }
126
129 EIGEN_DEVICE_FUNC inline void normalize() { coeffs().normalize(); }
132 EIGEN_DEVICE_FUNC inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
133
139 template<class OtherDerived> EIGEN_DEVICE_FUNC inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
140
141 template<class OtherDerived> EIGEN_DEVICE_FUNC Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
142
144 EIGEN_DEVICE_FUNC inline Matrix3 toRotationMatrix() const;
145
147 template<typename Derived1, typename Derived2>
148 EIGEN_DEVICE_FUNC Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
149
150 template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
151 template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*= (const QuaternionBase<OtherDerived>& q);
152
154 EIGEN_DEVICE_FUNC Quaternion<Scalar> inverse() const;
155
157 EIGEN_DEVICE_FUNC Quaternion<Scalar> conjugate() const;
158
159 template<class OtherDerived> EIGEN_DEVICE_FUNC Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const;
160
165 template<class OtherDerived>
166 EIGEN_DEVICE_FUNC inline bool operator==(const QuaternionBase<OtherDerived>& other) const
167 { return coeffs() == other.coeffs(); }
168
173 template<class OtherDerived>
174 EIGEN_DEVICE_FUNC inline bool operator!=(const QuaternionBase<OtherDerived>& other) const
175 { return coeffs() != other.coeffs(); }
176
181 template<class OtherDerived>
182 EIGEN_DEVICE_FUNC bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
183 { return coeffs().isApprox(other.coeffs(), prec); }
184
186 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;
187
188 #ifdef EIGEN_PARSED_BY_DOXYGEN
194 template<typename NewScalarType>
195 EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const;
196
197 #else
198
199 template<typename NewScalarType>
200 EIGEN_DEVICE_FUNC inline
201 typename internal::enable_if<internal::is_same<Scalar,NewScalarType>::value,const Derived&>::type cast() const
202 {
203 return derived();
204 }
205
206 template<typename NewScalarType>
207 EIGEN_DEVICE_FUNC inline
208 typename internal::enable_if<!internal::is_same<Scalar,NewScalarType>::value,Quaternion<NewScalarType> >::type cast() const
209 {
210 return Quaternion<NewScalarType>(coeffs().template cast<NewScalarType>());
211 }
212 #endif
213
214#ifndef EIGEN_NO_IO
215 friend std::ostream& operator<<(std::ostream& s, const QuaternionBase<Derived>& q) {
216 s << q.x() << "i + " << q.y() << "j + " << q.z() << "k" << " + " << q.w();
217 return s;
218 }
219#endif
220
221#ifdef EIGEN_QUATERNIONBASE_PLUGIN
222# include EIGEN_QUATERNIONBASE_PLUGIN
223#endif
224protected:
225 EIGEN_DEFAULT_COPY_CONSTRUCTOR(QuaternionBase)
226 EIGEN_DEFAULT_EMPTY_CONSTRUCTOR_AND_DESTRUCTOR(QuaternionBase)
227};
228
229/***************************************************************************
230* Definition/implementation of Quaternion<Scalar>
231***************************************************************************/
232
258namespace internal {
259template<typename _Scalar,int _Options>
260struct traits<Quaternion<_Scalar,_Options> >
261{
262 typedef Quaternion<_Scalar,_Options> PlainObject;
263 typedef _Scalar Scalar;
264 typedef Matrix<_Scalar,4,1,_Options> Coefficients;
265 enum{
266 Alignment = internal::traits<Coefficients>::Alignment,
267 Flags = LvalueBit
268 };
269};
270}
271
272template<typename _Scalar, int _Options>
273class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >
274{
275public:
277 enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };
278
279 typedef _Scalar Scalar;
280
281 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)
282 using Base::operator*=;
283
284 typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
285 typedef typename Base::AngleAxisType AngleAxisType;
286
288 EIGEN_DEVICE_FUNC inline Quaternion() {}
289
297 EIGEN_DEVICE_FUNC inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}
298
300 EIGEN_DEVICE_FUNC explicit inline Quaternion(const Scalar* data) : m_coeffs(data) {}
301
303 template<class Derived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); }
304
306 EIGEN_DEVICE_FUNC explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
307
312 template<typename Derived>
313 EIGEN_DEVICE_FUNC explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
314
316 template<typename OtherScalar, int OtherOptions>
317 EIGEN_DEVICE_FUNC explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other)
318 { m_coeffs = other.coeffs().template cast<Scalar>(); }
319
320#if EIGEN_HAS_RVALUE_REFERENCES
321 // We define a copy constructor, which means we don't get an implicit move constructor or assignment operator.
323 EIGEN_DEVICE_FUNC inline Quaternion(Quaternion&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_constructible<Scalar>::value)
324 : m_coeffs(std::move(other.coeffs()))
325 {}
326
328 EIGEN_DEVICE_FUNC Quaternion& operator=(Quaternion&& other) EIGEN_NOEXCEPT_IF(std::is_nothrow_move_assignable<Scalar>::value)
329 {
330 m_coeffs = std::move(other.coeffs());
331 return *this;
332 }
333#endif
334
335 EIGEN_DEVICE_FUNC static Quaternion UnitRandom();
336
337 template<typename Derived1, typename Derived2>
338 EIGEN_DEVICE_FUNC static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
339
340 EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs;}
341 EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
342
343 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(NeedsAlignment))
344
345#ifdef EIGEN_QUATERNION_PLUGIN
346# include EIGEN_QUATERNION_PLUGIN
347#endif
348
349protected:
350 Coefficients m_coeffs;
351
352#ifndef EIGEN_PARSED_BY_DOXYGEN
353 static EIGEN_STRONG_INLINE void _check_template_params()
354 {
355 EIGEN_STATIC_ASSERT( (_Options & DontAlign) == _Options,
356 INVALID_MATRIX_TEMPLATE_PARAMETERS)
357 }
358#endif
359};
360
367
368/***************************************************************************
369* Specialization of Map<Quaternion<Scalar>>
370***************************************************************************/
371
372namespace internal {
373 template<typename _Scalar, int _Options>
374 struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
375 {
376 typedef Map<Matrix<_Scalar,4,1>, _Options> Coefficients;
377 };
378}
379
380namespace internal {
381 template<typename _Scalar, int _Options>
382 struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
383 {
384 typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
385 typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
386 enum {
387 Flags = TraitsBase::Flags & ~LvalueBit
388 };
389 };
390}
391
403template<typename _Scalar, int _Options>
404class Map<const Quaternion<_Scalar>, _Options >
405 : public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
406{
407 public:
409
410 typedef _Scalar Scalar;
411 typedef typename internal::traits<Map>::Coefficients Coefficients;
412 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
413 using Base::operator*=;
414
421 EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
422
423 EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
424
425 protected:
426 const Coefficients m_coeffs;
427};
428
440template<typename _Scalar, int _Options>
441class Map<Quaternion<_Scalar>, _Options >
442 : public QuaternionBase<Map<Quaternion<_Scalar>, _Options> >
443{
444 public:
445 typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Base;
446
447 typedef _Scalar Scalar;
448 typedef typename internal::traits<Map>::Coefficients Coefficients;
449 EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
450 using Base::operator*=;
451
458 EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}
459
460 EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
461 EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
462
463 protected:
464 Coefficients m_coeffs;
465};
466
479
480/***************************************************************************
481* Implementation of QuaternionBase methods
482***************************************************************************/
483
484// Generic Quaternion * Quaternion product
485// This product can be specialized for a given architecture via the Arch template argument.
486namespace internal {
487template<int Arch, class Derived1, class Derived2, typename Scalar> struct quat_product
488{
489 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){
490 return Quaternion<Scalar>
491 (
492 a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
493 a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
494 a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
495 a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
496 );
497 }
498};
499}
500
502template <class Derived>
503template <class OtherDerived>
504EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
506{
507 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
508 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
509 return internal::quat_product<Architecture::Target, Derived, OtherDerived,
510 typename internal::traits<Derived>::Scalar>::run(*this, other);
511}
512
514template <class Derived>
515template <class OtherDerived>
516EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
517{
518 derived() = derived() * other.derived();
519 return derived();
520}
521
529template <class Derived>
530EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3
532{
533 // Note that this algorithm comes from the optimization by hand
534 // of the conversion to a Matrix followed by a Matrix/Vector product.
535 // It appears to be much faster than the common algorithm found
536 // in the literature (30 versus 39 flops). It also requires two
537 // Vector3 as temporaries.
538 Vector3 uv = this->vec().cross(v);
539 uv += uv;
540 return v + this->w() * uv + this->vec().cross(uv);
541}
542
543template<class Derived>
544EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)
545{
546 coeffs() = other.coeffs();
547 return derived();
548}
549
550template<class Derived>
551template<class OtherDerived>
552EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
553{
554 coeffs() = other.coeffs();
555 return derived();
556}
557
560template<class Derived>
561EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
562{
563 EIGEN_USING_STD(cos)
564 EIGEN_USING_STD(sin)
565 Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
566 this->w() = cos(ha);
567 this->vec() = sin(ha) * aa.axis();
568 return derived();
569}
570
577template<class Derived>
578template<class MatrixDerived>
579EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
580{
581 EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
582 YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
583 internal::quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
584 return derived();
585}
586
590template<class Derived>
591EIGEN_DEVICE_FUNC inline typename QuaternionBase<Derived>::Matrix3
593{
594 // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
595 // if not inlined then the cost of the return by value is huge ~ +35%,
596 // however, not inlining this function is an order of magnitude slower, so
597 // it has to be inlined, and so the return by value is not an issue
598 Matrix3 res;
599
600 const Scalar tx = Scalar(2)*this->x();
601 const Scalar ty = Scalar(2)*this->y();
602 const Scalar tz = Scalar(2)*this->z();
603 const Scalar twx = tx*this->w();
604 const Scalar twy = ty*this->w();
605 const Scalar twz = tz*this->w();
606 const Scalar txx = tx*this->x();
607 const Scalar txy = ty*this->x();
608 const Scalar txz = tz*this->x();
609 const Scalar tyy = ty*this->y();
610 const Scalar tyz = tz*this->y();
611 const Scalar tzz = tz*this->z();
612
613 res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
614 res.coeffRef(0,1) = txy-twz;
615 res.coeffRef(0,2) = txz+twy;
616 res.coeffRef(1,0) = txy+twz;
617 res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
618 res.coeffRef(1,2) = tyz-twx;
619 res.coeffRef(2,0) = txz-twy;
620 res.coeffRef(2,1) = tyz+twx;
621 res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
622
623 return res;
624}
625
636template<class Derived>
637template<typename Derived1, typename Derived2>
639{
640 EIGEN_USING_STD(sqrt)
641 Vector3 v0 = a.normalized();
642 Vector3 v1 = b.normalized();
643 Scalar c = v1.dot(v0);
644
645 // if dot == -1, vectors are nearly opposites
646 // => accurately compute the rotation axis by computing the
647 // intersection of the two planes. This is done by solving:
648 // x^T v0 = 0
649 // x^T v1 = 0
650 // under the constraint:
651 // ||x|| = 1
652 // which yields a singular value problem
653 if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())
654 {
655 c = numext::maxi(c,Scalar(-1));
656 Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
658 Vector3 axis = svd.matrixV().col(2);
659
660 Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
661 this->w() = sqrt(w2);
662 this->vec() = axis * sqrt(Scalar(1) - w2);
663 return derived();
664 }
665 Vector3 axis = v0.cross(v1);
666 Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
667 Scalar invs = Scalar(1)/s;
668 this->vec() = axis * invs;
669 this->w() = s * Scalar(0.5);
670
671 return derived();
672}
673
678template<typename Scalar, int Options>
680{
681 EIGEN_USING_STD(sqrt)
682 EIGEN_USING_STD(sin)
683 EIGEN_USING_STD(cos)
684 const Scalar u1 = internal::random<Scalar>(0, 1),
685 u2 = internal::random<Scalar>(0, 2*EIGEN_PI),
686 u3 = internal::random<Scalar>(0, 2*EIGEN_PI);
687 const Scalar a = sqrt(Scalar(1) - u1),
688 b = sqrt(u1);
689 return Quaternion (a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3));
690}
691
692
703template<typename Scalar, int Options>
704template<typename Derived1, typename Derived2>
706{
707 Quaternion quat;
708 quat.setFromTwoVectors(a, b);
709 return quat;
710}
711
712
719template <class Derived>
721{
722 // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
723 Scalar n2 = this->squaredNorm();
724 if (n2 > Scalar(0))
725 return Quaternion<Scalar>(conjugate().coeffs() / n2);
726 else
727 {
728 // return an invalid result to flag the error
729 return Quaternion<Scalar>(Coefficients::Zero());
730 }
731}
732
733// Generic conjugate of a Quaternion
734namespace internal {
735template<int Arch, class Derived, typename Scalar> struct quat_conj
736{
737 EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived>& q){
738 return Quaternion<Scalar>(q.w(),-q.x(),-q.y(),-q.z());
739 }
740};
741}
742
749template <class Derived>
750EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar>
752{
753 return internal::quat_conj<Architecture::Target, Derived,
754 typename internal::traits<Derived>::Scalar>::run(*this);
755
756}
757
761template <class Derived>
762template <class OtherDerived>
763EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar
765{
766 EIGEN_USING_STD(atan2)
767 Quaternion<Scalar> d = (*this) * other.conjugate();
768 return Scalar(2) * atan2( d.vec().norm(), numext::abs(d.w()) );
769}
770
771
772
779template <class Derived>
780template <class OtherDerived>
783{
784 EIGEN_USING_STD(acos)
785 EIGEN_USING_STD(sin)
786 const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();
787 Scalar d = this->dot(other);
788 Scalar absD = numext::abs(d);
789
790 Scalar scale0;
791 Scalar scale1;
792
793 if(absD>=one)
794 {
795 scale0 = Scalar(1) - t;
796 scale1 = t;
797 }
798 else
799 {
800 // theta is the angle between the 2 quaternions
801 Scalar theta = acos(absD);
802 Scalar sinTheta = sin(theta);
803
804 scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
805 scale1 = sin( ( t * theta) ) / sinTheta;
806 }
807 if(d<Scalar(0)) scale1 = -scale1;
808
809 return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
810}
811
812namespace internal {
813
814// set from a rotation matrix
815template<typename Other>
816struct quaternionbase_assign_impl<Other,3,3>
817{
818 typedef typename Other::Scalar Scalar;
819 template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& a_mat)
820 {
821 const typename internal::nested_eval<Other,2>::type mat(a_mat);
822 EIGEN_USING_STD(sqrt)
823 // This algorithm comes from "Quaternion Calculus and Fast Animation",
824 // Ken Shoemake, 1987 SIGGRAPH course notes
825 Scalar t = mat.trace();
826 if (t > Scalar(0))
827 {
828 t = sqrt(t + Scalar(1.0));
829 q.w() = Scalar(0.5)*t;
830 t = Scalar(0.5)/t;
831 q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
832 q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
833 q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
834 }
835 else
836 {
837 Index i = 0;
838 if (mat.coeff(1,1) > mat.coeff(0,0))
839 i = 1;
840 if (mat.coeff(2,2) > mat.coeff(i,i))
841 i = 2;
842 Index j = (i+1)%3;
843 Index k = (j+1)%3;
844
845 t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
846 q.coeffs().coeffRef(i) = Scalar(0.5) * t;
847 t = Scalar(0.5)/t;
848 q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
849 q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
850 q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
851 }
852 }
853};
854
855// set from a vector of coefficients assumed to be a quaternion
856template<typename Other>
857struct quaternionbase_assign_impl<Other,4,1>
858{
859 typedef typename Other::Scalar Scalar;
860 template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& vec)
861 {
862 q.coeffs() = vec;
863 }
864};
865
866} // end namespace internal
867
868} // end namespace Eigen
869
870#endif // EIGEN_QUATERNION_H
Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.
Definition: AngleAxis.h:50
Scalar angle() const
Definition: AngleAxis.h:91
const Vector3 & axis() const
Definition: AngleAxis.h:96
Derived & derived()
Definition: EigenBase.h:46
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: JacobiSVD.h:490
Map(Scalar *coeffs)
Definition: Quaternion.h:458
Map(const Scalar *coeffs)
Definition: Quaternion.h:421
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:96
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
const PlainObject normalized() const
Definition: Dot.h:124
The matrix class, also used for vectors and row-vectors.
Definition: Matrix.h:180
Scalar & coeffRef(Index rowId, Index colId)
Definition: PlainObjectBase.h:175
Base class for quaternion expressions.
Definition: Quaternion.h:36
Scalar squaredNorm() const
Definition: Quaternion.h:120
QuaternionBase & setIdentity()
Definition: Quaternion.h:115
Quaternion< Scalar > normalized() const
Definition: Quaternion.h:132
internal::traits< Derived >::Coefficients & coeffs()
Definition: Quaternion.h:93
internal::cast_return_type< Derived, Quaternion< NewScalarType > >::type cast() const
VectorBlock< Coefficients, 3 > vec()
Definition: Quaternion.h:87
const VectorBlock< const Coefficients, 3 > vec() const
Definition: Quaternion.h:84
static Quaternion< Scalar > Identity()
Definition: Quaternion.h:111
bool operator!=(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:174
Quaternion< Scalar > conjugate() const
Definition: Quaternion.h:751
NonConstCoeffReturnType y()
Definition: Quaternion.h:77
bool isApprox(const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Quaternion.h:182
void normalize()
Definition: Quaternion.h:129
Derived & setFromTwoVectors(const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Definition: Quaternion.h:638
CoeffReturnType z() const
Definition: Quaternion.h:70
NonConstCoeffReturnType x()
Definition: Quaternion.h:75
Matrix3 toRotationMatrix() const
Definition: Quaternion.h:592
Matrix< Scalar, 3, 1 > Vector3
Definition: Quaternion.h:57
NonConstCoeffReturnType z()
Definition: Quaternion.h:79
Scalar dot(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:139
Derived & operator=(const AngleAxisType &aa)
Definition: Quaternion.h:561
Vector3 _transformVector(const Vector3 &v) const
Definition: Quaternion.h:531
CoeffReturnType y() const
Definition: Quaternion.h:68
Scalar norm() const
Definition: Quaternion.h:125
Quaternion< Scalar > inverse() const
Definition: Quaternion.h:720
CoeffReturnType w() const
Definition: Quaternion.h:72
Matrix< Scalar, 3, 3 > Matrix3
Definition: Quaternion.h:59
const internal::traits< Derived >::Coefficients & coeffs() const
Definition: Quaternion.h:90
bool operator==(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:166
NonConstCoeffReturnType w()
Definition: Quaternion.h:81
AngleAxis< Scalar > AngleAxisType
Definition: Quaternion.h:61
Derived & operator*=(const QuaternionBase< OtherDerived > &q)
Definition: Quaternion.h:516
CoeffReturnType x() const
Definition: Quaternion.h:66
The quaternion class used to represent 3D orientations and rotations.
Definition: Quaternion.h:274
Quaternion(const QuaternionBase< Derived > &other)
Definition: Quaternion.h:303
static Quaternion UnitRandom()
Definition: Quaternion.h:679
Quaternion(const AngleAxisType &aa)
Definition: Quaternion.h:306
Quaternion(const Quaternion< OtherScalar, OtherOptions > &other)
Definition: Quaternion.h:317
Quaternion(const MatrixBase< Derived > &other)
Definition: Quaternion.h:313
Quaternion()
Definition: Quaternion.h:288
Quaternion(const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
Definition: Quaternion.h:297
Quaternion(const Scalar *data)
Definition: Quaternion.h:300
Common base class for compact rotation representations.
Definition: RotationBase.h:30
friend RotationMatrixType operator*(const EigenBase< OtherDerived > &l, const Derived &r)
Definition: RotationBase.h:76
const MatrixVType & matrixV() const
Definition: SVDBase.h:117
Expression of a fixed-size or dynamic-size sub-vector.
Definition: VectorBlock.h:60
@ Aligned
Definition: Constants.h:240
@ DontAlign
Definition: Constants.h:325
@ ComputeFullV
Definition: Constants.h:397
const unsigned int LvalueBit
Definition: Constants.h:144
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:233