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Eigen  3.3.90 (git rev 704798d1df4866be335ca013da19a44791f85a7e)
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
13 namespace Eigen {
14 
15 
16 /***************************************************************************
17 * Definition of QuaternionBase<Derived>
18 * The implementation is at the end of the file
19 ***************************************************************************/
20 
21 namespace internal {
22 template<typename Other,
23  int OtherRows=Other::RowsAtCompileTime,
24  int OtherCols=Other::ColsAtCompileTime>
25 struct quaternionbase_assign_impl;
26 }
27 
34 template<class Derived>
35 class QuaternionBase : public RotationBase<Derived, 3>
36 {
37  public:
38  typedef RotationBase<Derived, 3> Base;
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 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
189 
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
224 protected:
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 
258 namespace internal {
259 template<typename _Scalar,int _Options>
260 struct 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 
272 template<typename _Scalar, int _Options>
273 class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >
274 {
275 public:
276  typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base;
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 
349 protected:
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 
372 namespace 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 
380 namespace 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 
403 template<typename _Scalar, int _Options>
404 class 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 
440 template<typename _Scalar, int _Options>
441 class 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.
486 namespace internal {
487 template<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 
502 template <class Derived>
503 template <class OtherDerived>
504 EIGEN_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 
514 template <class Derived>
515 template <class OtherDerived>
516 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
517 {
518  derived() = derived() * other.derived();
519  return derived();
520 }
521 
529 template <class Derived>
530 EIGEN_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 
543 template<class Derived>
544 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)
545 {
546  coeffs() = other.coeffs();
547  return derived();
548 }
549 
550 template<class Derived>
551 template<class OtherDerived>
552 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
553 {
554  coeffs() = other.coeffs();
555  return derived();
556 }
557 
560 template<class Derived>
561 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
562 {
563  EIGEN_USING_STD_MATH(cos)
564  EIGEN_USING_STD_MATH(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 
577 template<class Derived>
578 template<class MatrixDerived>
579 EIGEN_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 
590 template<class Derived>
591 EIGEN_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 
636 template<class Derived>
637 template<typename Derived1, typename Derived2>
638 EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
639 {
640  EIGEN_USING_STD_MATH(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 
678 template<typename Scalar, int Options>
680 {
681  EIGEN_USING_STD_MATH(sqrt)
682  EIGEN_USING_STD_MATH(sin)
683  EIGEN_USING_STD_MATH(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 
703 template<typename Scalar, int Options>
704 template<typename Derived1, typename Derived2>
706 {
707  Quaternion quat;
708  quat.setFromTwoVectors(a, b);
709  return quat;
710 }
711 
712 
719 template <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
734 namespace internal {
735 template<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 
749 template <class Derived>
750 EIGEN_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 
761 template <class Derived>
762 template <class OtherDerived>
763 EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar
765 {
766  EIGEN_USING_STD_MATH(atan2)
767  Quaternion<Scalar> d = (*this) * other.conjugate();
768  return Scalar(2) * atan2( d.vec().norm(), numext::abs(d.w()) );
769 }
770 
771 
772 
779 template <class Derived>
780 template <class OtherDerived>
783 {
784  EIGEN_USING_STD_MATH(acos)
785  EIGEN_USING_STD_MATH(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 
812 namespace internal {
813 
814 // set from a rotation matrix
815 template<typename Other>
816 struct 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_MATH(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
856 template<typename Other>
857 struct 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
Eigen::QuaternionBase::operator!=
bool operator!=(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:174
Eigen::QuaternionBase::y
NonConstCoeffReturnType y()
Definition: Quaternion.h:77
Eigen
Namespace containing all symbols from the Eigen library.
Definition: Core:134
Eigen::QuaternionBase::inverse
Quaternion< Scalar > inverse() const
Definition: Quaternion.h:720
Eigen::AngleAxis::axis
const Vector3 & axis() const
Definition: AngleAxis.h:96
Eigen::ComputeFullV
@ ComputeFullV
Definition: Constants.h:387
Eigen::QuaternionBase::normalize
void normalize()
Definition: Quaternion.h:129
Eigen::sqrt
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Eigen::QuaternionBase::x
CoeffReturnType x() const
Definition: Quaternion.h:66
Eigen::Quaternion::Quaternion
Quaternion(const MatrixBase< Derived > &other)
Definition: Quaternion.h:313
Eigen::QuaternionMapAlignedf
Map< Quaternion< float >, Aligned > QuaternionMapAlignedf
Definition: Quaternion.h:475
Eigen::QuaternionBase::z
NonConstCoeffReturnType z()
Definition: Quaternion.h:79
Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >::derived
Derived & derived()
Definition: EigenBase.h:46
Eigen::sin
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sin_op< typename Derived::Scalar >, const Derived > sin(const Eigen::ArrayBase< Derived > &x)
Eigen::AngleAxis
Represents a 3D rotation as a rotation angle around an arbitrary 3D axis.
Definition: ForwardDeclarations.h:290
Eigen::QuaternionBase::dot
Scalar dot(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:139
Eigen::QuaternionMapd
Map< Quaternion< double >, 0 > QuaternionMapd
Definition: Quaternion.h:472
Eigen::Quaternion::Quaternion
Quaternion(const AngleAxisType &aa)
Definition: Quaternion.h:306
Eigen::QuaternionBase::z
CoeffReturnType z() const
Definition: Quaternion.h:70
Eigen::DontAlign
@ DontAlign
Definition: Constants.h:324
Eigen::QuaternionBase::AngleAxisType
AngleAxis< Scalar > AngleAxisType
Definition: Quaternion.h:61
Eigen::QuaternionBase::_transformVector
Vector3 _transformVector(const Vector3 &v) const
Definition: Quaternion.h:531
Eigen::Quaternion::Quaternion
Quaternion(const QuaternionBase< Derived > &other)
Definition: Quaternion.h:303
Eigen::QuaternionBase::setFromTwoVectors
Derived & setFromTwoVectors(const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Definition: Quaternion.h:638
Eigen::QuaternionBase::setIdentity
QuaternionBase & setIdentity()
Definition: Quaternion.h:115
Eigen::Quaternion::Quaternion
Quaternion(const Scalar *data)
Definition: Quaternion.h:300
Eigen::QuaternionBase::vec
const VectorBlock< const Coefficients, 3 > vec() const
Definition: Quaternion.h:84
Eigen::QuaternionBase::toRotationMatrix
Matrix3 toRotationMatrix() const
Definition: Quaternion.h:592
Eigen::QuaternionBase::normalized
Quaternion< Scalar > normalized() const
Definition: Quaternion.h:132
Eigen::QuaternionBase::conjugate
Quaternion< Scalar > conjugate() const
Definition: Quaternion.h:751
Eigen::LvalueBit
const unsigned int LvalueBit
Definition: Constants.h:143
Eigen::Quaternion::UnitRandom
static Quaternion UnitRandom()
Definition: Quaternion.h:679
Eigen::QuaternionBase::isApprox
bool isApprox(const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Quaternion.h:182
Eigen::acos
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acos_op< typename Derived::Scalar >, const Derived > acos(const Eigen::ArrayBase< Derived > &x)
Eigen::QuaternionBase::y
CoeffReturnType y() const
Definition: Quaternion.h:68
Eigen::Quaternion::Quaternion
Quaternion(const Scalar &w, const Scalar &x, const Scalar &y, const Scalar &z)
Definition: Quaternion.h:297
Eigen::QuaternionBase::x
NonConstCoeffReturnType x()
Definition: Quaternion.h:75
Eigen::QuaternionBase::w
NonConstCoeffReturnType w()
Definition: Quaternion.h:81
Eigen::Map< Quaternion< _Scalar >, _Options >::Map
Map(Scalar *coeffs)
Definition: Quaternion.h:458
Eigen::Quaternionf
Quaternion< float > Quaternionf
Definition: Quaternion.h:363
Eigen::PlainObjectBase::coeffRef
Scalar & coeffRef(Index rowId, Index colId)
Definition: PlainObjectBase.h:183
Eigen::QuaternionBase::cast
internal::cast_return_type< Derived, Quaternion< NewScalarType > >::type cast() const
Eigen::Quaterniond
Quaternion< double > Quaterniond
Definition: Quaternion.h:366
Eigen::AutoAlign
@ AutoAlign
Definition: Constants.h:322
Eigen::Map
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:94
Eigen::cos
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cos_op< typename Derived::Scalar >, const Derived > cos(const Eigen::ArrayBase< Derived > &x)
Eigen::JacobiSVD
Two-sided Jacobi SVD decomposition of a rectangular matrix.
Definition: ForwardDeclarations.h:278
Eigen::QuaternionBase::norm
Scalar norm() const
Definition: Quaternion.h:125
Eigen::Quaternion
The quaternion class used to represent 3D orientations and rotations.
Definition: ForwardDeclarations.h:293
Eigen::AngleAxis::angle
Scalar angle() const
Definition: AngleAxis.h:91
Eigen::QuaternionBase::coeffs
const internal::traits< Derived >::Coefficients & coeffs() const
Definition: Quaternion.h:90
Eigen::Quaternion::Quaternion
Quaternion()
Definition: Quaternion.h:288
Eigen::QuaternionBase::Vector3
Matrix< Scalar, 3, 1 > Vector3
Definition: Quaternion.h:57
Eigen::QuaternionBase::Matrix3
Matrix< Scalar, 3, 3 > Matrix3
Definition: Quaternion.h:59
Eigen::QuaternionBase::Identity
static Quaternion< Scalar > Identity()
Definition: Quaternion.h:111
Eigen::QuaternionBase::operator==
bool operator==(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:166
Eigen::QuaternionBase::operator*=
Derived & operator*=(const QuaternionBase< OtherDerived > &q)
Definition: Quaternion.h:516
Eigen::QuaternionMapf
Map< Quaternion< float >, 0 > QuaternionMapf
Definition: Quaternion.h:469
Eigen::VectorBlock
Expression of a fixed-size or dynamic-size sub-vector.
Definition: ForwardDeclarations.h:85
Eigen::Quaternion::Quaternion
Quaternion(const Quaternion< OtherScalar, OtherOptions > &other)
Definition: Quaternion.h:317
Eigen::QuaternionBase::vec
VectorBlock< Coefficients, 3 > vec()
Definition: Quaternion.h:87
Eigen::Matrix< Scalar, 3, 1 >
Eigen::MatrixBase
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
Eigen::QuaternionBase::coeffs
internal::traits< Derived >::Coefficients & coeffs()
Definition: Quaternion.h:93
Eigen::QuaternionBase::w
CoeffReturnType w() const
Definition: Quaternion.h:72
Eigen::QuaternionBase::squaredNorm
Scalar squaredNorm() const
Definition: Quaternion.h:120
Eigen::Map< const Quaternion< _Scalar >, _Options >::Map
Map(const Scalar *coeffs)
Definition: Quaternion.h:421
Eigen::QuaternionMapAlignedd
Map< Quaternion< double >, Aligned > QuaternionMapAlignedd
Definition: Quaternion.h:478
Eigen::QuaternionBase
Base class for quaternion expressions.
Definition: ForwardDeclarations.h:288
Eigen::NumTraits
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:191
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:42
Eigen::Aligned
@ Aligned
Definition: Constants.h:239
Eigen::MatrixBase::normalized
const PlainObject normalized() const
Definition: Dot.h:124