Eigen  3.3.7
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;
57  typedef Matrix<Scalar,3,1> Vector3;
59  typedef Matrix<Scalar,3,3> Matrix3;
61  typedef AngleAxis<Scalar> AngleAxisType;
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 bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
167  { return coeffs().isApprox(other.coeffs(), prec); }
168 
170  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;
171 
172  #ifdef EIGEN_PARSED_BY_DOXYGEN
173 
178  template<typename NewScalarType>
179  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const;
180 
181  #else
182 
183  template<typename NewScalarType>
184  EIGEN_DEVICE_FUNC inline
185  typename internal::enable_if<internal::is_same<Scalar,NewScalarType>::value,const Derived&>::type cast() const
186  {
187  return derived();
188  }
189 
190  template<typename NewScalarType>
191  EIGEN_DEVICE_FUNC inline
192  typename internal::enable_if<!internal::is_same<Scalar,NewScalarType>::value,Quaternion<NewScalarType> >::type cast() const
193  {
194  return Quaternion<NewScalarType>(coeffs().template cast<NewScalarType>());
195  }
196  #endif
197 
198 #ifdef EIGEN_QUATERNIONBASE_PLUGIN
199 # include EIGEN_QUATERNIONBASE_PLUGIN
200 #endif
201 };
202 
203 /***************************************************************************
204 * Definition/implementation of Quaternion<Scalar>
205 ***************************************************************************/
206 
232 namespace internal {
233 template<typename _Scalar,int _Options>
234 struct traits<Quaternion<_Scalar,_Options> >
235 {
236  typedef Quaternion<_Scalar,_Options> PlainObject;
237  typedef _Scalar Scalar;
238  typedef Matrix<_Scalar,4,1,_Options> Coefficients;
239  enum{
240  Alignment = internal::traits<Coefficients>::Alignment,
241  Flags = LvalueBit
242  };
243 };
244 }
245 
246 template<typename _Scalar, int _Options>
247 class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >
248 {
249 public:
250  typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base;
251  enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };
252 
253  typedef _Scalar Scalar;
254 
255  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)
256  using Base::operator*=;
257 
258  typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
259  typedef typename Base::AngleAxisType AngleAxisType;
260 
262  EIGEN_DEVICE_FUNC inline Quaternion() {}
263 
271  EIGEN_DEVICE_FUNC inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}
272 
274  EIGEN_DEVICE_FUNC explicit inline Quaternion(const Scalar* data) : m_coeffs(data) {}
275 
277  template<class Derived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); }
278 
280  EIGEN_DEVICE_FUNC explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
281 
286  template<typename Derived>
287  EIGEN_DEVICE_FUNC explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
288 
290  template<typename OtherScalar, int OtherOptions>
291  EIGEN_DEVICE_FUNC explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other)
292  { m_coeffs = other.coeffs().template cast<Scalar>(); }
293 
294  EIGEN_DEVICE_FUNC static Quaternion UnitRandom();
295 
296  template<typename Derived1, typename Derived2>
297  EIGEN_DEVICE_FUNC static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
298 
299  EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs;}
300  EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
301 
302  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(NeedsAlignment))
303 
304 #ifdef EIGEN_QUATERNION_PLUGIN
305 # include EIGEN_QUATERNION_PLUGIN
306 #endif
307 
308 protected:
309  Coefficients m_coeffs;
310 
311 #ifndef EIGEN_PARSED_BY_DOXYGEN
312  static EIGEN_STRONG_INLINE void _check_template_params()
313  {
314  EIGEN_STATIC_ASSERT( (_Options & DontAlign) == _Options,
315  INVALID_MATRIX_TEMPLATE_PARAMETERS)
316  }
317 #endif
318 };
319 
322 typedef Quaternion<float> Quaternionf;
325 typedef Quaternion<double> Quaterniond;
326 
327 /***************************************************************************
328 * Specialization of Map<Quaternion<Scalar>>
329 ***************************************************************************/
330 
331 namespace internal {
332  template<typename _Scalar, int _Options>
333  struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
334  {
335  typedef Map<Matrix<_Scalar,4,1>, _Options> Coefficients;
336  };
337 }
338 
339 namespace internal {
340  template<typename _Scalar, int _Options>
341  struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
342  {
343  typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
344  typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
345  enum {
346  Flags = TraitsBase::Flags & ~LvalueBit
347  };
348  };
349 }
350 
362 template<typename _Scalar, int _Options>
363 class Map<const Quaternion<_Scalar>, _Options >
364  : public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
365 {
366  public:
367  typedef QuaternionBase<Map<const Quaternion<_Scalar>, _Options> > Base;
368 
369  typedef _Scalar Scalar;
370  typedef typename internal::traits<Map>::Coefficients Coefficients;
371  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
372  using Base::operator*=;
373 
380  EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
381 
382  EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
383 
384  protected:
385  const Coefficients m_coeffs;
386 };
387 
399 template<typename _Scalar, int _Options>
400 class Map<Quaternion<_Scalar>, _Options >
401  : public QuaternionBase<Map<Quaternion<_Scalar>, _Options> >
402 {
403  public:
404  typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Base;
405 
406  typedef _Scalar Scalar;
407  typedef typename internal::traits<Map>::Coefficients Coefficients;
408  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
409  using Base::operator*=;
410 
417  EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}
418 
419  EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
420  EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
421 
422  protected:
423  Coefficients m_coeffs;
424 };
425 
438 
439 /***************************************************************************
440 * Implementation of QuaternionBase methods
441 ***************************************************************************/
442 
443 // Generic Quaternion * Quaternion product
444 // This product can be specialized for a given architecture via the Arch template argument.
445 namespace internal {
446 template<int Arch, class Derived1, class Derived2, typename Scalar> struct quat_product
447 {
448  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){
449  return Quaternion<Scalar>
450  (
451  a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
452  a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
453  a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
454  a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
455  );
456  }
457 };
458 }
459 
461 template <class Derived>
462 template <class OtherDerived>
463 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
464 QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
465 {
466  EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
467  YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
468  return internal::quat_product<Architecture::Target, Derived, OtherDerived,
469  typename internal::traits<Derived>::Scalar>::run(*this, other);
470 }
471 
473 template <class Derived>
474 template <class OtherDerived>
475 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
476 {
477  derived() = derived() * other.derived();
478  return derived();
479 }
480 
488 template <class Derived>
489 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3
490 QuaternionBase<Derived>::_transformVector(const Vector3& v) const
491 {
492  // Note that this algorithm comes from the optimization by hand
493  // of the conversion to a Matrix followed by a Matrix/Vector product.
494  // It appears to be much faster than the common algorithm found
495  // in the literature (30 versus 39 flops). It also requires two
496  // Vector3 as temporaries.
497  Vector3 uv = this->vec().cross(v);
498  uv += uv;
499  return v + this->w() * uv + this->vec().cross(uv);
500 }
501 
502 template<class Derived>
503 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)
504 {
505  coeffs() = other.coeffs();
506  return derived();
507 }
508 
509 template<class Derived>
510 template<class OtherDerived>
511 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
512 {
513  coeffs() = other.coeffs();
514  return derived();
515 }
516 
519 template<class Derived>
520 EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
521 {
522  EIGEN_USING_STD_MATH(cos)
523  EIGEN_USING_STD_MATH(sin)
524  Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
525  this->w() = cos(ha);
526  this->vec() = sin(ha) * aa.axis();
527  return derived();
528 }
529 
536 template<class Derived>
537 template<class MatrixDerived>
538 EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
539 {
540  EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
541  YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
542  internal::quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
543  return derived();
544 }
545 
549 template<class Derived>
550 EIGEN_DEVICE_FUNC inline typename QuaternionBase<Derived>::Matrix3
552 {
553  // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
554  // if not inlined then the cost of the return by value is huge ~ +35%,
555  // however, not inlining this function is an order of magnitude slower, so
556  // it has to be inlined, and so the return by value is not an issue
557  Matrix3 res;
558 
559  const Scalar tx = Scalar(2)*this->x();
560  const Scalar ty = Scalar(2)*this->y();
561  const Scalar tz = Scalar(2)*this->z();
562  const Scalar twx = tx*this->w();
563  const Scalar twy = ty*this->w();
564  const Scalar twz = tz*this->w();
565  const Scalar txx = tx*this->x();
566  const Scalar txy = ty*this->x();
567  const Scalar txz = tz*this->x();
568  const Scalar tyy = ty*this->y();
569  const Scalar tyz = tz*this->y();
570  const Scalar tzz = tz*this->z();
571 
572  res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
573  res.coeffRef(0,1) = txy-twz;
574  res.coeffRef(0,2) = txz+twy;
575  res.coeffRef(1,0) = txy+twz;
576  res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
577  res.coeffRef(1,2) = tyz-twx;
578  res.coeffRef(2,0) = txz-twy;
579  res.coeffRef(2,1) = tyz+twx;
580  res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
581 
582  return res;
583 }
584 
595 template<class Derived>
596 template<typename Derived1, typename Derived2>
597 EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
598 {
599  EIGEN_USING_STD_MATH(sqrt)
600  Vector3 v0 = a.normalized();
601  Vector3 v1 = b.normalized();
602  Scalar c = v1.dot(v0);
603 
604  // if dot == -1, vectors are nearly opposites
605  // => accurately compute the rotation axis by computing the
606  // intersection of the two planes. This is done by solving:
607  // x^T v0 = 0
608  // x^T v1 = 0
609  // under the constraint:
610  // ||x|| = 1
611  // which yields a singular value problem
612  if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())
613  {
614  c = numext::maxi(c,Scalar(-1));
615  Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
616  JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
617  Vector3 axis = svd.matrixV().col(2);
618 
619  Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
620  this->w() = sqrt(w2);
621  this->vec() = axis * sqrt(Scalar(1) - w2);
622  return derived();
623  }
624  Vector3 axis = v0.cross(v1);
625  Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
626  Scalar invs = Scalar(1)/s;
627  this->vec() = axis * invs;
628  this->w() = s * Scalar(0.5);
629 
630  return derived();
631 }
632 
637 template<typename Scalar, int Options>
638 EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::UnitRandom()
639 {
640  EIGEN_USING_STD_MATH(sqrt)
641  EIGEN_USING_STD_MATH(sin)
642  EIGEN_USING_STD_MATH(cos)
643  const Scalar u1 = internal::random<Scalar>(0, 1),
644  u2 = internal::random<Scalar>(0, 2*EIGEN_PI),
645  u3 = internal::random<Scalar>(0, 2*EIGEN_PI);
646  const Scalar a = sqrt(1 - u1),
647  b = sqrt(u1);
648  return Quaternion (a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3));
649 }
650 
651 
662 template<typename Scalar, int Options>
663 template<typename Derived1, typename Derived2>
664 EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
665 {
666  Quaternion quat;
667  quat.setFromTwoVectors(a, b);
668  return quat;
669 }
670 
671 
678 template <class Derived>
679 EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const
680 {
681  // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite() ??
682  Scalar n2 = this->squaredNorm();
683  if (n2 > Scalar(0))
684  return Quaternion<Scalar>(conjugate().coeffs() / n2);
685  else
686  {
687  // return an invalid result to flag the error
688  return Quaternion<Scalar>(Coefficients::Zero());
689  }
690 }
691 
692 // Generic conjugate of a Quaternion
693 namespace internal {
694 template<int Arch, class Derived, typename Scalar> struct quat_conj
695 {
696  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived>& q){
697  return Quaternion<Scalar>(q.w(),-q.x(),-q.y(),-q.z());
698  }
699 };
700 }
701 
708 template <class Derived>
709 EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar>
711 {
712  return internal::quat_conj<Architecture::Target, Derived,
713  typename internal::traits<Derived>::Scalar>::run(*this);
714 
715 }
716 
720 template <class Derived>
721 template <class OtherDerived>
722 EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar
723 QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
724 {
725  EIGEN_USING_STD_MATH(atan2)
726  Quaternion<Scalar> d = (*this) * other.conjugate();
727  return Scalar(2) * atan2( d.vec().norm(), numext::abs(d.w()) );
728 }
729 
730 
731 
738 template <class Derived>
739 template <class OtherDerived>
740 EIGEN_DEVICE_FUNC Quaternion<typename internal::traits<Derived>::Scalar>
741 QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const
742 {
743  EIGEN_USING_STD_MATH(acos)
744  EIGEN_USING_STD_MATH(sin)
745  const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();
746  Scalar d = this->dot(other);
747  Scalar absD = numext::abs(d);
748 
749  Scalar scale0;
750  Scalar scale1;
751 
752  if(absD>=one)
753  {
754  scale0 = Scalar(1) - t;
755  scale1 = t;
756  }
757  else
758  {
759  // theta is the angle between the 2 quaternions
760  Scalar theta = acos(absD);
761  Scalar sinTheta = sin(theta);
762 
763  scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
764  scale1 = sin( ( t * theta) ) / sinTheta;
765  }
766  if(d<Scalar(0)) scale1 = -scale1;
767 
768  return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
769 }
770 
771 namespace internal {
772 
773 // set from a rotation matrix
774 template<typename Other>
775 struct quaternionbase_assign_impl<Other,3,3>
776 {
777  typedef typename Other::Scalar Scalar;
778  template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& a_mat)
779  {
780  const typename internal::nested_eval<Other,2>::type mat(a_mat);
781  EIGEN_USING_STD_MATH(sqrt)
782  // This algorithm comes from "Quaternion Calculus and Fast Animation",
783  // Ken Shoemake, 1987 SIGGRAPH course notes
784  Scalar t = mat.trace();
785  if (t > Scalar(0))
786  {
787  t = sqrt(t + Scalar(1.0));
788  q.w() = Scalar(0.5)*t;
789  t = Scalar(0.5)/t;
790  q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
791  q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
792  q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
793  }
794  else
795  {
796  Index i = 0;
797  if (mat.coeff(1,1) > mat.coeff(0,0))
798  i = 1;
799  if (mat.coeff(2,2) > mat.coeff(i,i))
800  i = 2;
801  Index j = (i+1)%3;
802  Index k = (j+1)%3;
803 
804  t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
805  q.coeffs().coeffRef(i) = Scalar(0.5) * t;
806  t = Scalar(0.5)/t;
807  q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
808  q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
809  q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
810  }
811  }
812 };
813 
814 // set from a vector of coefficients assumed to be a quaternion
815 template<typename Other>
816 struct quaternionbase_assign_impl<Other,4,1>
817 {
818  typedef typename Other::Scalar Scalar;
819  template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& vec)
820  {
821  q.coeffs() = vec;
822  }
823 };
824 
825 } // end namespace internal
826 
827 } // end namespace Eigen
828 
829 #endif // EIGEN_QUATERNION_H
Eigen::QuaternionBase::Vector3
Matrix< Scalar, 3, 1 > Vector3
Definition: Quaternion.h:56
Eigen
Namespace containing all symbols from the Eigen library.
Definition: Core:306
Eigen::QuaternionBase::dot
Scalar dot(const QuaternionBase< OtherDerived > &other) const
Definition: Quaternion.h:138
Eigen::QuaternionBase::w
CoeffReturnType w() const
Definition: Quaternion.h:71
Eigen::ComputeFullV
Definition: Constants.h:387
Eigen::sqrt
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_sqrt_op< typename Derived::Scalar >, const Derived > sqrt(const Eigen::ArrayBase< Derived > &x)
Eigen::QuaternionMapAlignedf
Map< Quaternion< float >, Aligned > QuaternionMapAlignedf
Definition: Quaternion.h:431
Eigen::DenseCoeffsBase< Derived, DirectWriteAccessors >::derived
Derived & derived()
Definition: EigenBase.h:45
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:266
Eigen::QuaternionMapd
Map< Quaternion< double >, 0 > QuaternionMapd
Definition: Quaternion.h:428
Eigen::QuaternionBase::norm
Scalar norm() const
Definition: Quaternion.h:124
Eigen::QuaternionBase::cast
internal::cast_return_type< Derived, Quaternion< NewScalarType > >::type cast() const
Eigen::QuaternionBase::Identity
static Quaternion< Scalar > Identity()
Definition: Quaternion.h:110
Eigen::AngleAxis::angle
Scalar angle() const
Definition: AngleAxis.h:91
Eigen::DontAlign
Definition: Constants.h:326
Eigen::QuaternionBase::isApprox
bool isApprox(const QuaternionBase< OtherDerived > &other, const RealScalar &prec=NumTraits< Scalar >::dummy_precision()) const
Definition: Quaternion.h:165
Eigen::Quaternion::UnitRandom
static Quaternion UnitRandom()
Definition: Quaternion.h:634
Eigen::QuaternionBase::z
CoeffReturnType z() const
Definition: Quaternion.h:69
Eigen::QuaternionBase::operator*=
Derived & operator*=(const QuaternionBase< OtherDerived > &q)
Definition: Quaternion.h:471
Eigen::QuaternionBase::squaredNorm
Scalar squaredNorm() const
Definition: Quaternion.h:119
Eigen::QuaternionBase::vec
const VectorBlock< const Coefficients, 3 > vec() const
Definition: Quaternion.h:83
Eigen::QuaternionBase::normalized
Quaternion< Scalar > normalized() const
Definition: Quaternion.h:131
Eigen::QuaternionBase::AngleAxisType
AngleAxis< Scalar > AngleAxisType
Definition: Quaternion.h:60
Eigen::LvalueBit
const unsigned int LvalueBit
Definition: Constants.h:139
Eigen::acos
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_acos_op< typename Derived::Scalar >, const Derived > acos(const Eigen::ArrayBase< Derived > &x)
Eigen::QuaternionBase::setFromTwoVectors
Derived & setFromTwoVectors(const MatrixBase< Derived1 > &a, const MatrixBase< Derived2 > &b)
Definition: Quaternion.h:593
Eigen::QuaternionBase::normalize
void normalize()
Definition: Quaternion.h:128
Eigen::Quaternionf
Quaternion< float > Quaternionf
Definition: Quaternion.h:320
Eigen::Quaterniond
Quaternion< double > Quaterniond
Definition: Quaternion.h:323
Eigen::QuaternionBase::inverse
Quaternion< Scalar > inverse() const
Definition: Quaternion.h:675
Eigen::AutoAlign
Definition: Constants.h:324
Eigen::Map
A matrix or vector expression mapping an existing array of data.
Definition: Map.h:94
Eigen::RotationBase< Quaternion< _Scalar, _Options >, 3 >::Scalar
internal::traits< Quaternion< _Scalar, _Options > >::Scalar Scalar
Definition: RotationBase.h:34
Eigen::Map::Map
Map(PointerArgType dataPtr, const StrideType &stride=StrideType())
Definition: Map.h:129
Eigen::cos
const Eigen::CwiseUnaryOp< Eigen::internal::scalar_cos_op< typename Derived::Scalar >, const Derived > cos(const Eigen::ArrayBase< Derived > &x)
Eigen::Quaternion
The quaternion class used to represent 3D orientations and rotations.
Definition: ForwardDeclarations.h:269
Eigen::QuaternionBase::y
CoeffReturnType y() const
Definition: Quaternion.h:67
Eigen::QuaternionMapf
Map< Quaternion< float >, 0 > QuaternionMapf
Definition: Quaternion.h:425
Eigen::QuaternionBase::_transformVector
Vector3 _transformVector(const Vector3 &v) const
Definition: Quaternion.h:486
Eigen::QuaternionBase::x
CoeffReturnType x() const
Definition: Quaternion.h:65
Eigen::QuaternionBase::setIdentity
QuaternionBase & setIdentity()
Definition: Quaternion.h:114
Eigen::QuaternionBase::conjugate
Quaternion< Scalar > conjugate() const
Definition: Quaternion.h:706
Eigen::QuaternionBase::toRotationMatrix
Matrix3 toRotationMatrix() const
Definition: Quaternion.h:547
Eigen::QuaternionBase::Matrix3
Matrix< Scalar, 3, 3 > Matrix3
Definition: Quaternion.h:58
Eigen::Quaternion::Quaternion
Quaternion()
Definition: Quaternion.h:260
Eigen::Matrix< Scalar, 3, 1 >
Eigen::MatrixBase
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:48
Eigen::QuaternionBase::coeffs
const internal::traits< Derived >::Coefficients & coeffs() const
Definition: Quaternion.h:89
Eigen::QuaternionMapAlignedd
Map< Quaternion< double >, Aligned > QuaternionMapAlignedd
Definition: Quaternion.h:434
Eigen::QuaternionBase
Base class for quaternion expressions.
Definition: ForwardDeclarations.h:264
Eigen::NumTraits
Holds information about the various numeric (i.e. scalar) types allowed by Eigen.
Definition: NumTraits.h:150
Eigen::AngleAxis::axis
const Vector3 & axis() const
Definition: AngleAxis.h:96
Eigen::Index
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:33
Eigen::Aligned
Definition: Constants.h:235