don't index Eigen

1 files changed, 0 insertions, 814 deletions

diff --git a/eigen/Eigen/src/Geometry/Quaternion.h b/eigen/Eigen/src/Geometry/Quaternion.h
deleted file mode 100644
index c3fd8c3..0000000
--- a/eigen/Eigen/src/Geometry/Quaternion.h
+++ /dev/null
@@ -1,814 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008-2010 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2009 Mathieu Gautier <mathieu.gautier@cea.fr>
-//
-// This Source Code Form is subject to the terms of the Mozilla
-// Public License v. 2.0. If a copy of the MPL was not distributed
-// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
-
-#ifndef EIGEN_QUATERNION_H
-#define EIGEN_QUATERNION_H
-namespace Eigen { 
-
-
-/***************************************************************************
-* Definition of QuaternionBase<Derived>
-* The implementation is at the end of the file
-***************************************************************************/
-
-namespace internal {
-template<typename Other,
-         int OtherRows=Other::RowsAtCompileTime,
-         int OtherCols=Other::ColsAtCompileTime>
-struct quaternionbase_assign_impl;
-}
-
-/** \geometry_module \ingroup Geometry_Module
-  * \class QuaternionBase
-  * \brief Base class for quaternion expressions
-  * \tparam Derived derived type (CRTP)
-  * \sa class Quaternion
-  */
-template<class Derived>
-class QuaternionBase : public RotationBase<Derived, 3>
-{
- public:
-  typedef RotationBase<Derived, 3> Base;
-
-  using Base::operator*;
-  using Base::derived;
-
-  typedef typename internal::traits<Derived>::Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
-  typedef typename internal::traits<Derived>::Coefficients Coefficients;
-  typedef typename Coefficients::CoeffReturnType CoeffReturnType;
-  typedef typename internal::conditional<bool(internal::traits<Derived>::Flags&LvalueBit),
-                                        Scalar&, CoeffReturnType>::type NonConstCoeffReturnType;
-
-
-  enum {
-    Flags = Eigen::internal::traits<Derived>::Flags
-  };
-
- // typedef typename Matrix<Scalar,4,1> Coefficients;
-  /** the type of a 3D vector */
-  typedef Matrix<Scalar,3,1> Vector3;
-  /** the equivalent rotation matrix type */
-  typedef Matrix<Scalar,3,3> Matrix3;
-  /** the equivalent angle-axis type */
-  typedef AngleAxis<Scalar> AngleAxisType;
-
-
-
-  /** \returns the \c x coefficient */
-  EIGEN_DEVICE_FUNC inline CoeffReturnType x() const { return this->derived().coeffs().coeff(0); }
-  /** \returns the \c y coefficient */
-  EIGEN_DEVICE_FUNC inline CoeffReturnType y() const { return this->derived().coeffs().coeff(1); }
-  /** \returns the \c z coefficient */
-  EIGEN_DEVICE_FUNC inline CoeffReturnType z() const { return this->derived().coeffs().coeff(2); }
-  /** \returns the \c w coefficient */
-  EIGEN_DEVICE_FUNC inline CoeffReturnType w() const { return this->derived().coeffs().coeff(3); }
-
-  /** \returns a reference to the \c x coefficient (if Derived is a non-const lvalue) */
-  EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType x() { return this->derived().coeffs().x(); }
-  /** \returns a reference to the \c y coefficient (if Derived is a non-const lvalue) */
-  EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType y() { return this->derived().coeffs().y(); }
-  /** \returns a reference to the \c z coefficient (if Derived is a non-const lvalue) */
-  EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType z() { return this->derived().coeffs().z(); }
-  /** \returns a reference to the \c w coefficient (if Derived is a non-const lvalue) */
-  EIGEN_DEVICE_FUNC inline NonConstCoeffReturnType w() { return this->derived().coeffs().w(); }
-
-  /** \returns a read-only vector expression of the imaginary part (x,y,z) */
-  EIGEN_DEVICE_FUNC inline const VectorBlock<const Coefficients,3> vec() const { return coeffs().template head<3>(); }
-
-  /** \returns a vector expression of the imaginary part (x,y,z) */
-  EIGEN_DEVICE_FUNC inline VectorBlock<Coefficients,3> vec() { return coeffs().template head<3>(); }
-
-  /** \returns a read-only vector expression of the coefficients (x,y,z,w) */
-  EIGEN_DEVICE_FUNC inline const typename internal::traits<Derived>::Coefficients& coeffs() const { return derived().coeffs(); }
-
-  /** \returns a vector expression of the coefficients (x,y,z,w) */
-  EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Coefficients& coeffs() { return derived().coeffs(); }
-
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& operator=(const QuaternionBase<Derived>& other);
-  template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator=(const QuaternionBase<OtherDerived>& other);
-
-// disabled this copy operator as it is giving very strange compilation errors when compiling
-// test_stdvector with GCC 4.4.2. This looks like a GCC bug though, so feel free to re-enable it if it's
-// useful; however notice that we already have the templated operator= above and e.g. in MatrixBase
-// we didn't have to add, in addition to templated operator=, such a non-templated copy operator.
-//  Derived& operator=(const QuaternionBase& other)
-//  { return operator=<Derived>(other); }
-
-  EIGEN_DEVICE_FUNC Derived& operator=(const AngleAxisType& aa);
-  template<class OtherDerived> EIGEN_DEVICE_FUNC Derived& operator=(const MatrixBase<OtherDerived>& m);
-
-  /** \returns a quaternion representing an identity rotation
-    * \sa MatrixBase::Identity()
-    */
-  EIGEN_DEVICE_FUNC static inline Quaternion<Scalar> Identity() { return Quaternion<Scalar>(Scalar(1), Scalar(0), Scalar(0), Scalar(0)); }
-
-  /** \sa QuaternionBase::Identity(), MatrixBase::setIdentity()
-    */
-  EIGEN_DEVICE_FUNC inline QuaternionBase& setIdentity() { coeffs() << Scalar(0), Scalar(0), Scalar(0), Scalar(1); return *this; }
-
-  /** \returns the squared norm of the quaternion's coefficients
-    * \sa QuaternionBase::norm(), MatrixBase::squaredNorm()
-    */
-  EIGEN_DEVICE_FUNC inline Scalar squaredNorm() const { return coeffs().squaredNorm(); }
-
-  /** \returns the norm of the quaternion's coefficients
-    * \sa QuaternionBase::squaredNorm(), MatrixBase::norm()
-    */
-  EIGEN_DEVICE_FUNC inline Scalar norm() const { return coeffs().norm(); }
-
-  /** Normalizes the quaternion \c *this
-    * \sa normalized(), MatrixBase::normalize() */
-  EIGEN_DEVICE_FUNC inline void normalize() { coeffs().normalize(); }
-  /** \returns a normalized copy of \c *this
-    * \sa normalize(), MatrixBase::normalized() */
-  EIGEN_DEVICE_FUNC inline Quaternion<Scalar> normalized() const { return Quaternion<Scalar>(coeffs().normalized()); }
-
-    /** \returns the dot product of \c *this and \a other
-    * Geometrically speaking, the dot product of two unit quaternions
-    * corresponds to the cosine of half the angle between the two rotations.
-    * \sa angularDistance()
-    */
-  template<class OtherDerived> EIGEN_DEVICE_FUNC inline Scalar dot(const QuaternionBase<OtherDerived>& other) const { return coeffs().dot(other.coeffs()); }
-
-  template<class OtherDerived> EIGEN_DEVICE_FUNC Scalar angularDistance(const QuaternionBase<OtherDerived>& other) const;
-
-  /** \returns an equivalent 3x3 rotation matrix */
-  EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix() const;
-
-  /** \returns the quaternion which transform \a a into \a b through a rotation */
-  template<typename Derived1, typename Derived2>
-  EIGEN_DEVICE_FUNC Derived& setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
-
-  template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<Scalar> operator* (const QuaternionBase<OtherDerived>& q) const;
-  template<class OtherDerived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& operator*= (const QuaternionBase<OtherDerived>& q);
-
-  /** \returns the quaternion describing the inverse rotation */
-  EIGEN_DEVICE_FUNC Quaternion<Scalar> inverse() const;
-
-  /** \returns the conjugated quaternion */
-  EIGEN_DEVICE_FUNC Quaternion<Scalar> conjugate() const;
-
-  template<class OtherDerived> EIGEN_DEVICE_FUNC Quaternion<Scalar> slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const;
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  template<class OtherDerived>
-  EIGEN_DEVICE_FUNC bool isApprox(const QuaternionBase<OtherDerived>& other, const RealScalar& prec = NumTraits<Scalar>::dummy_precision()) const
-  { return coeffs().isApprox(other.coeffs(), prec); }
-
-  /** return the result vector of \a v through the rotation*/
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Vector3 _transformVector(const Vector3& v) const;
-
-  /** \returns \c *this with scalar type casted to \a NewScalarType
-    *
-    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
-    * then this function smartly returns a const reference to \c *this.
-    */
-  template<typename NewScalarType>
-  EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type cast() const
-  {
-    return typename internal::cast_return_type<Derived,Quaternion<NewScalarType> >::type(derived());
-  }
-
-#ifdef EIGEN_QUATERNIONBASE_PLUGIN
-# include EIGEN_QUATERNIONBASE_PLUGIN
-#endif
-};
-
-/***************************************************************************
-* Definition/implementation of Quaternion<Scalar>
-***************************************************************************/
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class Quaternion
-  *
-  * \brief The quaternion class used to represent 3D orientations and rotations
-  *
-  * \tparam _Scalar the scalar type, i.e., the type of the coefficients
-  * \tparam _Options controls the memory alignment of the coefficients. Can be \# AutoAlign or \# DontAlign. Default is AutoAlign.
-  *
-  * This class represents a quaternion \f$ w+xi+yj+zk \f$ that is a convenient representation of
-  * orientations and rotations of objects in three dimensions. Compared to other representations
-  * like Euler angles or 3x3 matrices, quaternions offer the following advantages:
-  * \li \b compact storage (4 scalars)
-  * \li \b efficient to compose (28 flops),
-  * \li \b stable spherical interpolation
-  *
-  * The following two typedefs are provided for convenience:
-  * \li \c Quaternionf for \c float
-  * \li \c Quaterniond for \c double
-  *
-  * \warning Operations interpreting the quaternion as rotation have undefined behavior if the quaternion is not normalized.
-  *
-  * \sa  class AngleAxis, class Transform
-  */
-
-namespace internal {
-template<typename _Scalar,int _Options>
-struct traits<Quaternion<_Scalar,_Options> >
-{
-  typedef Quaternion<_Scalar,_Options> PlainObject;
-  typedef _Scalar Scalar;
-  typedef Matrix<_Scalar,4,1,_Options> Coefficients;
-  enum{
-    Alignment = internal::traits<Coefficients>::Alignment,
-    Flags = LvalueBit
-  };
-};
-}
-
-template<typename _Scalar, int _Options>
-class Quaternion : public QuaternionBase<Quaternion<_Scalar,_Options> >
-{
-public:
-  typedef QuaternionBase<Quaternion<_Scalar,_Options> > Base;
-  enum { NeedsAlignment = internal::traits<Quaternion>::Alignment>0 };
-
-  typedef _Scalar Scalar;
-
-  EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Quaternion)
-  using Base::operator*=;
-
-  typedef typename internal::traits<Quaternion>::Coefficients Coefficients;
-  typedef typename Base::AngleAxisType AngleAxisType;
-
-  /** Default constructor leaving the quaternion uninitialized. */
-  EIGEN_DEVICE_FUNC inline Quaternion() {}
-
-  /** Constructs and initializes the quaternion \f$ w+xi+yj+zk \f$ from
-    * its four coefficients \a w, \a x, \a y and \a z.
-    *
-    * \warning Note the order of the arguments: the real \a w coefficient first,
-    * while internally the coefficients are stored in the following order:
-    * [\c x, \c y, \c z, \c w]
-    */
-  EIGEN_DEVICE_FUNC inline Quaternion(const Scalar& w, const Scalar& x, const Scalar& y, const Scalar& z) : m_coeffs(x, y, z, w){}
-
-  /** Constructs and initialize a quaternion from the array data */
-  EIGEN_DEVICE_FUNC explicit inline Quaternion(const Scalar* data) : m_coeffs(data) {}
-
-  /** Copy constructor */
-  template<class Derived> EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion(const QuaternionBase<Derived>& other) { this->Base::operator=(other); }
-
-  /** Constructs and initializes a quaternion from the angle-axis \a aa */
-  EIGEN_DEVICE_FUNC explicit inline Quaternion(const AngleAxisType& aa) { *this = aa; }
-
-  /** Constructs and initializes a quaternion from either:
-    *  - a rotation matrix expression,
-    *  - a 4D vector expression representing quaternion coefficients.
-    */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC explicit inline Quaternion(const MatrixBase<Derived>& other) { *this = other; }
-
-  /** Explicit copy constructor with scalar conversion */
-  template<typename OtherScalar, int OtherOptions>
-  EIGEN_DEVICE_FUNC explicit inline Quaternion(const Quaternion<OtherScalar, OtherOptions>& other)
-  { m_coeffs = other.coeffs().template cast<Scalar>(); }
-
-  EIGEN_DEVICE_FUNC static Quaternion UnitRandom();
-
-  template<typename Derived1, typename Derived2>
-  EIGEN_DEVICE_FUNC static Quaternion FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b);
-
-  EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs;}
-  EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
-
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF(bool(NeedsAlignment))
-  
-#ifdef EIGEN_QUATERNION_PLUGIN
-# include EIGEN_QUATERNION_PLUGIN
-#endif
-
-protected:
-  Coefficients m_coeffs;
-  
-#ifndef EIGEN_PARSED_BY_DOXYGEN
-    static EIGEN_STRONG_INLINE void _check_template_params()
-    {
-      EIGEN_STATIC_ASSERT( (_Options & DontAlign) == _Options,
-        INVALID_MATRIX_TEMPLATE_PARAMETERS)
-    }
-#endif
-};
-
-/** \ingroup Geometry_Module
-  * single precision quaternion type */
-typedef Quaternion<float> Quaternionf;
-/** \ingroup Geometry_Module
-  * double precision quaternion type */
-typedef Quaternion<double> Quaterniond;
-
-/***************************************************************************
-* Specialization of Map<Quaternion<Scalar>>
-***************************************************************************/
-
-namespace internal {
-  template<typename _Scalar, int _Options>
-  struct traits<Map<Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
-  {
-    typedef Map<Matrix<_Scalar,4,1>, _Options> Coefficients;
-  };
-}
-
-namespace internal {
-  template<typename _Scalar, int _Options>
-  struct traits<Map<const Quaternion<_Scalar>, _Options> > : traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> >
-  {
-    typedef Map<const Matrix<_Scalar,4,1>, _Options> Coefficients;
-    typedef traits<Quaternion<_Scalar, (int(_Options)&Aligned)==Aligned ? AutoAlign : DontAlign> > TraitsBase;
-    enum {
-      Flags = TraitsBase::Flags & ~LvalueBit
-    };
-  };
-}
-
-/** \ingroup Geometry_Module
-  * \brief Quaternion expression mapping a constant memory buffer
-  *
-  * \tparam _Scalar the type of the Quaternion coefficients
-  * \tparam _Options see class Map
-  *
-  * This is a specialization of class Map for Quaternion. This class allows to view
-  * a 4 scalar memory buffer as an Eigen's Quaternion object.
-  *
-  * \sa class Map, class Quaternion, class QuaternionBase
-  */
-template<typename _Scalar, int _Options>
-class Map<const Quaternion<_Scalar>, _Options >
-  : public QuaternionBase<Map<const Quaternion<_Scalar>, _Options> >
-{
-  public:
-    typedef QuaternionBase<Map<const Quaternion<_Scalar>, _Options> > Base;
-
-    typedef _Scalar Scalar;
-    typedef typename internal::traits<Map>::Coefficients Coefficients;
-    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
-    using Base::operator*=;
-
-    /** Constructs a Mapped Quaternion object from the pointer \a coeffs
-      *
-      * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
-      * \code *coeffs == {x, y, z, w} \endcode
-      *
-      * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
-    EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(const Scalar* coeffs) : m_coeffs(coeffs) {}
-
-    EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs;}
-
-  protected:
-    const Coefficients m_coeffs;
-};
-
-/** \ingroup Geometry_Module
-  * \brief Expression of a quaternion from a memory buffer
-  *
-  * \tparam _Scalar the type of the Quaternion coefficients
-  * \tparam _Options see class Map
-  *
-  * This is a specialization of class Map for Quaternion. This class allows to view
-  * a 4 scalar memory buffer as an Eigen's  Quaternion object.
-  *
-  * \sa class Map, class Quaternion, class QuaternionBase
-  */
-template<typename _Scalar, int _Options>
-class Map<Quaternion<_Scalar>, _Options >
-  : public QuaternionBase<Map<Quaternion<_Scalar>, _Options> >
-{
-  public:
-    typedef QuaternionBase<Map<Quaternion<_Scalar>, _Options> > Base;
-
-    typedef _Scalar Scalar;
-    typedef typename internal::traits<Map>::Coefficients Coefficients;
-    EIGEN_INHERIT_ASSIGNMENT_OPERATORS(Map)
-    using Base::operator*=;
-
-    /** Constructs a Mapped Quaternion object from the pointer \a coeffs
-      *
-      * The pointer \a coeffs must reference the four coefficients of Quaternion in the following order:
-      * \code *coeffs == {x, y, z, w} \endcode
-      *
-      * If the template parameter _Options is set to #Aligned, then the pointer coeffs must be aligned. */
-    EIGEN_DEVICE_FUNC explicit EIGEN_STRONG_INLINE Map(Scalar* coeffs) : m_coeffs(coeffs) {}
-
-    EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
-    EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
-
-  protected:
-    Coefficients m_coeffs;
-};
-
-/** \ingroup Geometry_Module
-  * Map an unaligned array of single precision scalars as a quaternion */
-typedef Map<Quaternion<float>, 0>         QuaternionMapf;
-/** \ingroup Geometry_Module
-  * Map an unaligned array of double precision scalars as a quaternion */
-typedef Map<Quaternion<double>, 0>        QuaternionMapd;
-/** \ingroup Geometry_Module
-  * Map a 16-byte aligned array of single precision scalars as a quaternion */
-typedef Map<Quaternion<float>, Aligned>   QuaternionMapAlignedf;
-/** \ingroup Geometry_Module
-  * Map a 16-byte aligned array of double precision scalars as a quaternion */
-typedef Map<Quaternion<double>, Aligned>  QuaternionMapAlignedd;
-
-/***************************************************************************
-* Implementation of QuaternionBase methods
-***************************************************************************/
-
-// Generic Quaternion * Quaternion product
-// This product can be specialized for a given architecture via the Arch template argument.
-namespace internal {
-template<int Arch, class Derived1, class Derived2, typename Scalar> struct quat_product
-{
-  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived1>& a, const QuaternionBase<Derived2>& b){
-    return Quaternion<Scalar>
-    (
-      a.w() * b.w() - a.x() * b.x() - a.y() * b.y() - a.z() * b.z(),
-      a.w() * b.x() + a.x() * b.w() + a.y() * b.z() - a.z() * b.y(),
-      a.w() * b.y() + a.y() * b.w() + a.z() * b.x() - a.x() * b.z(),
-      a.w() * b.z() + a.z() * b.w() + a.x() * b.y() - a.y() * b.x()
-    );
-  }
-};
-}
-
-/** \returns the concatenation of two rotations as a quaternion-quaternion product */
-template <class Derived>
-template <class OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Quaternion<typename internal::traits<Derived>::Scalar>
-QuaternionBase<Derived>::operator* (const QuaternionBase<OtherDerived>& other) const
-{
-  EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename OtherDerived::Scalar>::value),
-   YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
-  return internal::quat_product<Architecture::Target, Derived, OtherDerived,
-                         typename internal::traits<Derived>::Scalar>::run(*this, other);
-}
-
-/** \sa operator*(Quaternion) */
-template <class Derived>
-template <class OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator*= (const QuaternionBase<OtherDerived>& other)
-{
-  derived() = derived() * other.derived();
-  return derived();
-}
-
-/** Rotation of a vector by a quaternion.
-  * \remarks If the quaternion is used to rotate several points (>1)
-  * then it is much more efficient to first convert it to a 3x3 Matrix.
-  * Comparison of the operation cost for n transformations:
-  *   - Quaternion2:    30n
-  *   - Via a Matrix3: 24 + 15n
-  */
-template <class Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename QuaternionBase<Derived>::Vector3
-QuaternionBase<Derived>::_transformVector(const Vector3& v) const
-{
-    // Note that this algorithm comes from the optimization by hand
-    // of the conversion to a Matrix followed by a Matrix/Vector product.
-    // It appears to be much faster than the common algorithm found
-    // in the literature (30 versus 39 flops). It also requires two
-    // Vector3 as temporaries.
-    Vector3 uv = this->vec().cross(v);
-    uv += uv;
-    return v + this->w() * uv + this->vec().cross(uv);
-}
-
-template<class Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE QuaternionBase<Derived>& QuaternionBase<Derived>::operator=(const QuaternionBase<Derived>& other)
-{
-  coeffs() = other.coeffs();
-  return derived();
-}
-
-template<class Derived>
-template<class OtherDerived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const QuaternionBase<OtherDerived>& other)
-{
-  coeffs() = other.coeffs();
-  return derived();
-}
-
-/** Set \c *this from an angle-axis \a aa and returns a reference to \c *this
-  */
-template<class Derived>
-EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE Derived& QuaternionBase<Derived>::operator=(const AngleAxisType& aa)
-{
-  EIGEN_USING_STD_MATH(cos)
-  EIGEN_USING_STD_MATH(sin)
-  Scalar ha = Scalar(0.5)*aa.angle(); // Scalar(0.5) to suppress precision loss warnings
-  this->w() = cos(ha);
-  this->vec() = sin(ha) * aa.axis();
-  return derived();
-}
-
-/** Set \c *this from the expression \a xpr:
-  *   - if \a xpr is a 4x1 vector, then \a xpr is assumed to be a quaternion
-  *   - if \a xpr is a 3x3 matrix, then \a xpr is assumed to be rotation matrix
-  *     and \a xpr is converted to a quaternion
-  */
-
-template<class Derived>
-template<class MatrixDerived>
-EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::operator=(const MatrixBase<MatrixDerived>& xpr)
-{
-  EIGEN_STATIC_ASSERT((internal::is_same<typename Derived::Scalar, typename MatrixDerived::Scalar>::value),
-   YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
-  internal::quaternionbase_assign_impl<MatrixDerived>::run(*this, xpr.derived());
-  return derived();
-}
-
-/** Convert the quaternion to a 3x3 rotation matrix. The quaternion is required to
-  * be normalized, otherwise the result is undefined.
-  */
-template<class Derived>
-EIGEN_DEVICE_FUNC inline typename QuaternionBase<Derived>::Matrix3
-QuaternionBase<Derived>::toRotationMatrix(void) const
-{
-  // NOTE if inlined, then gcc 4.2 and 4.4 get rid of the temporary (not gcc 4.3 !!)
-  // if not inlined then the cost of the return by value is huge ~ +35%,
-  // however, not inlining this function is an order of magnitude slower, so
-  // it has to be inlined, and so the return by value is not an issue
-  Matrix3 res;
-
-  const Scalar tx  = Scalar(2)*this->x();
-  const Scalar ty  = Scalar(2)*this->y();
-  const Scalar tz  = Scalar(2)*this->z();
-  const Scalar twx = tx*this->w();
-  const Scalar twy = ty*this->w();
-  const Scalar twz = tz*this->w();
-  const Scalar txx = tx*this->x();
-  const Scalar txy = ty*this->x();
-  const Scalar txz = tz*this->x();
-  const Scalar tyy = ty*this->y();
-  const Scalar tyz = tz*this->y();
-  const Scalar tzz = tz*this->z();
-
-  res.coeffRef(0,0) = Scalar(1)-(tyy+tzz);
-  res.coeffRef(0,1) = txy-twz;
-  res.coeffRef(0,2) = txz+twy;
-  res.coeffRef(1,0) = txy+twz;
-  res.coeffRef(1,1) = Scalar(1)-(txx+tzz);
-  res.coeffRef(1,2) = tyz-twx;
-  res.coeffRef(2,0) = txz-twy;
-  res.coeffRef(2,1) = tyz+twx;
-  res.coeffRef(2,2) = Scalar(1)-(txx+tyy);
-
-  return res;
-}
-
-/** Sets \c *this to be a quaternion representing a rotation between
-  * the two arbitrary vectors \a a and \a b. In other words, the built
-  * rotation represent a rotation sending the line of direction \a a
-  * to the line of direction \a b, both lines passing through the origin.
-  *
-  * \returns a reference to \c *this.
-  *
-  * Note that the two input vectors do \b not have to be normalized, and
-  * do not need to have the same norm.
-  */
-template<class Derived>
-template<typename Derived1, typename Derived2>
-EIGEN_DEVICE_FUNC inline Derived& QuaternionBase<Derived>::setFromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
-{
-  EIGEN_USING_STD_MATH(sqrt)
-  Vector3 v0 = a.normalized();
-  Vector3 v1 = b.normalized();
-  Scalar c = v1.dot(v0);
-
-  // if dot == -1, vectors are nearly opposites
-  // => accurately compute the rotation axis by computing the
-  //    intersection of the two planes. This is done by solving:
-  //       x^T v0 = 0
-  //       x^T v1 = 0
-  //    under the constraint:
-  //       ||x|| = 1
-  //    which yields a singular value problem
-  if (c < Scalar(-1)+NumTraits<Scalar>::dummy_precision())
-  {
-    c = numext::maxi(c,Scalar(-1));
-    Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
-    JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
-    Vector3 axis = svd.matrixV().col(2);
-
-    Scalar w2 = (Scalar(1)+c)*Scalar(0.5);
-    this->w() = sqrt(w2);
-    this->vec() = axis * sqrt(Scalar(1) - w2);
-    return derived();
-  }
-  Vector3 axis = v0.cross(v1);
-  Scalar s = sqrt((Scalar(1)+c)*Scalar(2));
-  Scalar invs = Scalar(1)/s;
-  this->vec() = axis * invs;
-  this->w() = s * Scalar(0.5);
-
-  return derived();
-}
-
-/** \returns a random unit quaternion following a uniform distribution law on SO(3)
-  *
-  * \note The implementation is based on http://planning.cs.uiuc.edu/node198.html
-  */
-template<typename Scalar, int Options>
-EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::UnitRandom()
-{
-  EIGEN_USING_STD_MATH(sqrt)
-  EIGEN_USING_STD_MATH(sin)
-  EIGEN_USING_STD_MATH(cos)
-  const Scalar u1 = internal::random<Scalar>(0, 1),
-               u2 = internal::random<Scalar>(0, 2*EIGEN_PI),
-               u3 = internal::random<Scalar>(0, 2*EIGEN_PI);
-  const Scalar a = sqrt(1 - u1),
-               b = sqrt(u1);
-  return Quaternion (a * sin(u2), a * cos(u2), b * sin(u3), b * cos(u3));
-}
-
-
-/** Returns a quaternion representing a rotation between
-  * the two arbitrary vectors \a a and \a b. In other words, the built
-  * rotation represent a rotation sending the line of direction \a a
-  * to the line of direction \a b, both lines passing through the origin.
-  *
-  * \returns resulting quaternion
-  *
-  * Note that the two input vectors do \b not have to be normalized, and
-  * do not need to have the same norm.
-  */
-template<typename Scalar, int Options>
-template<typename Derived1, typename Derived2>
-EIGEN_DEVICE_FUNC Quaternion<Scalar,Options> Quaternion<Scalar,Options>::FromTwoVectors(const MatrixBase<Derived1>& a, const MatrixBase<Derived2>& b)
-{
-    Quaternion quat;
-    quat.setFromTwoVectors(a, b);
-    return quat;
-}
-
-
-/** \returns the multiplicative inverse of \c *this
-  * Note that in most cases, i.e., if you simply want the opposite rotation,
-  * and/or the quaternion is normalized, then it is enough to use the conjugate.
-  *
-  * \sa QuaternionBase::conjugate()
-  */
-template <class Derived>
-EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar> QuaternionBase<Derived>::inverse() const
-{
-  // FIXME should this function be called multiplicativeInverse and conjugate() be called inverse() or opposite()  ??
-  Scalar n2 = this->squaredNorm();
-  if (n2 > Scalar(0))
-    return Quaternion<Scalar>(conjugate().coeffs() / n2);
-  else
-  {
-    // return an invalid result to flag the error
-    return Quaternion<Scalar>(Coefficients::Zero());
-  }
-}
-
-// Generic conjugate of a Quaternion
-namespace internal {
-template<int Arch, class Derived, typename Scalar> struct quat_conj
-{
-  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE Quaternion<Scalar> run(const QuaternionBase<Derived>& q){
-    return Quaternion<Scalar>(q.w(),-q.x(),-q.y(),-q.z());
-  }
-};
-}
-                         
-/** \returns the conjugate of the \c *this which is equal to the multiplicative inverse
-  * if the quaternion is normalized.
-  * The conjugate of a quaternion represents the opposite rotation.
-  *
-  * \sa Quaternion2::inverse()
-  */
-template <class Derived>
-EIGEN_DEVICE_FUNC inline Quaternion<typename internal::traits<Derived>::Scalar>
-QuaternionBase<Derived>::conjugate() const
-{
-  return internal::quat_conj<Architecture::Target, Derived,
-                         typename internal::traits<Derived>::Scalar>::run(*this);
-                         
-}
-
-/** \returns the angle (in radian) between two rotations
-  * \sa dot()
-  */
-template <class Derived>
-template <class OtherDerived>
-EIGEN_DEVICE_FUNC inline typename internal::traits<Derived>::Scalar
-QuaternionBase<Derived>::angularDistance(const QuaternionBase<OtherDerived>& other) const
-{
-  EIGEN_USING_STD_MATH(atan2)
-  Quaternion<Scalar> d = (*this) * other.conjugate();
-  return Scalar(2) * atan2( d.vec().norm(), numext::abs(d.w()) );
-}
-
- 
-    
-/** \returns the spherical linear interpolation between the two quaternions
-  * \c *this and \a other at the parameter \a t in [0;1].
-  * 
-  * This represents an interpolation for a constant motion between \c *this and \a other,
-  * see also http://en.wikipedia.org/wiki/Slerp.
-  */
-template <class Derived>
-template <class OtherDerived>
-EIGEN_DEVICE_FUNC Quaternion<typename internal::traits<Derived>::Scalar>
-QuaternionBase<Derived>::slerp(const Scalar& t, const QuaternionBase<OtherDerived>& other) const
-{
-  EIGEN_USING_STD_MATH(acos)
-  EIGEN_USING_STD_MATH(sin)
-  const Scalar one = Scalar(1) - NumTraits<Scalar>::epsilon();
-  Scalar d = this->dot(other);
-  Scalar absD = numext::abs(d);
-
-  Scalar scale0;
-  Scalar scale1;
-
-  if(absD>=one)
-  {
-    scale0 = Scalar(1) - t;
-    scale1 = t;
-  }
-  else
-  {
-    // theta is the angle between the 2 quaternions
-    Scalar theta = acos(absD);
-    Scalar sinTheta = sin(theta);
-
-    scale0 = sin( ( Scalar(1) - t ) * theta) / sinTheta;
-    scale1 = sin( ( t * theta) ) / sinTheta;
-  }
-  if(d<Scalar(0)) scale1 = -scale1;
-
-  return Quaternion<Scalar>(scale0 * coeffs() + scale1 * other.coeffs());
-}
-
-namespace internal {
-
-// set from a rotation matrix
-template<typename Other>
-struct quaternionbase_assign_impl<Other,3,3>
-{
-  typedef typename Other::Scalar Scalar;
-  template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& a_mat)
-  {
-    const typename internal::nested_eval<Other,2>::type mat(a_mat);
-    EIGEN_USING_STD_MATH(sqrt)
-    // This algorithm comes from  "Quaternion Calculus and Fast Animation",
-    // Ken Shoemake, 1987 SIGGRAPH course notes
-    Scalar t = mat.trace();
-    if (t > Scalar(0))
-    {
-      t = sqrt(t + Scalar(1.0));
-      q.w() = Scalar(0.5)*t;
-      t = Scalar(0.5)/t;
-      q.x() = (mat.coeff(2,1) - mat.coeff(1,2)) * t;
-      q.y() = (mat.coeff(0,2) - mat.coeff(2,0)) * t;
-      q.z() = (mat.coeff(1,0) - mat.coeff(0,1)) * t;
-    }
-    else
-    {
-      Index i = 0;
-      if (mat.coeff(1,1) > mat.coeff(0,0))
-        i = 1;
-      if (mat.coeff(2,2) > mat.coeff(i,i))
-        i = 2;
-      Index j = (i+1)%3;
-      Index k = (j+1)%3;
-
-      t = sqrt(mat.coeff(i,i)-mat.coeff(j,j)-mat.coeff(k,k) + Scalar(1.0));
-      q.coeffs().coeffRef(i) = Scalar(0.5) * t;
-      t = Scalar(0.5)/t;
-      q.w() = (mat.coeff(k,j)-mat.coeff(j,k))*t;
-      q.coeffs().coeffRef(j) = (mat.coeff(j,i)+mat.coeff(i,j))*t;
-      q.coeffs().coeffRef(k) = (mat.coeff(k,i)+mat.coeff(i,k))*t;
-    }
-  }
-};
-
-// set from a vector of coefficients assumed to be a quaternion
-template<typename Other>
-struct quaternionbase_assign_impl<Other,4,1>
-{
-  typedef typename Other::Scalar Scalar;
-  template<class Derived> EIGEN_DEVICE_FUNC static inline void run(QuaternionBase<Derived>& q, const Other& vec)
-  {
-    q.coeffs() = vec;
-  }
-};
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_QUATERNION_H