don't index Eigen

15 files changed, 0 insertions, 5427 deletions

diff --git a/eigen/Eigen/src/Geometry/AlignedBox.h b/eigen/Eigen/src/Geometry/AlignedBox.h
deleted file mode 100644
index 066eae4..0000000
--- a/eigen/Eigen/src/Geometry/AlignedBox.h
+++ /dev/null
@@ -1,392 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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_ALIGNEDBOX_H
-#define EIGEN_ALIGNEDBOX_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  *
-  * \class AlignedBox
-  *
-  * \brief An axis aligned box
-  *
-  * \tparam _Scalar the type of the scalar coefficients
-  * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
-  *
-  * This class represents an axis aligned box as a pair of the minimal and maximal corners.
-  * \warning The result of most methods is undefined when applied to an empty box. You can check for empty boxes using isEmpty().
-  * \sa alignedboxtypedefs
-  */
-template <typename _Scalar, int _AmbientDim>
-class AlignedBox
-{
-public:
-EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
-  enum { AmbientDimAtCompileTime = _AmbientDim };
-  typedef _Scalar                                   Scalar;
-  typedef NumTraits<Scalar>                         ScalarTraits;
-  typedef Eigen::Index                              Index; ///< \deprecated since Eigen 3.3
-  typedef typename ScalarTraits::Real               RealScalar;
-  typedef typename ScalarTraits::NonInteger         NonInteger;
-  typedef Matrix<Scalar,AmbientDimAtCompileTime,1>  VectorType;
-  typedef CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const VectorType, const VectorType> VectorTypeSum;
-
-  /** Define constants to name the corners of a 1D, 2D or 3D axis aligned bounding box */
-  enum CornerType
-  {
-    /** 1D names @{ */
-    Min=0, Max=1,
-    /** @} */
-
-    /** Identifier for 2D corner @{ */
-    BottomLeft=0, BottomRight=1,
-    TopLeft=2, TopRight=3,
-    /** @} */
-
-    /** Identifier for 3D corner  @{ */
-    BottomLeftFloor=0, BottomRightFloor=1,
-    TopLeftFloor=2, TopRightFloor=3,
-    BottomLeftCeil=4, BottomRightCeil=5,
-    TopLeftCeil=6, TopRightCeil=7
-    /** @} */
-  };
-
-
-  /** Default constructor initializing a null box. */
-  EIGEN_DEVICE_FUNC inline AlignedBox()
-  { if (AmbientDimAtCompileTime!=Dynamic) setEmpty(); }
-
-  /** Constructs a null box with \a _dim the dimension of the ambient space. */
-  EIGEN_DEVICE_FUNC inline explicit AlignedBox(Index _dim) : m_min(_dim), m_max(_dim)
-  { setEmpty(); }
-
-  /** Constructs a box with extremities \a _min and \a _max.
-   * \warning If either component of \a _min is larger than the same component of \a _max, the constructed box is empty. */
-  template<typename OtherVectorType1, typename OtherVectorType2>
-  EIGEN_DEVICE_FUNC inline AlignedBox(const OtherVectorType1& _min, const OtherVectorType2& _max) : m_min(_min), m_max(_max) {}
-
-  /** Constructs a box containing a single point \a p. */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline explicit AlignedBox(const MatrixBase<Derived>& p) : m_min(p), m_max(m_min)
-  { }
-
-  EIGEN_DEVICE_FUNC ~AlignedBox() {}
-
-  /** \returns the dimension in which the box holds */
-  EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_min.size() : Index(AmbientDimAtCompileTime); }
-
-  /** \deprecated use isEmpty() */
-  EIGEN_DEVICE_FUNC inline bool isNull() const { return isEmpty(); }
-
-  /** \deprecated use setEmpty() */
-  EIGEN_DEVICE_FUNC inline void setNull() { setEmpty(); }
-
-  /** \returns true if the box is empty.
-   * \sa setEmpty */
-  EIGEN_DEVICE_FUNC inline bool isEmpty() const { return (m_min.array() > m_max.array()).any(); }
-
-  /** Makes \c *this an empty box.
-   * \sa isEmpty */
-  EIGEN_DEVICE_FUNC inline void setEmpty()
-  {
-    m_min.setConstant( ScalarTraits::highest() );
-    m_max.setConstant( ScalarTraits::lowest() );
-  }
-
-  /** \returns the minimal corner */
-  EIGEN_DEVICE_FUNC inline const VectorType& (min)() const { return m_min; }
-  /** \returns a non const reference to the minimal corner */
-  EIGEN_DEVICE_FUNC inline VectorType& (min)() { return m_min; }
-  /** \returns the maximal corner */
-  EIGEN_DEVICE_FUNC inline const VectorType& (max)() const { return m_max; }
-  /** \returns a non const reference to the maximal corner */
-  EIGEN_DEVICE_FUNC inline VectorType& (max)() { return m_max; }
-
-  /** \returns the center of the box */
-  EIGEN_DEVICE_FUNC inline const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(VectorTypeSum, RealScalar, quotient)
-  center() const
-  { return (m_min+m_max)/RealScalar(2); }
-
-  /** \returns the lengths of the sides of the bounding box.
-    * Note that this function does not get the same
-    * result for integral or floating scalar types: see
-    */
-  EIGEN_DEVICE_FUNC inline const CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> sizes() const
-  { return m_max - m_min; }
-
-  /** \returns the volume of the bounding box */
-  EIGEN_DEVICE_FUNC inline Scalar volume() const
-  { return sizes().prod(); }
-
-  /** \returns an expression for the bounding box diagonal vector
-    * if the length of the diagonal is needed: diagonal().norm()
-    * will provide it.
-    */
-  EIGEN_DEVICE_FUNC inline CwiseBinaryOp< internal::scalar_difference_op<Scalar,Scalar>, const VectorType, const VectorType> diagonal() const
-  { return sizes(); }
-
-  /** \returns the vertex of the bounding box at the corner defined by
-    * the corner-id corner. It works only for a 1D, 2D or 3D bounding box.
-    * For 1D bounding boxes corners are named by 2 enum constants:
-    * BottomLeft and BottomRight.
-    * For 2D bounding boxes, corners are named by 4 enum constants:
-    * BottomLeft, BottomRight, TopLeft, TopRight.
-    * For 3D bounding boxes, the following names are added:
-    * BottomLeftCeil, BottomRightCeil, TopLeftCeil, TopRightCeil.
-    */
-  EIGEN_DEVICE_FUNC inline VectorType corner(CornerType corner) const
-  {
-    EIGEN_STATIC_ASSERT(_AmbientDim <= 3, THIS_METHOD_IS_ONLY_FOR_VECTORS_OF_A_SPECIFIC_SIZE);
-
-    VectorType res;
-
-    Index mult = 1;
-    for(Index d=0; d<dim(); ++d)
-    {
-      if( mult & corner ) res[d] = m_max[d];
-      else                res[d] = m_min[d];
-      mult *= 2;
-    }
-    return res;
-  }
-
-  /** \returns a random point inside the bounding box sampled with
-   * a uniform distribution */
-  EIGEN_DEVICE_FUNC inline VectorType sample() const
-  {
-    VectorType r(dim());
-    for(Index d=0; d<dim(); ++d)
-    {
-      if(!ScalarTraits::IsInteger)
-      {
-        r[d] = m_min[d] + (m_max[d]-m_min[d])
-             * internal::random<Scalar>(Scalar(0), Scalar(1));
-      }
-      else
-        r[d] = internal::random(m_min[d], m_max[d]);
-    }
-    return r;
-  }
-
-  /** \returns true if the point \a p is inside the box \c *this. */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline bool contains(const MatrixBase<Derived>& p) const
-  {
-    typename internal::nested_eval<Derived,2>::type p_n(p.derived());
-    return (m_min.array()<=p_n.array()).all() && (p_n.array()<=m_max.array()).all();
-  }
-
-  /** \returns true if the box \a b is entirely inside the box \c *this. */
-  EIGEN_DEVICE_FUNC inline bool contains(const AlignedBox& b) const
-  { return (m_min.array()<=(b.min)().array()).all() && ((b.max)().array()<=m_max.array()).all(); }
-
-  /** \returns true if the box \a b is intersecting the box \c *this.
-   * \sa intersection, clamp */
-  EIGEN_DEVICE_FUNC inline bool intersects(const AlignedBox& b) const
-  { return (m_min.array()<=(b.max)().array()).all() && ((b.min)().array()<=m_max.array()).all(); }
-
-  /** Extends \c *this such that it contains the point \a p and returns a reference to \c *this.
-   * \sa extend(const AlignedBox&) */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline AlignedBox& extend(const MatrixBase<Derived>& p)
-  {
-    typename internal::nested_eval<Derived,2>::type p_n(p.derived());
-    m_min = m_min.cwiseMin(p_n);
-    m_max = m_max.cwiseMax(p_n);
-    return *this;
-  }
-
-  /** Extends \c *this such that it contains the box \a b and returns a reference to \c *this.
-   * \sa merged, extend(const MatrixBase&) */
-  EIGEN_DEVICE_FUNC inline AlignedBox& extend(const AlignedBox& b)
-  {
-    m_min = m_min.cwiseMin(b.m_min);
-    m_max = m_max.cwiseMax(b.m_max);
-    return *this;
-  }
-
-  /** Clamps \c *this by the box \a b and returns a reference to \c *this.
-   * \note If the boxes don't intersect, the resulting box is empty.
-   * \sa intersection(), intersects() */
-  EIGEN_DEVICE_FUNC inline AlignedBox& clamp(const AlignedBox& b)
-  {
-    m_min = m_min.cwiseMax(b.m_min);
-    m_max = m_max.cwiseMin(b.m_max);
-    return *this;
-  }
-
-  /** Returns an AlignedBox that is the intersection of \a b and \c *this
-   * \note If the boxes don't intersect, the resulting box is empty.
-   * \sa intersects(), clamp, contains()  */
-  EIGEN_DEVICE_FUNC inline AlignedBox intersection(const AlignedBox& b) const
-  {return AlignedBox(m_min.cwiseMax(b.m_min), m_max.cwiseMin(b.m_max)); }
-
-  /** Returns an AlignedBox that is the union of \a b and \c *this.
-   * \note Merging with an empty box may result in a box bigger than \c *this. 
-   * \sa extend(const AlignedBox&) */
-  EIGEN_DEVICE_FUNC inline AlignedBox merged(const AlignedBox& b) const
-  { return AlignedBox(m_min.cwiseMin(b.m_min), m_max.cwiseMax(b.m_max)); }
-
-  /** Translate \c *this by the vector \a t and returns a reference to \c *this. */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline AlignedBox& translate(const MatrixBase<Derived>& a_t)
-  {
-    const typename internal::nested_eval<Derived,2>::type t(a_t.derived());
-    m_min += t;
-    m_max += t;
-    return *this;
-  }
-
-  /** \returns the squared distance between the point \a p and the box \c *this,
-    * and zero if \a p is inside the box.
-    * \sa exteriorDistance(const MatrixBase&), squaredExteriorDistance(const AlignedBox&)
-    */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const MatrixBase<Derived>& p) const;
-
-  /** \returns the squared distance between the boxes \a b and \c *this,
-    * and zero if the boxes intersect.
-    * \sa exteriorDistance(const AlignedBox&), squaredExteriorDistance(const MatrixBase&)
-    */
-  EIGEN_DEVICE_FUNC inline Scalar squaredExteriorDistance(const AlignedBox& b) const;
-
-  /** \returns the distance between the point \a p and the box \c *this,
-    * and zero if \a p is inside the box.
-    * \sa squaredExteriorDistance(const MatrixBase&), exteriorDistance(const AlignedBox&)
-    */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const MatrixBase<Derived>& p) const
-  { EIGEN_USING_STD_MATH(sqrt) return sqrt(NonInteger(squaredExteriorDistance(p))); }
-
-  /** \returns the distance between the boxes \a b and \c *this,
-    * and zero if the boxes intersect.
-    * \sa squaredExteriorDistance(const AlignedBox&), exteriorDistance(const MatrixBase&)
-    */
-  EIGEN_DEVICE_FUNC inline NonInteger exteriorDistance(const AlignedBox& b) const
-  { EIGEN_USING_STD_MATH(sqrt) return sqrt(NonInteger(squaredExteriorDistance(b))); }
-
-  /** \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<AlignedBox,
-           AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type cast() const
-  {
-    return typename internal::cast_return_type<AlignedBox,
-                    AlignedBox<NewScalarType,AmbientDimAtCompileTime> >::type(*this);
-  }
-
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType>
-  EIGEN_DEVICE_FUNC inline explicit AlignedBox(const AlignedBox<OtherScalarType,AmbientDimAtCompileTime>& other)
-  {
-    m_min = (other.min)().template cast<Scalar>();
-    m_max = (other.max)().template cast<Scalar>();
-  }
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  EIGEN_DEVICE_FUNC bool isApprox(const AlignedBox& other, const RealScalar& prec = ScalarTraits::dummy_precision()) const
-  { return m_min.isApprox(other.m_min, prec) && m_max.isApprox(other.m_max, prec); }
-
-protected:
-
-  VectorType m_min, m_max;
-};
-
-
-
-template<typename Scalar,int AmbientDim>
-template<typename Derived>
-EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const MatrixBase<Derived>& a_p) const
-{
-  typename internal::nested_eval<Derived,2*AmbientDim>::type p(a_p.derived());
-  Scalar dist2(0);
-  Scalar aux;
-  for (Index k=0; k<dim(); ++k)
-  {
-    if( m_min[k] > p[k] )
-    {
-      aux = m_min[k] - p[k];
-      dist2 += aux*aux;
-    }
-    else if( p[k] > m_max[k] )
-    {
-      aux = p[k] - m_max[k];
-      dist2 += aux*aux;
-    }
-  }
-  return dist2;
-}
-
-template<typename Scalar,int AmbientDim>
-EIGEN_DEVICE_FUNC inline Scalar AlignedBox<Scalar,AmbientDim>::squaredExteriorDistance(const AlignedBox& b) const
-{
-  Scalar dist2(0);
-  Scalar aux;
-  for (Index k=0; k<dim(); ++k)
-  {
-    if( m_min[k] > b.m_max[k] )
-    {
-      aux = m_min[k] - b.m_max[k];
-      dist2 += aux*aux;
-    }
-    else if( b.m_min[k] > m_max[k] )
-    {
-      aux = b.m_min[k] - m_max[k];
-      dist2 += aux*aux;
-    }
-  }
-  return dist2;
-}
-
-/** \defgroup alignedboxtypedefs Global aligned box typedefs
-  *
-  * \ingroup Geometry_Module
-  *
-  * Eigen defines several typedef shortcuts for most common aligned box types.
-  *
-  * The general patterns are the following:
-  *
-  * \c AlignedBoxSizeType where \c Size can be \c 1, \c 2,\c 3,\c 4 for fixed size boxes or \c X for dynamic size,
-  * and where \c Type can be \c i for integer, \c f for float, \c d for double.
-  *
-  * For example, \c AlignedBox3d is a fixed-size 3x3 aligned box type of doubles, and \c AlignedBoxXf is a dynamic-size aligned box of floats.
-  *
-  * \sa class AlignedBox
-  */
-
-#define EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Size, SizeSuffix)    \
-/** \ingroup alignedboxtypedefs */                                 \
-typedef AlignedBox<Type, Size>   AlignedBox##SizeSuffix##TypeSuffix;
-
-#define EIGEN_MAKE_TYPEDEFS_ALL_SIZES(Type, TypeSuffix) \
-EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 1, 1) \
-EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 2, 2) \
-EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 3, 3) \
-EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, 4, 4) \
-EIGEN_MAKE_TYPEDEFS(Type, TypeSuffix, Dynamic, X)
-
-EIGEN_MAKE_TYPEDEFS_ALL_SIZES(int,                  i)
-EIGEN_MAKE_TYPEDEFS_ALL_SIZES(float,                f)
-EIGEN_MAKE_TYPEDEFS_ALL_SIZES(double,               d)
-
-#undef EIGEN_MAKE_TYPEDEFS_ALL_SIZES
-#undef EIGEN_MAKE_TYPEDEFS
-
-} // end namespace Eigen
-
-#endif // EIGEN_ALIGNEDBOX_H
diff --git a/eigen/Eigen/src/Geometry/AngleAxis.h b/eigen/Eigen/src/Geometry/AngleAxis.h
deleted file mode 100644
index 83ee1be..0000000
--- a/eigen/Eigen/src/Geometry/AngleAxis.h
+++ /dev/null
@@ -1,247 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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_ANGLEAXIS_H
-#define EIGEN_ANGLEAXIS_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class AngleAxis
-  *
-  * \brief Represents a 3D rotation as a rotation angle around an arbitrary 3D axis
-  *
-  * \param _Scalar the scalar type, i.e., the type of the coefficients.
-  *
-  * \warning When setting up an AngleAxis object, the axis vector \b must \b be \b normalized.
-  *
-  * The following two typedefs are provided for convenience:
-  * \li \c AngleAxisf for \c float
-  * \li \c AngleAxisd for \c double
-  *
-  * Combined with MatrixBase::Unit{X,Y,Z}, AngleAxis can be used to easily
-  * mimic Euler-angles. Here is an example:
-  * \include AngleAxis_mimic_euler.cpp
-  * Output: \verbinclude AngleAxis_mimic_euler.out
-  *
-  * \note This class is not aimed to be used to store a rotation transformation,
-  * but rather to make easier the creation of other rotation (Quaternion, rotation Matrix)
-  * and transformation objects.
-  *
-  * \sa class Quaternion, class Transform, MatrixBase::UnitX()
-  */
-
-namespace internal {
-template<typename _Scalar> struct traits<AngleAxis<_Scalar> >
-{
-  typedef _Scalar Scalar;
-};
-}
-
-template<typename _Scalar>
-class AngleAxis : public RotationBase<AngleAxis<_Scalar>,3>
-{
-  typedef RotationBase<AngleAxis<_Scalar>,3> Base;
-
-public:
-
-  using Base::operator*;
-
-  enum { Dim = 3 };
-  /** the scalar type of the coefficients */
-  typedef _Scalar Scalar;
-  typedef Matrix<Scalar,3,3> Matrix3;
-  typedef Matrix<Scalar,3,1> Vector3;
-  typedef Quaternion<Scalar> QuaternionType;
-
-protected:
-
-  Vector3 m_axis;
-  Scalar m_angle;
-
-public:
-
-  /** Default constructor without initialization. */
-  EIGEN_DEVICE_FUNC AngleAxis() {}
-  /** Constructs and initialize the angle-axis rotation from an \a angle in radian
-    * and an \a axis which \b must \b be \b normalized.
-    *
-    * \warning If the \a axis vector is not normalized, then the angle-axis object
-    *          represents an invalid rotation. */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC 
-  inline AngleAxis(const Scalar& angle, const MatrixBase<Derived>& axis) : m_axis(axis), m_angle(angle) {}
-  /** Constructs and initialize the angle-axis rotation from a quaternion \a q.
-    * This function implicitly normalizes the quaternion \a q.
-    */
-  template<typename QuatDerived> 
-  EIGEN_DEVICE_FUNC inline explicit AngleAxis(const QuaternionBase<QuatDerived>& q) { *this = q; }
-  /** Constructs and initialize the angle-axis rotation from a 3x3 rotation matrix. */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline explicit AngleAxis(const MatrixBase<Derived>& m) { *this = m; }
-
-  /** \returns the value of the rotation angle in radian */
-  EIGEN_DEVICE_FUNC Scalar angle() const { return m_angle; }
-  /** \returns a read-write reference to the stored angle in radian */
-  EIGEN_DEVICE_FUNC Scalar& angle() { return m_angle; }
-
-  /** \returns the rotation axis */
-  EIGEN_DEVICE_FUNC const Vector3& axis() const { return m_axis; }
-  /** \returns a read-write reference to the stored rotation axis.
-    *
-    * \warning The rotation axis must remain a \b unit vector.
-    */
-  EIGEN_DEVICE_FUNC Vector3& axis() { return m_axis; }
-
-  /** Concatenates two rotations */
-  EIGEN_DEVICE_FUNC inline QuaternionType operator* (const AngleAxis& other) const
-  { return QuaternionType(*this) * QuaternionType(other); }
-
-  /** Concatenates two rotations */
-  EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& other) const
-  { return QuaternionType(*this) * other; }
-
-  /** Concatenates two rotations */
-  friend EIGEN_DEVICE_FUNC inline QuaternionType operator* (const QuaternionType& a, const AngleAxis& b)
-  { return a * QuaternionType(b); }
-
-  /** \returns the inverse rotation, i.e., an angle-axis with opposite rotation angle */
-  EIGEN_DEVICE_FUNC AngleAxis inverse() const
-  { return AngleAxis(-m_angle, m_axis); }
-
-  template<class QuatDerived>
-  EIGEN_DEVICE_FUNC AngleAxis& operator=(const QuaternionBase<QuatDerived>& q);
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC AngleAxis& operator=(const MatrixBase<Derived>& m);
-
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC AngleAxis& fromRotationMatrix(const MatrixBase<Derived>& m);
-  EIGEN_DEVICE_FUNC Matrix3 toRotationMatrix(void) 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<AngleAxis,AngleAxis<NewScalarType> >::type cast() const
-  { return typename internal::cast_return_type<AngleAxis,AngleAxis<NewScalarType> >::type(*this); }
-
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType>
-  EIGEN_DEVICE_FUNC inline explicit AngleAxis(const AngleAxis<OtherScalarType>& other)
-  {
-    m_axis = other.axis().template cast<Scalar>();
-    m_angle = Scalar(other.angle());
-  }
-
-  EIGEN_DEVICE_FUNC static inline const AngleAxis Identity() { return AngleAxis(Scalar(0), Vector3::UnitX()); }
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  EIGEN_DEVICE_FUNC bool isApprox(const AngleAxis& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
-  { return m_axis.isApprox(other.m_axis, prec) && internal::isApprox(m_angle,other.m_angle, prec); }
-};
-
-/** \ingroup Geometry_Module
-  * single precision angle-axis type */
-typedef AngleAxis<float> AngleAxisf;
-/** \ingroup Geometry_Module
-  * double precision angle-axis type */
-typedef AngleAxis<double> AngleAxisd;
-
-/** Set \c *this from a \b unit quaternion.
-  *
-  * The resulting axis is normalized, and the computed angle is in the [0,pi] range.
-  * 
-  * This function implicitly normalizes the quaternion \a q.
-  */
-template<typename Scalar>
-template<typename QuatDerived>
-EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const QuaternionBase<QuatDerived>& q)
-{
-  EIGEN_USING_STD_MATH(atan2)
-  EIGEN_USING_STD_MATH(abs)
-  Scalar n = q.vec().norm();
-  if(n<NumTraits<Scalar>::epsilon())
-    n = q.vec().stableNorm();
-
-  if (n != Scalar(0))
-  {
-    m_angle = Scalar(2)*atan2(n, abs(q.w()));
-    if(q.w() < Scalar(0))
-      n = -n;
-    m_axis  = q.vec() / n;
-  }
-  else
-  {
-    m_angle = Scalar(0);
-    m_axis << Scalar(1), Scalar(0), Scalar(0);
-  }
-  return *this;
-}
-
-/** Set \c *this from a 3x3 rotation matrix \a mat.
-  */
-template<typename Scalar>
-template<typename Derived>
-EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::operator=(const MatrixBase<Derived>& mat)
-{
-  // Since a direct conversion would not be really faster,
-  // let's use the robust Quaternion implementation:
-  return *this = QuaternionType(mat);
-}
-
-/**
-* \brief Sets \c *this from a 3x3 rotation matrix.
-**/
-template<typename Scalar>
-template<typename Derived>
-EIGEN_DEVICE_FUNC AngleAxis<Scalar>& AngleAxis<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
-{
-  return *this = QuaternionType(mat);
-}
-
-/** Constructs and \returns an equivalent 3x3 rotation matrix.
-  */
-template<typename Scalar>
-typename AngleAxis<Scalar>::Matrix3
-EIGEN_DEVICE_FUNC AngleAxis<Scalar>::toRotationMatrix(void) const
-{
-  EIGEN_USING_STD_MATH(sin)
-  EIGEN_USING_STD_MATH(cos)
-  Matrix3 res;
-  Vector3 sin_axis  = sin(m_angle) * m_axis;
-  Scalar c = cos(m_angle);
-  Vector3 cos1_axis = (Scalar(1)-c) * m_axis;
-
-  Scalar tmp;
-  tmp = cos1_axis.x() * m_axis.y();
-  res.coeffRef(0,1) = tmp - sin_axis.z();
-  res.coeffRef(1,0) = tmp + sin_axis.z();
-
-  tmp = cos1_axis.x() * m_axis.z();
-  res.coeffRef(0,2) = tmp + sin_axis.y();
-  res.coeffRef(2,0) = tmp - sin_axis.y();
-
-  tmp = cos1_axis.y() * m_axis.z();
-  res.coeffRef(1,2) = tmp - sin_axis.x();
-  res.coeffRef(2,1) = tmp + sin_axis.x();
-
-  res.diagonal() = (cos1_axis.cwiseProduct(m_axis)).array() + c;
-
-  return res;
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_ANGLEAXIS_H
diff --git a/eigen/Eigen/src/Geometry/EulerAngles.h b/eigen/Eigen/src/Geometry/EulerAngles.h
deleted file mode 100644
index c633268..0000000
--- a/eigen/Eigen/src/Geometry/EulerAngles.h
+++ /dev/null
@@ -1,114 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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_EULERANGLES_H
-#define EIGEN_EULERANGLES_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  *
-  * \returns the Euler-angles of the rotation matrix \c *this using the convention defined by the triplet (\a a0,\a a1,\a a2)
-  *
-  * Each of the three parameters \a a0,\a a1,\a a2 represents the respective rotation axis as an integer in {0,1,2}.
-  * For instance, in:
-  * \code Vector3f ea = mat.eulerAngles(2, 0, 2); \endcode
-  * "2" represents the z axis and "0" the x axis, etc. The returned angles are such that
-  * we have the following equality:
-  * \code
-  * mat == AngleAxisf(ea[0], Vector3f::UnitZ())
-  *      * AngleAxisf(ea[1], Vector3f::UnitX())
-  *      * AngleAxisf(ea[2], Vector3f::UnitZ()); \endcode
-  * This corresponds to the right-multiply conventions (with right hand side frames).
-  * 
-  * The returned angles are in the ranges [0:pi]x[-pi:pi]x[-pi:pi].
-  * 
-  * \sa class AngleAxis
-  */
-template<typename Derived>
-EIGEN_DEVICE_FUNC inline Matrix<typename MatrixBase<Derived>::Scalar,3,1>
-MatrixBase<Derived>::eulerAngles(Index a0, Index a1, Index a2) const
-{
-  EIGEN_USING_STD_MATH(atan2)
-  EIGEN_USING_STD_MATH(sin)
-  EIGEN_USING_STD_MATH(cos)
-  /* Implemented from Graphics Gems IV */
-  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Derived,3,3)
-
-  Matrix<Scalar,3,1> res;
-  typedef Matrix<typename Derived::Scalar,2,1> Vector2;
-
-  const Index odd = ((a0+1)%3 == a1) ? 0 : 1;
-  const Index i = a0;
-  const Index j = (a0 + 1 + odd)%3;
-  const Index k = (a0 + 2 - odd)%3;
-  
-  if (a0==a2)
-  {
-    res[0] = atan2(coeff(j,i), coeff(k,i));
-    if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0)))
-    {
-      if(res[0] > Scalar(0)) {
-        res[0] -= Scalar(EIGEN_PI);
-      }
-      else {
-        res[0] += Scalar(EIGEN_PI);
-      }
-      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
-      res[1] = -atan2(s2, coeff(i,i));
-    }
-    else
-    {
-      Scalar s2 = Vector2(coeff(j,i), coeff(k,i)).norm();
-      res[1] = atan2(s2, coeff(i,i));
-    }
-    
-    // With a=(0,1,0), we have i=0; j=1; k=2, and after computing the first two angles,
-    // we can compute their respective rotation, and apply its inverse to M. Since the result must
-    // be a rotation around x, we have:
-    //
-    //  c2  s1.s2 c1.s2                   1  0   0 
-    //  0   c1    -s1       *    M    =   0  c3  s3
-    //  -s2 s1.c2 c1.c2                   0 -s3  c3
-    //
-    //  Thus:  m11.c1 - m21.s1 = c3  &   m12.c1 - m22.s1 = s3
-    
-    Scalar s1 = sin(res[0]);
-    Scalar c1 = cos(res[0]);
-    res[2] = atan2(c1*coeff(j,k)-s1*coeff(k,k), c1*coeff(j,j) - s1 * coeff(k,j));
-  } 
-  else
-  {
-    res[0] = atan2(coeff(j,k), coeff(k,k));
-    Scalar c2 = Vector2(coeff(i,i), coeff(i,j)).norm();
-    if((odd && res[0]<Scalar(0)) || ((!odd) && res[0]>Scalar(0))) {
-      if(res[0] > Scalar(0)) {
-        res[0] -= Scalar(EIGEN_PI);
-      }
-      else {
-        res[0] += Scalar(EIGEN_PI);
-      }
-      res[1] = atan2(-coeff(i,k), -c2);
-    }
-    else
-      res[1] = atan2(-coeff(i,k), c2);
-    Scalar s1 = sin(res[0]);
-    Scalar c1 = cos(res[0]);
-    res[2] = atan2(s1*coeff(k,i)-c1*coeff(j,i), c1*coeff(j,j) - s1 * coeff(k,j));
-  }
-  if (!odd)
-    res = -res;
-  
-  return res;
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_EULERANGLES_H
diff --git a/eigen/Eigen/src/Geometry/Homogeneous.h b/eigen/Eigen/src/Geometry/Homogeneous.h
deleted file mode 100644
index 5f0da1a..0000000
--- a/eigen/Eigen/src/Geometry/Homogeneous.h
+++ /dev/null
@@ -1,497 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.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_HOMOGENEOUS_H
-#define EIGEN_HOMOGENEOUS_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class Homogeneous
-  *
-  * \brief Expression of one (or a set of) homogeneous vector(s)
-  *
-  * \param MatrixType the type of the object in which we are making homogeneous
-  *
-  * This class represents an expression of one (or a set of) homogeneous vector(s).
-  * It is the return type of MatrixBase::homogeneous() and most of the time
-  * this is the only way it is used.
-  *
-  * \sa MatrixBase::homogeneous()
-  */
-
-namespace internal {
-
-template<typename MatrixType,int Direction>
-struct traits<Homogeneous<MatrixType,Direction> >
- : traits<MatrixType>
-{
-  typedef typename traits<MatrixType>::StorageKind StorageKind;
-  typedef typename ref_selector<MatrixType>::type MatrixTypeNested;
-  typedef typename remove_reference<MatrixTypeNested>::type _MatrixTypeNested;
-  enum {
-    RowsPlusOne = (MatrixType::RowsAtCompileTime != Dynamic) ?
-                  int(MatrixType::RowsAtCompileTime) + 1 : Dynamic,
-    ColsPlusOne = (MatrixType::ColsAtCompileTime != Dynamic) ?
-                  int(MatrixType::ColsAtCompileTime) + 1 : Dynamic,
-    RowsAtCompileTime = Direction==Vertical  ?  RowsPlusOne : MatrixType::RowsAtCompileTime,
-    ColsAtCompileTime = Direction==Horizontal ? ColsPlusOne : MatrixType::ColsAtCompileTime,
-    MaxRowsAtCompileTime = RowsAtCompileTime,
-    MaxColsAtCompileTime = ColsAtCompileTime,
-    TmpFlags = _MatrixTypeNested::Flags & HereditaryBits,
-    Flags = ColsAtCompileTime==1 ? (TmpFlags & ~RowMajorBit)
-          : RowsAtCompileTime==1 ? (TmpFlags | RowMajorBit)
-          : TmpFlags
-  };
-};
-
-template<typename MatrixType,typename Lhs> struct homogeneous_left_product_impl;
-template<typename MatrixType,typename Rhs> struct homogeneous_right_product_impl;
-
-} // end namespace internal
-
-template<typename MatrixType,int _Direction> class Homogeneous
-  : public MatrixBase<Homogeneous<MatrixType,_Direction> >, internal::no_assignment_operator
-{
-  public:
-
-    typedef MatrixType NestedExpression;
-    enum { Direction = _Direction };
-
-    typedef MatrixBase<Homogeneous> Base;
-    EIGEN_DENSE_PUBLIC_INTERFACE(Homogeneous)
-
-    EIGEN_DEVICE_FUNC explicit inline Homogeneous(const MatrixType& matrix)
-      : m_matrix(matrix)
-    {}
-
-    EIGEN_DEVICE_FUNC inline Index rows() const { return m_matrix.rows() + (int(Direction)==Vertical   ? 1 : 0); }
-    EIGEN_DEVICE_FUNC inline Index cols() const { return m_matrix.cols() + (int(Direction)==Horizontal ? 1 : 0); }
-    
-    EIGEN_DEVICE_FUNC const NestedExpression& nestedExpression() const { return m_matrix; }
-
-    template<typename Rhs>
-    EIGEN_DEVICE_FUNC inline const Product<Homogeneous,Rhs>
-    operator* (const MatrixBase<Rhs>& rhs) const
-    {
-      eigen_assert(int(Direction)==Horizontal);
-      return Product<Homogeneous,Rhs>(*this,rhs.derived());
-    }
-
-    template<typename Lhs> friend
-    EIGEN_DEVICE_FUNC inline const Product<Lhs,Homogeneous>
-    operator* (const MatrixBase<Lhs>& lhs, const Homogeneous& rhs)
-    {
-      eigen_assert(int(Direction)==Vertical);
-      return Product<Lhs,Homogeneous>(lhs.derived(),rhs);
-    }
-
-    template<typename Scalar, int Dim, int Mode, int Options> friend
-    EIGEN_DEVICE_FUNC inline const Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous >
-    operator* (const Transform<Scalar,Dim,Mode,Options>& lhs, const Homogeneous& rhs)
-    {
-      eigen_assert(int(Direction)==Vertical);
-      return Product<Transform<Scalar,Dim,Mode,Options>, Homogeneous>(lhs,rhs);
-    }
-
-    template<typename Func>
-    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::result_of<Func(Scalar,Scalar)>::type
-    redux(const Func& func) const
-    {
-      return func(m_matrix.redux(func), Scalar(1));
-    }
-
-  protected:
-    typename MatrixType::Nested m_matrix;
-};
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \returns a vector expression that is one longer than the vector argument, with the value 1 symbolically appended as the last coefficient.
-  *
-  * This can be used to convert affine coordinates to homogeneous coordinates.
-  *
-  * \only_for_vectors
-  *
-  * Example: \include MatrixBase_homogeneous.cpp
-  * Output: \verbinclude MatrixBase_homogeneous.out
-  *
-  * \sa VectorwiseOp::homogeneous(), class Homogeneous
-  */
-template<typename Derived>
-EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::HomogeneousReturnType
-MatrixBase<Derived>::homogeneous() const
-{
-  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
-  return HomogeneousReturnType(derived());
-}
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \returns an expression where the value 1 is symbolically appended as the final coefficient to each column (or row) of the matrix.
-  *
-  * This can be used to convert affine coordinates to homogeneous coordinates.
-  *
-  * Example: \include VectorwiseOp_homogeneous.cpp
-  * Output: \verbinclude VectorwiseOp_homogeneous.out
-  *
-  * \sa MatrixBase::homogeneous(), class Homogeneous */
-template<typename ExpressionType, int Direction>
-EIGEN_DEVICE_FUNC inline Homogeneous<ExpressionType,Direction>
-VectorwiseOp<ExpressionType,Direction>::homogeneous() const
-{
-  return HomogeneousReturnType(_expression());
-}
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \brief homogeneous normalization
-  *
-  * \returns a vector expression of the N-1 first coefficients of \c *this divided by that last coefficient.
-  *
-  * This can be used to convert homogeneous coordinates to affine coordinates.
-  *
-  * It is essentially a shortcut for:
-  * \code
-    this->head(this->size()-1)/this->coeff(this->size()-1);
-    \endcode
-  *
-  * Example: \include MatrixBase_hnormalized.cpp
-  * Output: \verbinclude MatrixBase_hnormalized.out
-  *
-  * \sa VectorwiseOp::hnormalized() */
-template<typename Derived>
-EIGEN_DEVICE_FUNC inline const typename MatrixBase<Derived>::HNormalizedReturnType
-MatrixBase<Derived>::hnormalized() const
-{
-  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived);
-  return ConstStartMinusOne(derived(),0,0,
-    ColsAtCompileTime==1?size()-1:1,
-    ColsAtCompileTime==1?1:size()-1) / coeff(size()-1);
-}
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \brief column or row-wise homogeneous normalization
-  *
-  * \returns an expression of the first N-1 coefficients of each column (or row) of \c *this divided by the last coefficient of each column (or row).
-  *
-  * This can be used to convert homogeneous coordinates to affine coordinates.
-  *
-  * It is conceptually equivalent to calling MatrixBase::hnormalized() to each column (or row) of \c *this.
-  *
-  * Example: \include DirectionWise_hnormalized.cpp
-  * Output: \verbinclude DirectionWise_hnormalized.out
-  *
-  * \sa MatrixBase::hnormalized() */
-template<typename ExpressionType, int Direction>
-EIGEN_DEVICE_FUNC inline const typename VectorwiseOp<ExpressionType,Direction>::HNormalizedReturnType
-VectorwiseOp<ExpressionType,Direction>::hnormalized() const
-{
-  return HNormalized_Block(_expression(),0,0,
-      Direction==Vertical   ? _expression().rows()-1 : _expression().rows(),
-      Direction==Horizontal ? _expression().cols()-1 : _expression().cols()).cwiseQuotient(
-      Replicate<HNormalized_Factors,
-                Direction==Vertical   ? HNormalized_SizeMinusOne : 1,
-                Direction==Horizontal ? HNormalized_SizeMinusOne : 1>
-        (HNormalized_Factors(_expression(),
-          Direction==Vertical    ? _expression().rows()-1:0,
-          Direction==Horizontal  ? _expression().cols()-1:0,
-          Direction==Vertical    ? 1 : _expression().rows(),
-          Direction==Horizontal  ? 1 : _expression().cols()),
-         Direction==Vertical   ? _expression().rows()-1 : 1,
-         Direction==Horizontal ? _expression().cols()-1 : 1));
-}
-
-namespace internal {
-
-template<typename MatrixOrTransformType>
-struct take_matrix_for_product
-{
-  typedef MatrixOrTransformType type;
-  EIGEN_DEVICE_FUNC static const type& run(const type &x) { return x; }
-};
-
-template<typename Scalar, int Dim, int Mode,int Options>
-struct take_matrix_for_product<Transform<Scalar, Dim, Mode, Options> >
-{
-  typedef Transform<Scalar, Dim, Mode, Options> TransformType;
-  typedef typename internal::add_const<typename TransformType::ConstAffinePart>::type type;
-  EIGEN_DEVICE_FUNC static type run (const TransformType& x) { return x.affine(); }
-};
-
-template<typename Scalar, int Dim, int Options>
-struct take_matrix_for_product<Transform<Scalar, Dim, Projective, Options> >
-{
-  typedef Transform<Scalar, Dim, Projective, Options> TransformType;
-  typedef typename TransformType::MatrixType type;
-  EIGEN_DEVICE_FUNC static const type& run (const TransformType& x) { return x.matrix(); }
-};
-
-template<typename MatrixType,typename Lhs>
-struct traits<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
-{
-  typedef typename take_matrix_for_product<Lhs>::type LhsMatrixType;
-  typedef typename remove_all<MatrixType>::type MatrixTypeCleaned;
-  typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
-  typedef typename make_proper_matrix_type<
-                 typename traits<MatrixTypeCleaned>::Scalar,
-                 LhsMatrixTypeCleaned::RowsAtCompileTime,
-                 MatrixTypeCleaned::ColsAtCompileTime,
-                 MatrixTypeCleaned::PlainObject::Options,
-                 LhsMatrixTypeCleaned::MaxRowsAtCompileTime,
-                 MatrixTypeCleaned::MaxColsAtCompileTime>::type ReturnType;
-};
-
-template<typename MatrixType,typename Lhs>
-struct homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs>
-  : public ReturnByValue<homogeneous_left_product_impl<Homogeneous<MatrixType,Vertical>,Lhs> >
-{
-  typedef typename traits<homogeneous_left_product_impl>::LhsMatrixType LhsMatrixType;
-  typedef typename remove_all<LhsMatrixType>::type LhsMatrixTypeCleaned;
-  typedef typename remove_all<typename LhsMatrixTypeCleaned::Nested>::type LhsMatrixTypeNested;
-  EIGEN_DEVICE_FUNC homogeneous_left_product_impl(const Lhs& lhs, const MatrixType& rhs)
-    : m_lhs(take_matrix_for_product<Lhs>::run(lhs)),
-      m_rhs(rhs)
-  {}
-
-  EIGEN_DEVICE_FUNC inline Index rows() const { return m_lhs.rows(); }
-  EIGEN_DEVICE_FUNC inline Index cols() const { return m_rhs.cols(); }
-
-  template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
-  {
-    // FIXME investigate how to allow lazy evaluation of this product when possible
-    dst = Block<const LhsMatrixTypeNested,
-              LhsMatrixTypeNested::RowsAtCompileTime,
-              LhsMatrixTypeNested::ColsAtCompileTime==Dynamic?Dynamic:LhsMatrixTypeNested::ColsAtCompileTime-1>
-            (m_lhs,0,0,m_lhs.rows(),m_lhs.cols()-1) * m_rhs;
-    dst += m_lhs.col(m_lhs.cols()-1).rowwise()
-            .template replicate<MatrixType::ColsAtCompileTime>(m_rhs.cols());
-  }
-
-  typename LhsMatrixTypeCleaned::Nested m_lhs;
-  typename MatrixType::Nested m_rhs;
-};
-
-template<typename MatrixType,typename Rhs>
-struct traits<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
-{
-  typedef typename make_proper_matrix_type<typename traits<MatrixType>::Scalar,
-                 MatrixType::RowsAtCompileTime,
-                 Rhs::ColsAtCompileTime,
-                 MatrixType::PlainObject::Options,
-                 MatrixType::MaxRowsAtCompileTime,
-                 Rhs::MaxColsAtCompileTime>::type ReturnType;
-};
-
-template<typename MatrixType,typename Rhs>
-struct homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs>
-  : public ReturnByValue<homogeneous_right_product_impl<Homogeneous<MatrixType,Horizontal>,Rhs> >
-{
-  typedef typename remove_all<typename Rhs::Nested>::type RhsNested;
-  EIGEN_DEVICE_FUNC homogeneous_right_product_impl(const MatrixType& lhs, const Rhs& rhs)
-    : m_lhs(lhs), m_rhs(rhs)
-  {}
-
-  EIGEN_DEVICE_FUNC inline Index rows() const { return m_lhs.rows(); }
-  EIGEN_DEVICE_FUNC inline Index cols() const { return m_rhs.cols(); }
-
-  template<typename Dest> EIGEN_DEVICE_FUNC void evalTo(Dest& dst) const
-  {
-    // FIXME investigate how to allow lazy evaluation of this product when possible
-    dst = m_lhs * Block<const RhsNested,
-                        RhsNested::RowsAtCompileTime==Dynamic?Dynamic:RhsNested::RowsAtCompileTime-1,
-                        RhsNested::ColsAtCompileTime>
-            (m_rhs,0,0,m_rhs.rows()-1,m_rhs.cols());
-    dst += m_rhs.row(m_rhs.rows()-1).colwise()
-            .template replicate<MatrixType::RowsAtCompileTime>(m_lhs.rows());
-  }
-
-  typename MatrixType::Nested m_lhs;
-  typename Rhs::Nested m_rhs;
-};
-
-template<typename ArgType,int Direction>
-struct evaluator_traits<Homogeneous<ArgType,Direction> >
-{
-  typedef typename storage_kind_to_evaluator_kind<typename ArgType::StorageKind>::Kind Kind;
-  typedef HomogeneousShape Shape;  
-};
-
-template<> struct AssignmentKind<DenseShape,HomogeneousShape> { typedef Dense2Dense Kind; };
-
-
-template<typename ArgType,int Direction>
-struct unary_evaluator<Homogeneous<ArgType,Direction>, IndexBased>
-  : evaluator<typename Homogeneous<ArgType,Direction>::PlainObject >
-{
-  typedef Homogeneous<ArgType,Direction> XprType;
-  typedef typename XprType::PlainObject PlainObject;
-  typedef evaluator<PlainObject> Base;
-
-  EIGEN_DEVICE_FUNC explicit unary_evaluator(const XprType& op)
-    : Base(), m_temp(op)
-  {
-    ::new (static_cast<Base*>(this)) Base(m_temp);
-  }
-
-protected:
-  PlainObject m_temp;
-};
-
-// dense = homogeneous
-template< typename DstXprType, typename ArgType, typename Scalar>
-struct Assignment<DstXprType, Homogeneous<ArgType,Vertical>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
-{
-  typedef Homogeneous<ArgType,Vertical> SrcXprType;
-  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
-  {
-    Index dstRows = src.rows();
-    Index dstCols = src.cols();
-    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
-      dst.resize(dstRows, dstCols);
-
-    dst.template topRows<ArgType::RowsAtCompileTime>(src.nestedExpression().rows()) = src.nestedExpression();
-    dst.row(dst.rows()-1).setOnes();
-  }
-};
-
-// dense = homogeneous
-template< typename DstXprType, typename ArgType, typename Scalar>
-struct Assignment<DstXprType, Homogeneous<ArgType,Horizontal>, internal::assign_op<Scalar,typename ArgType::Scalar>, Dense2Dense>
-{
-  typedef Homogeneous<ArgType,Horizontal> SrcXprType;
-  EIGEN_DEVICE_FUNC static void run(DstXprType &dst, const SrcXprType &src, const internal::assign_op<Scalar,typename ArgType::Scalar> &)
-  {
-    Index dstRows = src.rows();
-    Index dstCols = src.cols();
-    if((dst.rows()!=dstRows) || (dst.cols()!=dstCols))
-      dst.resize(dstRows, dstCols);
-
-    dst.template leftCols<ArgType::ColsAtCompileTime>(src.nestedExpression().cols()) = src.nestedExpression();
-    dst.col(dst.cols()-1).setOnes();
-  }
-};
-
-template<typename LhsArg, typename Rhs, int ProductTag>
-struct generic_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs, HomogeneousShape, DenseShape, ProductTag>
-{
-  template<typename Dest>
-  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Homogeneous<LhsArg,Horizontal>& lhs, const Rhs& rhs)
-  {
-    homogeneous_right_product_impl<Homogeneous<LhsArg,Horizontal>, Rhs>(lhs.nestedExpression(), rhs).evalTo(dst);
-  }
-};
-
-template<typename Lhs,typename Rhs>
-struct homogeneous_right_product_refactoring_helper
-{
-  enum {
-    Dim  = Lhs::ColsAtCompileTime,
-    Rows = Lhs::RowsAtCompileTime
-  };
-  typedef typename Rhs::template ConstNRowsBlockXpr<Dim>::Type          LinearBlockConst;
-  typedef typename remove_const<LinearBlockConst>::type                 LinearBlock;
-  typedef typename Rhs::ConstRowXpr                                     ConstantColumn;
-  typedef Replicate<const ConstantColumn,Rows,1>                        ConstantBlock;
-  typedef Product<Lhs,LinearBlock,LazyProduct>                          LinearProduct;
-  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
-};
-
-template<typename Lhs, typename Rhs, int ProductTag>
-struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, HomogeneousShape, DenseShape>
- : public evaluator<typename homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs>::Xpr>
-{
-  typedef Product<Lhs, Rhs, LazyProduct> XprType;
-  typedef homogeneous_right_product_refactoring_helper<typename Lhs::NestedExpression,Rhs> helper;
-  typedef typename helper::ConstantBlock ConstantBlock;
-  typedef typename helper::Xpr RefactoredXpr;
-  typedef evaluator<RefactoredXpr> Base;
-  
-  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
-    : Base(  xpr.lhs().nestedExpression() .lazyProduct(  xpr.rhs().template topRows<helper::Dim>(xpr.lhs().nestedExpression().cols()) )
-            + ConstantBlock(xpr.rhs().row(xpr.rhs().rows()-1),xpr.lhs().rows(), 1) )
-  {}
-};
-
-template<typename Lhs, typename RhsArg, int ProductTag>
-struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
-{
-  template<typename Dest>
-  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
-  {
-    homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, Lhs>(lhs, rhs.nestedExpression()).evalTo(dst);
-  }
-};
-
-// TODO: the following specialization is to address a regression from 3.2 to 3.3
-// In the future, this path should be optimized.
-template<typename Lhs, typename RhsArg, int ProductTag>
-struct generic_product_impl<Lhs, Homogeneous<RhsArg,Vertical>, TriangularShape, HomogeneousShape, ProductTag>
-{
-  template<typename Dest>
-  static void evalTo(Dest& dst, const Lhs& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
-  {
-    dst.noalias() = lhs * rhs.eval();
-  }
-};
-
-template<typename Lhs,typename Rhs>
-struct homogeneous_left_product_refactoring_helper
-{
-  enum {
-    Dim = Rhs::RowsAtCompileTime,
-    Cols = Rhs::ColsAtCompileTime
-  };
-  typedef typename Lhs::template ConstNColsBlockXpr<Dim>::Type          LinearBlockConst;
-  typedef typename remove_const<LinearBlockConst>::type                 LinearBlock;
-  typedef typename Lhs::ConstColXpr                                     ConstantColumn;
-  typedef Replicate<const ConstantColumn,1,Cols>                        ConstantBlock;
-  typedef Product<LinearBlock,Rhs,LazyProduct>                          LinearProduct;
-  typedef CwiseBinaryOp<internal::scalar_sum_op<typename Lhs::Scalar,typename Rhs::Scalar>, const LinearProduct, const ConstantBlock> Xpr;
-};
-
-template<typename Lhs, typename Rhs, int ProductTag>
-struct product_evaluator<Product<Lhs, Rhs, LazyProduct>, ProductTag, DenseShape, HomogeneousShape>
- : public evaluator<typename homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression>::Xpr>
-{
-  typedef Product<Lhs, Rhs, LazyProduct> XprType;
-  typedef homogeneous_left_product_refactoring_helper<Lhs,typename Rhs::NestedExpression> helper;
-  typedef typename helper::ConstantBlock ConstantBlock;
-  typedef typename helper::Xpr RefactoredXpr;
-  typedef evaluator<RefactoredXpr> Base;
-  
-  EIGEN_DEVICE_FUNC explicit product_evaluator(const XprType& xpr)
-    : Base(   xpr.lhs().template leftCols<helper::Dim>(xpr.rhs().nestedExpression().rows()) .lazyProduct( xpr.rhs().nestedExpression() )
-            + ConstantBlock(xpr.lhs().col(xpr.lhs().cols()-1),1,xpr.rhs().cols()) )
-  {}
-};
-
-template<typename Scalar, int Dim, int Mode,int Options, typename RhsArg, int ProductTag>
-struct generic_product_impl<Transform<Scalar,Dim,Mode,Options>, Homogeneous<RhsArg,Vertical>, DenseShape, HomogeneousShape, ProductTag>
-{
-  typedef Transform<Scalar,Dim,Mode,Options> TransformType;
-  template<typename Dest>
-  EIGEN_DEVICE_FUNC static void evalTo(Dest& dst, const TransformType& lhs, const Homogeneous<RhsArg,Vertical>& rhs)
-  {
-    homogeneous_left_product_impl<Homogeneous<RhsArg,Vertical>, TransformType>(lhs, rhs.nestedExpression()).evalTo(dst);
-  }
-};
-
-template<typename ExpressionType, int Side, bool Transposed>
-struct permutation_matrix_product<ExpressionType, Side, Transposed, HomogeneousShape>
-  : public permutation_matrix_product<ExpressionType, Side, Transposed, DenseShape>
-{};
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_HOMOGENEOUS_H
diff --git a/eigen/Eigen/src/Geometry/Hyperplane.h b/eigen/Eigen/src/Geometry/Hyperplane.h
deleted file mode 100644
index 05929b2..0000000
--- a/eigen/Eigen/src/Geometry/Hyperplane.h
+++ /dev/null
@@ -1,282 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// 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_HYPERPLANE_H
-#define EIGEN_HYPERPLANE_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class Hyperplane
-  *
-  * \brief A hyperplane
-  *
-  * A hyperplane is an affine subspace of dimension n-1 in a space of dimension n.
-  * For example, a hyperplane in a plane is a line; a hyperplane in 3-space is a plane.
-  *
-  * \tparam _Scalar the scalar type, i.e., the type of the coefficients
-  * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
-  *             Notice that the dimension of the hyperplane is _AmbientDim-1.
-  *
-  * This class represents an hyperplane as the zero set of the implicit equation
-  * \f$ n \cdot x + d = 0 \f$ where \f$ n \f$ is a unit normal vector of the plane (linear part)
-  * and \f$ d \f$ is the distance (offset) to the origin.
-  */
-template <typename _Scalar, int _AmbientDim, int _Options>
-class Hyperplane
-{
-public:
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim==Dynamic ? Dynamic : _AmbientDim+1)
-  enum {
-    AmbientDimAtCompileTime = _AmbientDim,
-    Options = _Options
-  };
-  typedef _Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
-  typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
-  typedef Matrix<Scalar,AmbientDimAtCompileTime,1> VectorType;
-  typedef Matrix<Scalar,Index(AmbientDimAtCompileTime)==Dynamic
-                        ? Dynamic
-                        : Index(AmbientDimAtCompileTime)+1,1,Options> Coefficients;
-  typedef Block<Coefficients,AmbientDimAtCompileTime,1> NormalReturnType;
-  typedef const Block<const Coefficients,AmbientDimAtCompileTime,1> ConstNormalReturnType;
-
-  /** Default constructor without initialization */
-  EIGEN_DEVICE_FUNC inline Hyperplane() {}
-  
-  template<int OtherOptions>
-  EIGEN_DEVICE_FUNC Hyperplane(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)
-   : m_coeffs(other.coeffs())
-  {}
-
-  /** Constructs a dynamic-size hyperplane with \a _dim the dimension
-    * of the ambient space */
-  EIGEN_DEVICE_FUNC inline explicit Hyperplane(Index _dim) : m_coeffs(_dim+1) {}
-
-  /** Construct a plane from its normal \a n and a point \a e onto the plane.
-    * \warning the vector normal is assumed to be normalized.
-    */
-  EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const VectorType& e)
-    : m_coeffs(n.size()+1)
-  {
-    normal() = n;
-    offset() = -n.dot(e);
-  }
-
-  /** Constructs a plane from its normal \a n and distance to the origin \a d
-    * such that the algebraic equation of the plane is \f$ n \cdot x + d = 0 \f$.
-    * \warning the vector normal is assumed to be normalized.
-    */
-  EIGEN_DEVICE_FUNC inline Hyperplane(const VectorType& n, const Scalar& d)
-    : m_coeffs(n.size()+1)
-  {
-    normal() = n;
-    offset() = d;
-  }
-
-  /** Constructs a hyperplane passing through the two points. If the dimension of the ambient space
-    * is greater than 2, then there isn't uniqueness, so an arbitrary choice is made.
-    */
-  EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1)
-  {
-    Hyperplane result(p0.size());
-    result.normal() = (p1 - p0).unitOrthogonal();
-    result.offset() = -p0.dot(result.normal());
-    return result;
-  }
-
-  /** Constructs a hyperplane passing through the three points. The dimension of the ambient space
-    * is required to be exactly 3.
-    */
-  EIGEN_DEVICE_FUNC static inline Hyperplane Through(const VectorType& p0, const VectorType& p1, const VectorType& p2)
-  {
-    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 3)
-    Hyperplane result(p0.size());
-    VectorType v0(p2 - p0), v1(p1 - p0);
-    result.normal() = v0.cross(v1);
-    RealScalar norm = result.normal().norm();
-    if(norm <= v0.norm() * v1.norm() * NumTraits<RealScalar>::epsilon())
-    {
-      Matrix<Scalar,2,3> m; m << v0.transpose(), v1.transpose();
-      JacobiSVD<Matrix<Scalar,2,3> > svd(m, ComputeFullV);
-      result.normal() = svd.matrixV().col(2);
-    }
-    else
-      result.normal() /= norm;
-    result.offset() = -p0.dot(result.normal());
-    return result;
-  }
-
-  /** Constructs a hyperplane passing through the parametrized line \a parametrized.
-    * If the dimension of the ambient space is greater than 2, then there isn't uniqueness,
-    * so an arbitrary choice is made.
-    */
-  // FIXME to be consitent with the rest this could be implemented as a static Through function ??
-  EIGEN_DEVICE_FUNC explicit Hyperplane(const ParametrizedLine<Scalar, AmbientDimAtCompileTime>& parametrized)
-  {
-    normal() = parametrized.direction().unitOrthogonal();
-    offset() = -parametrized.origin().dot(normal());
-  }
-
-  EIGEN_DEVICE_FUNC ~Hyperplane() {}
-
-  /** \returns the dimension in which the plane holds */
-  EIGEN_DEVICE_FUNC inline Index dim() const { return AmbientDimAtCompileTime==Dynamic ? m_coeffs.size()-1 : Index(AmbientDimAtCompileTime); }
-
-  /** normalizes \c *this */
-  EIGEN_DEVICE_FUNC void normalize(void)
-  {
-    m_coeffs /= normal().norm();
-  }
-
-  /** \returns the signed distance between the plane \c *this and a point \a p.
-    * \sa absDistance()
-    */
-  EIGEN_DEVICE_FUNC inline Scalar signedDistance(const VectorType& p) const { return normal().dot(p) + offset(); }
-
-  /** \returns the absolute distance between the plane \c *this and a point \a p.
-    * \sa signedDistance()
-    */
-  EIGEN_DEVICE_FUNC inline Scalar absDistance(const VectorType& p) const { return numext::abs(signedDistance(p)); }
-
-  /** \returns the projection of a point \a p onto the plane \c *this.
-    */
-  EIGEN_DEVICE_FUNC inline VectorType projection(const VectorType& p) const { return p - signedDistance(p) * normal(); }
-
-  /** \returns a constant reference to the unit normal vector of the plane, which corresponds
-    * to the linear part of the implicit equation.
-    */
-  EIGEN_DEVICE_FUNC inline ConstNormalReturnType normal() const { return ConstNormalReturnType(m_coeffs,0,0,dim(),1); }
-
-  /** \returns a non-constant reference to the unit normal vector of the plane, which corresponds
-    * to the linear part of the implicit equation.
-    */
-  EIGEN_DEVICE_FUNC inline NormalReturnType normal() { return NormalReturnType(m_coeffs,0,0,dim(),1); }
-
-  /** \returns the distance to the origin, which is also the "constant term" of the implicit equation
-    * \warning the vector normal is assumed to be normalized.
-    */
-  EIGEN_DEVICE_FUNC inline const Scalar& offset() const { return m_coeffs.coeff(dim()); }
-
-  /** \returns a non-constant reference to the distance to the origin, which is also the constant part
-    * of the implicit equation */
-  EIGEN_DEVICE_FUNC inline Scalar& offset() { return m_coeffs(dim()); }
-
-  /** \returns a constant reference to the coefficients c_i of the plane equation:
-    * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
-    */
-  EIGEN_DEVICE_FUNC inline const Coefficients& coeffs() const { return m_coeffs; }
-
-  /** \returns a non-constant reference to the coefficients c_i of the plane equation:
-    * \f$ c_0*x_0 + ... + c_{d-1}*x_{d-1} + c_d = 0 \f$
-    */
-  EIGEN_DEVICE_FUNC inline Coefficients& coeffs() { return m_coeffs; }
-
-  /** \returns the intersection of *this with \a other.
-    *
-    * \warning The ambient space must be a plane, i.e. have dimension 2, so that \c *this and \a other are lines.
-    *
-    * \note If \a other is approximately parallel to *this, this method will return any point on *this.
-    */
-  EIGEN_DEVICE_FUNC VectorType intersection(const Hyperplane& other) const
-  {
-    EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
-    Scalar det = coeffs().coeff(0) * other.coeffs().coeff(1) - coeffs().coeff(1) * other.coeffs().coeff(0);
-    // since the line equations ax+by=c are normalized with a^2+b^2=1, the following tests
-    // whether the two lines are approximately parallel.
-    if(internal::isMuchSmallerThan(det, Scalar(1)))
-    {   // special case where the two lines are approximately parallel. Pick any point on the first line.
-        if(numext::abs(coeffs().coeff(1))>numext::abs(coeffs().coeff(0)))
-            return VectorType(coeffs().coeff(1), -coeffs().coeff(2)/coeffs().coeff(1)-coeffs().coeff(0));
-        else
-            return VectorType(-coeffs().coeff(2)/coeffs().coeff(0)-coeffs().coeff(1), coeffs().coeff(0));
-    }
-    else
-    {   // general case
-        Scalar invdet = Scalar(1) / det;
-        return VectorType(invdet*(coeffs().coeff(1)*other.coeffs().coeff(2)-other.coeffs().coeff(1)*coeffs().coeff(2)),
-                          invdet*(other.coeffs().coeff(0)*coeffs().coeff(2)-coeffs().coeff(0)*other.coeffs().coeff(2)));
-    }
-  }
-
-  /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
-    *
-    * \param mat the Dim x Dim transformation matrix
-    * \param traits specifies whether the matrix \a mat represents an #Isometry
-    *               or a more generic #Affine transformation. The default is #Affine.
-    */
-  template<typename XprType>
-  EIGEN_DEVICE_FUNC inline Hyperplane& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
-  {
-    if (traits==Affine)
-    {
-      normal() = mat.inverse().transpose() * normal();
-      m_coeffs /= normal().norm();
-    }
-    else if (traits==Isometry)
-      normal() = mat * normal();
-    else
-    {
-      eigen_assert(0 && "invalid traits value in Hyperplane::transform()");
-    }
-    return *this;
-  }
-
-  /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
-    *
-    * \param t the transformation of dimension Dim
-    * \param traits specifies whether the transformation \a t represents an #Isometry
-    *               or a more generic #Affine transformation. The default is #Affine.
-    *               Other kind of transformations are not supported.
-    */
-  template<int TrOptions>
-  EIGEN_DEVICE_FUNC inline Hyperplane& transform(const Transform<Scalar,AmbientDimAtCompileTime,Affine,TrOptions>& t,
-                                TransformTraits traits = Affine)
-  {
-    transform(t.linear(), traits);
-    offset() -= normal().dot(t.translation());
-    return *this;
-  }
-
-  /** \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<Hyperplane,
-           Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
-  {
-    return typename internal::cast_return_type<Hyperplane,
-                    Hyperplane<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
-  }
-
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType,int OtherOptions>
-  EIGEN_DEVICE_FUNC inline explicit Hyperplane(const Hyperplane<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
-  { m_coeffs = other.coeffs().template cast<Scalar>(); }
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  template<int OtherOptions>
-  EIGEN_DEVICE_FUNC bool isApprox(const Hyperplane<Scalar,AmbientDimAtCompileTime,OtherOptions>& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
-  { return m_coeffs.isApprox(other.m_coeffs, prec); }
-
-protected:
-
-  Coefficients m_coeffs;
-};
-
-} // end namespace Eigen
-
-#endif // EIGEN_HYPERPLANE_H
diff --git a/eigen/Eigen/src/Geometry/OrthoMethods.h b/eigen/Eigen/src/Geometry/OrthoMethods.h
deleted file mode 100644
index a035e63..0000000
--- a/eigen/Eigen/src/Geometry/OrthoMethods.h
+++ /dev/null
@@ -1,234 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2006-2008 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// 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_ORTHOMETHODS_H
-#define EIGEN_ORTHOMETHODS_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \returns the cross product of \c *this and \a other
-  *
-  * Here is a very good explanation of cross-product: http://xkcd.com/199/
-  * 
-  * With complex numbers, the cross product is implemented as
-  * \f$ (\mathbf{a}+i\mathbf{b}) \times (\mathbf{c}+i\mathbf{d}) = (\mathbf{a} \times \mathbf{c} - \mathbf{b} \times \mathbf{d}) - i(\mathbf{a} \times \mathbf{d} - \mathbf{b} \times \mathbf{c})\f$
-  * 
-  * \sa MatrixBase::cross3()
-  */
-template<typename Derived>
-template<typename OtherDerived>
-#ifndef EIGEN_PARSED_BY_DOXYGEN
-EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::template cross_product_return_type<OtherDerived>::type
-#else
-inline typename MatrixBase<Derived>::PlainObject
-#endif
-MatrixBase<Derived>::cross(const MatrixBase<OtherDerived>& other) const
-{
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,3)
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
-
-  // Note that there is no need for an expression here since the compiler
-  // optimize such a small temporary very well (even within a complex expression)
-  typename internal::nested_eval<Derived,2>::type lhs(derived());
-  typename internal::nested_eval<OtherDerived,2>::type rhs(other.derived());
-  return typename cross_product_return_type<OtherDerived>::type(
-    numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
-    numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
-    numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0))
-  );
-}
-
-namespace internal {
-
-template< int Arch,typename VectorLhs,typename VectorRhs,
-          typename Scalar = typename VectorLhs::Scalar,
-          bool Vectorizable = bool((VectorLhs::Flags&VectorRhs::Flags)&PacketAccessBit)>
-struct cross3_impl {
-  EIGEN_DEVICE_FUNC static inline typename internal::plain_matrix_type<VectorLhs>::type
-  run(const VectorLhs& lhs, const VectorRhs& rhs)
-  {
-    return typename internal::plain_matrix_type<VectorLhs>::type(
-      numext::conj(lhs.coeff(1) * rhs.coeff(2) - lhs.coeff(2) * rhs.coeff(1)),
-      numext::conj(lhs.coeff(2) * rhs.coeff(0) - lhs.coeff(0) * rhs.coeff(2)),
-      numext::conj(lhs.coeff(0) * rhs.coeff(1) - lhs.coeff(1) * rhs.coeff(0)),
-      0
-    );
-  }
-};
-
-}
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \returns the cross product of \c *this and \a other using only the x, y, and z coefficients
-  *
-  * The size of \c *this and \a other must be four. This function is especially useful
-  * when using 4D vectors instead of 3D ones to get advantage of SSE/AltiVec vectorization.
-  *
-  * \sa MatrixBase::cross()
-  */
-template<typename Derived>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC inline typename MatrixBase<Derived>::PlainObject
-MatrixBase<Derived>::cross3(const MatrixBase<OtherDerived>& other) const
-{
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(Derived,4)
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,4)
-
-  typedef typename internal::nested_eval<Derived,2>::type DerivedNested;
-  typedef typename internal::nested_eval<OtherDerived,2>::type OtherDerivedNested;
-  DerivedNested lhs(derived());
-  OtherDerivedNested rhs(other.derived());
-
-  return internal::cross3_impl<Architecture::Target,
-                        typename internal::remove_all<DerivedNested>::type,
-                        typename internal::remove_all<OtherDerivedNested>::type>::run(lhs,rhs);
-}
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \returns a matrix expression of the cross product of each column or row
-  * of the referenced expression with the \a other vector.
-  *
-  * The referenced matrix must have one dimension equal to 3.
-  * The result matrix has the same dimensions than the referenced one.
-  *
-  * \sa MatrixBase::cross() */
-template<typename ExpressionType, int Direction>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC 
-const typename VectorwiseOp<ExpressionType,Direction>::CrossReturnType
-VectorwiseOp<ExpressionType,Direction>::cross(const MatrixBase<OtherDerived>& other) const
-{
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,3)
-  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename OtherDerived::Scalar>::value),
-    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
-  
-  typename internal::nested_eval<ExpressionType,2>::type mat(_expression());
-  typename internal::nested_eval<OtherDerived,2>::type vec(other.derived());
-
-  CrossReturnType res(_expression().rows(),_expression().cols());
-  if(Direction==Vertical)
-  {
-    eigen_assert(CrossReturnType::RowsAtCompileTime==3 && "the matrix must have exactly 3 rows");
-    res.row(0) = (mat.row(1) * vec.coeff(2) - mat.row(2) * vec.coeff(1)).conjugate();
-    res.row(1) = (mat.row(2) * vec.coeff(0) - mat.row(0) * vec.coeff(2)).conjugate();
-    res.row(2) = (mat.row(0) * vec.coeff(1) - mat.row(1) * vec.coeff(0)).conjugate();
-  }
-  else
-  {
-    eigen_assert(CrossReturnType::ColsAtCompileTime==3 && "the matrix must have exactly 3 columns");
-    res.col(0) = (mat.col(1) * vec.coeff(2) - mat.col(2) * vec.coeff(1)).conjugate();
-    res.col(1) = (mat.col(2) * vec.coeff(0) - mat.col(0) * vec.coeff(2)).conjugate();
-    res.col(2) = (mat.col(0) * vec.coeff(1) - mat.col(1) * vec.coeff(0)).conjugate();
-  }
-  return res;
-}
-
-namespace internal {
-
-template<typename Derived, int Size = Derived::SizeAtCompileTime>
-struct unitOrthogonal_selector
-{
-  typedef typename plain_matrix_type<Derived>::type VectorType;
-  typedef typename traits<Derived>::Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
-  typedef Matrix<Scalar,2,1> Vector2;
-  EIGEN_DEVICE_FUNC
-  static inline VectorType run(const Derived& src)
-  {
-    VectorType perp = VectorType::Zero(src.size());
-    Index maxi = 0;
-    Index sndi = 0;
-    src.cwiseAbs().maxCoeff(&maxi);
-    if (maxi==0)
-      sndi = 1;
-    RealScalar invnm = RealScalar(1)/(Vector2() << src.coeff(sndi),src.coeff(maxi)).finished().norm();
-    perp.coeffRef(maxi) = -numext::conj(src.coeff(sndi)) * invnm;
-    perp.coeffRef(sndi) =  numext::conj(src.coeff(maxi)) * invnm;
-
-    return perp;
-   }
-};
-
-template<typename Derived>
-struct unitOrthogonal_selector<Derived,3>
-{
-  typedef typename plain_matrix_type<Derived>::type VectorType;
-  typedef typename traits<Derived>::Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
-  EIGEN_DEVICE_FUNC
-  static inline VectorType run(const Derived& src)
-  {
-    VectorType perp;
-    /* Let us compute the crossed product of *this with a vector
-     * that is not too close to being colinear to *this.
-     */
-
-    /* unless the x and y coords are both close to zero, we can
-     * simply take ( -y, x, 0 ) and normalize it.
-     */
-    if((!isMuchSmallerThan(src.x(), src.z()))
-    || (!isMuchSmallerThan(src.y(), src.z())))
-    {
-      RealScalar invnm = RealScalar(1)/src.template head<2>().norm();
-      perp.coeffRef(0) = -numext::conj(src.y())*invnm;
-      perp.coeffRef(1) = numext::conj(src.x())*invnm;
-      perp.coeffRef(2) = 0;
-    }
-    /* if both x and y are close to zero, then the vector is close
-     * to the z-axis, so it's far from colinear to the x-axis for instance.
-     * So we take the crossed product with (1,0,0) and normalize it.
-     */
-    else
-    {
-      RealScalar invnm = RealScalar(1)/src.template tail<2>().norm();
-      perp.coeffRef(0) = 0;
-      perp.coeffRef(1) = -numext::conj(src.z())*invnm;
-      perp.coeffRef(2) = numext::conj(src.y())*invnm;
-    }
-
-    return perp;
-   }
-};
-
-template<typename Derived>
-struct unitOrthogonal_selector<Derived,2>
-{
-  typedef typename plain_matrix_type<Derived>::type VectorType;
-  EIGEN_DEVICE_FUNC
-  static inline VectorType run(const Derived& src)
-  { return VectorType(-numext::conj(src.y()), numext::conj(src.x())).normalized(); }
-};
-
-} // end namespace internal
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \returns a unit vector which is orthogonal to \c *this
-  *
-  * The size of \c *this must be at least 2. If the size is exactly 2,
-  * then the returned vector is a counter clock wise rotation of \c *this, i.e., (-y,x).normalized().
-  *
-  * \sa cross()
-  */
-template<typename Derived>
-EIGEN_DEVICE_FUNC typename MatrixBase<Derived>::PlainObject
-MatrixBase<Derived>::unitOrthogonal() const
-{
-  EIGEN_STATIC_ASSERT_VECTOR_ONLY(Derived)
-  return internal::unitOrthogonal_selector<Derived>::run(derived());
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_ORTHOMETHODS_H
diff --git a/eigen/Eigen/src/Geometry/ParametrizedLine.h b/eigen/Eigen/src/Geometry/ParametrizedLine.h
deleted file mode 100644
index 1e985d8..0000000
--- a/eigen/Eigen/src/Geometry/ParametrizedLine.h
+++ /dev/null
@@ -1,195 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
-//
-// 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_PARAMETRIZEDLINE_H
-#define EIGEN_PARAMETRIZEDLINE_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class ParametrizedLine
-  *
-  * \brief A parametrized line
-  *
-  * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit
-  * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to
-  * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$.
-  *
-  * \tparam _Scalar the scalar type, i.e., the type of the coefficients
-  * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic.
-  */
-template <typename _Scalar, int _AmbientDim, int _Options>
-class ParametrizedLine
-{
-public:
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim)
-  enum {
-    AmbientDimAtCompileTime = _AmbientDim,
-    Options = _Options
-  };
-  typedef _Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
-  typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
-  typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType;
-
-  /** Default constructor without initialization */
-  EIGEN_DEVICE_FUNC inline ParametrizedLine() {}
-  
-  template<int OtherOptions>
-  EIGEN_DEVICE_FUNC ParametrizedLine(const ParametrizedLine<Scalar,AmbientDimAtCompileTime,OtherOptions>& other)
-   : m_origin(other.origin()), m_direction(other.direction())
-  {}
-
-  /** Constructs a dynamic-size line with \a _dim the dimension
-    * of the ambient space */
-  EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {}
-
-  /** Initializes a parametrized line of direction \a direction and origin \a origin.
-    * \warning the vector direction is assumed to be normalized.
-    */
-  EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction)
-    : m_origin(origin), m_direction(direction) {}
-
-  template <int OtherOptions>
-  EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);
-
-  /** Constructs a parametrized line going from \a p0 to \a p1. */
-  EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
-  { return ParametrizedLine(p0, (p1-p0).normalized()); }
-
-  EIGEN_DEVICE_FUNC ~ParametrizedLine() {}
-
-  /** \returns the dimension in which the line holds */
-  EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); }
-
-  EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; }
-  EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; }
-
-  EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; }
-  EIGEN_DEVICE_FUNC VectorType& direction() { return m_direction; }
-
-  /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
-    * \sa distance()
-    */
-  EIGEN_DEVICE_FUNC RealScalar squaredDistance(const VectorType& p) const
-  {
-    VectorType diff = p - origin();
-    return (diff - direction().dot(diff) * direction()).squaredNorm();
-  }
-  /** \returns the distance of a point \a p to its projection onto the line \c *this.
-    * \sa squaredDistance()
-    */
-  EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const { EIGEN_USING_STD_MATH(sqrt) return sqrt(squaredDistance(p)); }
-
-  /** \returns the projection of a point \a p onto the line \c *this. */
-  EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const
-  { return origin() + direction().dot(p-origin()) * direction(); }
-
-  EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const;
-  
-  template <int OtherOptions>
-  EIGEN_DEVICE_FUNC Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
- 
-  template <int OtherOptions>
-  EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
-  
-  template <int OtherOptions>
-  EIGEN_DEVICE_FUNC VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) 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<ParametrizedLine,
-           ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
-  {
-    return typename internal::cast_return_type<ParametrizedLine,
-                    ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
-  }
-
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType,int OtherOptions>
-  EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
-  {
-    m_origin = other.origin().template cast<Scalar>();
-    m_direction = other.direction().template cast<Scalar>();
-  }
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  EIGEN_DEVICE_FUNC bool isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
-  { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
-
-protected:
-
-  VectorType m_origin, m_direction;
-};
-
-/** Constructs a parametrized line from a 2D hyperplane
-  *
-  * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
-  */
-template <typename _Scalar, int _AmbientDim, int _Options>
-template <int OtherOptions>
-EIGEN_DEVICE_FUNC inline ParametrizedLine<_Scalar, _AmbientDim,_Options>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim,OtherOptions>& hyperplane)
-{
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
-  direction() = hyperplane.normal().unitOrthogonal();
-  origin() = -hyperplane.normal()*hyperplane.offset();
-}
-
-/** \returns the point at \a t along this line
-  */
-template <typename _Scalar, int _AmbientDim, int _Options>
-EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
-ParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt(const _Scalar& t) const
-{
-  return origin() + (direction()*t); 
-}
-
-/** \returns the parameter value of the intersection between \c *this and the given \a hyperplane
-  */
-template <typename _Scalar, int _AmbientDim, int _Options>
-template <int OtherOptions>
-EIGEN_DEVICE_FUNC inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
-{
-  return -(hyperplane.offset()+hyperplane.normal().dot(origin()))
-          / hyperplane.normal().dot(direction());
-}
-
-
-/** \deprecated use intersectionParameter()
-  * \returns the parameter value of the intersection between \c *this and the given \a hyperplane
-  */
-template <typename _Scalar, int _AmbientDim, int _Options>
-template <int OtherOptions>
-EIGEN_DEVICE_FUNC inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
-{
-  return intersectionParameter(hyperplane);
-}
-
-/** \returns the point of the intersection between \c *this and the given hyperplane
-  */
-template <typename _Scalar, int _AmbientDim, int _Options>
-template <int OtherOptions>
-EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
-ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
-{
-  return pointAt(intersectionParameter(hyperplane));
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_PARAMETRIZEDLINE_H
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
diff --git a/eigen/Eigen/src/Geometry/Rotation2D.h b/eigen/Eigen/src/Geometry/Rotation2D.h
deleted file mode 100644
index 884b7d0..0000000
--- a/eigen/Eigen/src/Geometry/Rotation2D.h
+++ /dev/null
@@ -1,199 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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_ROTATION2D_H
-#define EIGEN_ROTATION2D_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class Rotation2D
-  *
-  * \brief Represents a rotation/orientation in a 2 dimensional space.
-  *
-  * \tparam _Scalar the scalar type, i.e., the type of the coefficients
-  *
-  * This class is equivalent to a single scalar representing a counter clock wise rotation
-  * as a single angle in radian. It provides some additional features such as the automatic
-  * conversion from/to a 2x2 rotation matrix. Moreover this class aims to provide a similar
-  * interface to Quaternion in order to facilitate the writing of generic algorithms
-  * dealing with rotations.
-  *
-  * \sa class Quaternion, class Transform
-  */
-
-namespace internal {
-
-template<typename _Scalar> struct traits<Rotation2D<_Scalar> >
-{
-  typedef _Scalar Scalar;
-};
-} // end namespace internal
-
-template<typename _Scalar>
-class Rotation2D : public RotationBase<Rotation2D<_Scalar>,2>
-{
-  typedef RotationBase<Rotation2D<_Scalar>,2> Base;
-
-public:
-
-  using Base::operator*;
-
-  enum { Dim = 2 };
-  /** the scalar type of the coefficients */
-  typedef _Scalar Scalar;
-  typedef Matrix<Scalar,2,1> Vector2;
-  typedef Matrix<Scalar,2,2> Matrix2;
-
-protected:
-
-  Scalar m_angle;
-
-public:
-
-  /** Construct a 2D counter clock wise rotation from the angle \a a in radian. */
-  EIGEN_DEVICE_FUNC explicit inline Rotation2D(const Scalar& a) : m_angle(a) {}
-  
-  /** Default constructor wihtout initialization. The represented rotation is undefined. */
-  EIGEN_DEVICE_FUNC Rotation2D() {}
-
-  /** Construct a 2D rotation from a 2x2 rotation matrix \a mat.
-    *
-    * \sa fromRotationMatrix()
-    */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC explicit Rotation2D(const MatrixBase<Derived>& m)
-  {
-    fromRotationMatrix(m.derived());
-  }
-
-  /** \returns the rotation angle */
-  EIGEN_DEVICE_FUNC inline Scalar angle() const { return m_angle; }
-
-  /** \returns a read-write reference to the rotation angle */
-  EIGEN_DEVICE_FUNC inline Scalar& angle() { return m_angle; }
-  
-  /** \returns the rotation angle in [0,2pi] */
-  EIGEN_DEVICE_FUNC inline Scalar smallestPositiveAngle() const {
-    Scalar tmp = numext::fmod(m_angle,Scalar(2*EIGEN_PI));
-    return tmp<Scalar(0) ? tmp + Scalar(2*EIGEN_PI) : tmp;
-  }
-  
-  /** \returns the rotation angle in [-pi,pi] */
-  EIGEN_DEVICE_FUNC inline Scalar smallestAngle() const {
-    Scalar tmp = numext::fmod(m_angle,Scalar(2*EIGEN_PI));
-    if(tmp>Scalar(EIGEN_PI))       tmp -= Scalar(2*EIGEN_PI);
-    else if(tmp<-Scalar(EIGEN_PI)) tmp += Scalar(2*EIGEN_PI);
-    return tmp;
-  }
-
-  /** \returns the inverse rotation */
-  EIGEN_DEVICE_FUNC inline Rotation2D inverse() const { return Rotation2D(-m_angle); }
-
-  /** Concatenates two rotations */
-  EIGEN_DEVICE_FUNC inline Rotation2D operator*(const Rotation2D& other) const
-  { return Rotation2D(m_angle + other.m_angle); }
-
-  /** Concatenates two rotations */
-  EIGEN_DEVICE_FUNC inline Rotation2D& operator*=(const Rotation2D& other)
-  { m_angle += other.m_angle; return *this; }
-
-  /** Applies the rotation to a 2D vector */
-  EIGEN_DEVICE_FUNC Vector2 operator* (const Vector2& vec) const
-  { return toRotationMatrix() * vec; }
-  
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC Rotation2D& fromRotationMatrix(const MatrixBase<Derived>& m);
-  EIGEN_DEVICE_FUNC Matrix2 toRotationMatrix() const;
-
-  /** Set \c *this from a 2x2 rotation matrix \a mat.
-    * In other words, this function extract the rotation angle from the rotation matrix.
-    *
-    * This method is an alias for fromRotationMatrix()
-    *
-    * \sa fromRotationMatrix()
-    */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC Rotation2D& operator=(const  MatrixBase<Derived>& m)
-  { return fromRotationMatrix(m.derived()); }
-
-  /** \returns the spherical interpolation between \c *this and \a other using
-    * parameter \a t. It is in fact equivalent to a linear interpolation.
-    */
-  EIGEN_DEVICE_FUNC inline Rotation2D slerp(const Scalar& t, const Rotation2D& other) const
-  {
-    Scalar dist = Rotation2D(other.m_angle-m_angle).smallestAngle();
-    return Rotation2D(m_angle + dist*t);
-  }
-
-  /** \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<Rotation2D,Rotation2D<NewScalarType> >::type cast() const
-  { return typename internal::cast_return_type<Rotation2D,Rotation2D<NewScalarType> >::type(*this); }
-
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType>
-  EIGEN_DEVICE_FUNC inline explicit Rotation2D(const Rotation2D<OtherScalarType>& other)
-  {
-    m_angle = Scalar(other.angle());
-  }
-
-  EIGEN_DEVICE_FUNC static inline Rotation2D Identity() { return Rotation2D(0); }
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  EIGEN_DEVICE_FUNC bool isApprox(const Rotation2D& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
-  { return internal::isApprox(m_angle,other.m_angle, prec); }
-  
-};
-
-/** \ingroup Geometry_Module
-  * single precision 2D rotation type */
-typedef Rotation2D<float> Rotation2Df;
-/** \ingroup Geometry_Module
-  * double precision 2D rotation type */
-typedef Rotation2D<double> Rotation2Dd;
-
-/** Set \c *this from a 2x2 rotation matrix \a mat.
-  * In other words, this function extract the rotation angle
-  * from the rotation matrix.
-  */
-template<typename Scalar>
-template<typename Derived>
-EIGEN_DEVICE_FUNC Rotation2D<Scalar>& Rotation2D<Scalar>::fromRotationMatrix(const MatrixBase<Derived>& mat)
-{
-  EIGEN_USING_STD_MATH(atan2)
-  EIGEN_STATIC_ASSERT(Derived::RowsAtCompileTime==2 && Derived::ColsAtCompileTime==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
-  m_angle = atan2(mat.coeff(1,0), mat.coeff(0,0));
-  return *this;
-}
-
-/** Constructs and \returns an equivalent 2x2 rotation matrix.
-  */
-template<typename Scalar>
-typename Rotation2D<Scalar>::Matrix2
-EIGEN_DEVICE_FUNC Rotation2D<Scalar>::toRotationMatrix(void) const
-{
-  EIGEN_USING_STD_MATH(sin)
-  EIGEN_USING_STD_MATH(cos)
-  Scalar sinA = sin(m_angle);
-  Scalar cosA = cos(m_angle);
-  return (Matrix2() << cosA, -sinA, sinA, cosA).finished();
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_ROTATION2D_H
diff --git a/eigen/Eigen/src/Geometry/RotationBase.h b/eigen/Eigen/src/Geometry/RotationBase.h
deleted file mode 100644
index f0ee0bd..0000000
--- a/eigen/Eigen/src/Geometry/RotationBase.h
+++ /dev/null
@@ -1,206 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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_ROTATIONBASE_H
-#define EIGEN_ROTATIONBASE_H
-
-namespace Eigen { 
-
-// forward declaration
-namespace internal {
-template<typename RotationDerived, typename MatrixType, bool IsVector=MatrixType::IsVectorAtCompileTime>
-struct rotation_base_generic_product_selector;
-}
-
-/** \class RotationBase
-  *
-  * \brief Common base class for compact rotation representations
-  *
-  * \tparam Derived is the derived type, i.e., a rotation type
-  * \tparam _Dim the dimension of the space
-  */
-template<typename Derived, int _Dim>
-class RotationBase
-{
-  public:
-    enum { Dim = _Dim };
-    /** the scalar type of the coefficients */
-    typedef typename internal::traits<Derived>::Scalar Scalar;
-
-    /** corresponding linear transformation matrix type */
-    typedef Matrix<Scalar,Dim,Dim> RotationMatrixType;
-    typedef Matrix<Scalar,Dim,1> VectorType;
-
-  public:
-    EIGEN_DEVICE_FUNC inline const Derived& derived() const { return *static_cast<const Derived*>(this); }
-    EIGEN_DEVICE_FUNC inline Derived& derived() { return *static_cast<Derived*>(this); }
-
-    /** \returns an equivalent rotation matrix */
-    EIGEN_DEVICE_FUNC inline RotationMatrixType toRotationMatrix() const { return derived().toRotationMatrix(); }
-
-    /** \returns an equivalent rotation matrix 
-      * This function is added to be conform with the Transform class' naming scheme.
-      */
-    EIGEN_DEVICE_FUNC inline RotationMatrixType matrix() const { return derived().toRotationMatrix(); }
-
-    /** \returns the inverse rotation */
-    EIGEN_DEVICE_FUNC inline Derived inverse() const { return derived().inverse(); }
-
-    /** \returns the concatenation of the rotation \c *this with a translation \a t */
-    EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Isometry> operator*(const Translation<Scalar,Dim>& t) const
-    { return Transform<Scalar,Dim,Isometry>(*this) * t; }
-
-    /** \returns the concatenation of the rotation \c *this with a uniform scaling \a s */
-    EIGEN_DEVICE_FUNC inline RotationMatrixType operator*(const UniformScaling<Scalar>& s) const
-    { return toRotationMatrix() * s.factor(); }
-
-    /** \returns the concatenation of the rotation \c *this with a generic expression \a e
-      * \a e can be:
-      *  - a DimxDim linear transformation matrix
-      *  - a DimxDim diagonal matrix (axis aligned scaling)
-      *  - a vector of size Dim
-      */
-    template<typename OtherDerived>
-    EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE typename internal::rotation_base_generic_product_selector<Derived,OtherDerived,OtherDerived::IsVectorAtCompileTime>::ReturnType
-    operator*(const EigenBase<OtherDerived>& e) const
-    { return internal::rotation_base_generic_product_selector<Derived,OtherDerived>::run(derived(), e.derived()); }
-
-    /** \returns the concatenation of a linear transformation \a l with the rotation \a r */
-    template<typename OtherDerived> friend
-    EIGEN_DEVICE_FUNC inline RotationMatrixType operator*(const EigenBase<OtherDerived>& l, const Derived& r)
-    { return l.derived() * r.toRotationMatrix(); }
-
-    /** \returns the concatenation of a scaling \a l with the rotation \a r */
-    EIGEN_DEVICE_FUNC friend inline Transform<Scalar,Dim,Affine> operator*(const DiagonalMatrix<Scalar,Dim>& l, const Derived& r)
-    { 
-      Transform<Scalar,Dim,Affine> res(r);
-      res.linear().applyOnTheLeft(l);
-      return res;
-    }
-
-    /** \returns the concatenation of the rotation \c *this with a transformation \a t */
-    template<int Mode, int Options>
-    EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode> operator*(const Transform<Scalar,Dim,Mode,Options>& t) const
-    { return toRotationMatrix() * t; }
-
-    template<typename OtherVectorType>
-    EIGEN_DEVICE_FUNC inline VectorType _transformVector(const OtherVectorType& v) const
-    { return toRotationMatrix() * v; }
-};
-
-namespace internal {
-
-// implementation of the generic product rotation * matrix
-template<typename RotationDerived, typename MatrixType>
-struct rotation_base_generic_product_selector<RotationDerived,MatrixType,false>
-{
-  enum { Dim = RotationDerived::Dim };
-  typedef Matrix<typename RotationDerived::Scalar,Dim,Dim> ReturnType;
-  EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r, const MatrixType& m)
-  { return r.toRotationMatrix() * m; }
-};
-
-template<typename RotationDerived, typename Scalar, int Dim, int MaxDim>
-struct rotation_base_generic_product_selector< RotationDerived, DiagonalMatrix<Scalar,Dim,MaxDim>, false >
-{
-  typedef Transform<Scalar,Dim,Affine> ReturnType;
-  EIGEN_DEVICE_FUNC static inline ReturnType run(const RotationDerived& r, const DiagonalMatrix<Scalar,Dim,MaxDim>& m)
-  {
-    ReturnType res(r);
-    res.linear() *= m;
-    return res;
-  }
-};
-
-template<typename RotationDerived,typename OtherVectorType>
-struct rotation_base_generic_product_selector<RotationDerived,OtherVectorType,true>
-{
-  enum { Dim = RotationDerived::Dim };
-  typedef Matrix<typename RotationDerived::Scalar,Dim,1> ReturnType;
-  EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE ReturnType run(const RotationDerived& r, const OtherVectorType& v)
-  {
-    return r._transformVector(v);
-  }
-};
-
-} // end namespace internal
-
-/** \geometry_module
-  *
-  * \brief Constructs a Dim x Dim rotation matrix from the rotation \a r
-  */
-template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
-::Matrix(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
-{
-  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
-  *this = r.toRotationMatrix();
-}
-
-/** \geometry_module
-  *
-  * \brief Set a Dim x Dim rotation matrix from the rotation \a r
-  */
-template<typename _Scalar, int _Rows, int _Cols, int _Storage, int _MaxRows, int _MaxCols>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>&
-Matrix<_Scalar, _Rows, _Cols, _Storage, _MaxRows, _MaxCols>
-::operator=(const RotationBase<OtherDerived,ColsAtCompileTime>& r)
-{
-  EIGEN_STATIC_ASSERT_MATRIX_SPECIFIC_SIZE(Matrix,int(OtherDerived::Dim),int(OtherDerived::Dim))
-  return *this = r.toRotationMatrix();
-}
-
-namespace internal {
-
-/** \internal
-  *
-  * Helper function to return an arbitrary rotation object to a rotation matrix.
-  *
-  * \tparam Scalar the numeric type of the matrix coefficients
-  * \tparam Dim the dimension of the current space
-  *
-  * It returns a Dim x Dim fixed size matrix.
-  *
-  * Default specializations are provided for:
-  *   - any scalar type (2D),
-  *   - any matrix expression,
-  *   - any type based on RotationBase (e.g., Quaternion, AngleAxis, Rotation2D)
-  *
-  * Currently toRotationMatrix is only used by Transform.
-  *
-  * \sa class Transform, class Rotation2D, class Quaternion, class AngleAxis
-  */
-template<typename Scalar, int Dim>
-EIGEN_DEVICE_FUNC static inline Matrix<Scalar,2,2> toRotationMatrix(const Scalar& s)
-{
-  EIGEN_STATIC_ASSERT(Dim==2,YOU_MADE_A_PROGRAMMING_MISTAKE)
-  return Rotation2D<Scalar>(s).toRotationMatrix();
-}
-
-template<typename Scalar, int Dim, typename OtherDerived>
-EIGEN_DEVICE_FUNC static inline Matrix<Scalar,Dim,Dim> toRotationMatrix(const RotationBase<OtherDerived,Dim>& r)
-{
-  return r.toRotationMatrix();
-}
-
-template<typename Scalar, int Dim, typename OtherDerived>
-EIGEN_DEVICE_FUNC static inline const MatrixBase<OtherDerived>& toRotationMatrix(const MatrixBase<OtherDerived>& mat)
-{
-  EIGEN_STATIC_ASSERT(OtherDerived::RowsAtCompileTime==Dim && OtherDerived::ColsAtCompileTime==Dim,
-    YOU_MADE_A_PROGRAMMING_MISTAKE)
-  return mat;
-}
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_ROTATIONBASE_H
diff --git a/eigen/Eigen/src/Geometry/Scaling.h b/eigen/Eigen/src/Geometry/Scaling.h
deleted file mode 100644
index f58ca03..0000000
--- a/eigen/Eigen/src/Geometry/Scaling.h
+++ /dev/null
@@ -1,170 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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_SCALING_H
-#define EIGEN_SCALING_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class Scaling
-  *
-  * \brief Represents a generic uniform scaling transformation
-  *
-  * \tparam _Scalar the scalar type, i.e., the type of the coefficients.
-  *
-  * This class represent a uniform scaling transformation. It is the return
-  * type of Scaling(Scalar), and most of the time this is the only way it
-  * is used. In particular, this class is not aimed to be used to store a scaling transformation,
-  * but rather to make easier the constructions and updates of Transform objects.
-  *
-  * To represent an axis aligned scaling, use the DiagonalMatrix class.
-  *
-  * \sa Scaling(), class DiagonalMatrix, MatrixBase::asDiagonal(), class Translation, class Transform
-  */
-template<typename _Scalar>
-class UniformScaling
-{
-public:
-  /** the scalar type of the coefficients */
-  typedef _Scalar Scalar;
-
-protected:
-
-  Scalar m_factor;
-
-public:
-
-  /** Default constructor without initialization. */
-  UniformScaling() {}
-  /** Constructs and initialize a uniform scaling transformation */
-  explicit inline UniformScaling(const Scalar& s) : m_factor(s) {}
-
-  inline const Scalar& factor() const { return m_factor; }
-  inline Scalar& factor() { return m_factor; }
-
-  /** Concatenates two uniform scaling */
-  inline UniformScaling operator* (const UniformScaling& other) const
-  { return UniformScaling(m_factor * other.factor()); }
-
-  /** Concatenates a uniform scaling and a translation */
-  template<int Dim>
-  inline Transform<Scalar,Dim,Affine> operator* (const Translation<Scalar,Dim>& t) const;
-
-  /** Concatenates a uniform scaling and an affine transformation */
-  template<int Dim, int Mode, int Options>
-  inline Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Mode)> operator* (const Transform<Scalar,Dim, Mode, Options>& t) const
-  {
-    Transform<Scalar,Dim,(int(Mode)==int(Isometry)?Affine:Mode)> res = t;
-    res.prescale(factor());
-    return res;
-  }
-
-  /** Concatenates a uniform scaling and a linear transformation matrix */
-  // TODO returns an expression
-  template<typename Derived>
-  inline typename internal::plain_matrix_type<Derived>::type operator* (const MatrixBase<Derived>& other) const
-  { return other * m_factor; }
-
-  template<typename Derived,int Dim>
-  inline Matrix<Scalar,Dim,Dim> operator*(const RotationBase<Derived,Dim>& r) const
-  { return r.toRotationMatrix() * m_factor; }
-
-  /** \returns the inverse scaling */
-  inline UniformScaling inverse() const
-  { return UniformScaling(Scalar(1)/m_factor); }
-
-  /** \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>
-  inline UniformScaling<NewScalarType> cast() const
-  { return UniformScaling<NewScalarType>(NewScalarType(m_factor)); }
-
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType>
-  inline explicit UniformScaling(const UniformScaling<OtherScalarType>& other)
-  { m_factor = Scalar(other.factor()); }
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  bool isApprox(const UniformScaling& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
-  { return internal::isApprox(m_factor, other.factor(), prec); }
-
-};
-
-/** \addtogroup Geometry_Module */
-//@{
-
-/** Concatenates a linear transformation matrix and a uniform scaling
-  * \relates UniformScaling
-  */
-// NOTE this operator is defiend in MatrixBase and not as a friend function
-// of UniformScaling to fix an internal crash of Intel's ICC
-template<typename Derived,typename Scalar>
-EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(Derived,Scalar,product)
-operator*(const MatrixBase<Derived>& matrix, const UniformScaling<Scalar>& s)
-{ return matrix.derived() * s.factor(); }
-
-/** Constructs a uniform scaling from scale factor \a s */
-inline UniformScaling<float> Scaling(float s) { return UniformScaling<float>(s); }
-/** Constructs a uniform scaling from scale factor \a s */
-inline UniformScaling<double> Scaling(double s) { return UniformScaling<double>(s); }
-/** Constructs a uniform scaling from scale factor \a s */
-template<typename RealScalar>
-inline UniformScaling<std::complex<RealScalar> > Scaling(const std::complex<RealScalar>& s)
-{ return UniformScaling<std::complex<RealScalar> >(s); }
-
-/** Constructs a 2D axis aligned scaling */
-template<typename Scalar>
-inline DiagonalMatrix<Scalar,2> Scaling(const Scalar& sx, const Scalar& sy)
-{ return DiagonalMatrix<Scalar,2>(sx, sy); }
-/** Constructs a 3D axis aligned scaling */
-template<typename Scalar>
-inline DiagonalMatrix<Scalar,3> Scaling(const Scalar& sx, const Scalar& sy, const Scalar& sz)
-{ return DiagonalMatrix<Scalar,3>(sx, sy, sz); }
-
-/** Constructs an axis aligned scaling expression from vector expression \a coeffs
-  * This is an alias for coeffs.asDiagonal()
-  */
-template<typename Derived>
-inline const DiagonalWrapper<const Derived> Scaling(const MatrixBase<Derived>& coeffs)
-{ return coeffs.asDiagonal(); }
-
-/** \deprecated */
-typedef DiagonalMatrix<float, 2> AlignedScaling2f;
-/** \deprecated */
-typedef DiagonalMatrix<double,2> AlignedScaling2d;
-/** \deprecated */
-typedef DiagonalMatrix<float, 3> AlignedScaling3f;
-/** \deprecated */
-typedef DiagonalMatrix<double,3> AlignedScaling3d;
-//@}
-
-template<typename Scalar>
-template<int Dim>
-inline Transform<Scalar,Dim,Affine>
-UniformScaling<Scalar>::operator* (const Translation<Scalar,Dim>& t) const
-{
-  Transform<Scalar,Dim,Affine> res;
-  res.matrix().setZero();
-  res.linear().diagonal().fill(factor());
-  res.translation() = factor() * t.vector();
-  res(Dim,Dim) = Scalar(1);
-  return res;
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_SCALING_H
diff --git a/eigen/Eigen/src/Geometry/Transform.h b/eigen/Eigen/src/Geometry/Transform.h
deleted file mode 100644
index 3f31ee4..0000000
--- a/eigen/Eigen/src/Geometry/Transform.h
+++ /dev/null
@@ -1,1542 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
-// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
-// Copyright (C) 2010 Hauke Heibel <hauke.heibel@gmail.com>
-//
-// 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_TRANSFORM_H
-#define EIGEN_TRANSFORM_H
-
-namespace Eigen { 
-
-namespace internal {
-
-template<typename Transform>
-struct transform_traits
-{
-  enum
-  {
-    Dim = Transform::Dim,
-    HDim = Transform::HDim,
-    Mode = Transform::Mode,
-    IsProjective = (int(Mode)==int(Projective))
-  };
-};
-
-template< typename TransformType,
-          typename MatrixType,
-          int Case = transform_traits<TransformType>::IsProjective ? 0
-                   : int(MatrixType::RowsAtCompileTime) == int(transform_traits<TransformType>::HDim) ? 1
-                   : 2,
-          int RhsCols = MatrixType::ColsAtCompileTime>
-struct transform_right_product_impl;
-
-template< typename Other,
-          int Mode,
-          int Options,
-          int Dim,
-          int HDim,
-          int OtherRows=Other::RowsAtCompileTime,
-          int OtherCols=Other::ColsAtCompileTime>
-struct transform_left_product_impl;
-
-template< typename Lhs,
-          typename Rhs,
-          bool AnyProjective = 
-            transform_traits<Lhs>::IsProjective ||
-            transform_traits<Rhs>::IsProjective>
-struct transform_transform_product_impl;
-
-template< typename Other,
-          int Mode,
-          int Options,
-          int Dim,
-          int HDim,
-          int OtherRows=Other::RowsAtCompileTime,
-          int OtherCols=Other::ColsAtCompileTime>
-struct transform_construct_from_matrix;
-
-template<typename TransformType> struct transform_take_affine_part;
-
-template<typename _Scalar, int _Dim, int _Mode, int _Options>
-struct traits<Transform<_Scalar,_Dim,_Mode,_Options> >
-{
-  typedef _Scalar Scalar;
-  typedef Eigen::Index StorageIndex;
-  typedef Dense StorageKind;
-  enum {
-    Dim1 = _Dim==Dynamic ? _Dim : _Dim + 1,
-    RowsAtCompileTime = _Mode==Projective ? Dim1 : _Dim,
-    ColsAtCompileTime = Dim1,
-    MaxRowsAtCompileTime = RowsAtCompileTime,
-    MaxColsAtCompileTime = ColsAtCompileTime,
-    Flags = 0
-  };
-};
-
-template<int Mode> struct transform_make_affine;
-
-} // end namespace internal
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class Transform
-  *
-  * \brief Represents an homogeneous transformation in a N dimensional space
-  *
-  * \tparam _Scalar the scalar type, i.e., the type of the coefficients
-  * \tparam _Dim the dimension of the space
-  * \tparam _Mode the type of the transformation. Can be:
-  *              - #Affine: the transformation is stored as a (Dim+1)^2 matrix,
-  *                         where the last row is assumed to be [0 ... 0 1].
-  *              - #AffineCompact: the transformation is stored as a (Dim)x(Dim+1) matrix.
-  *              - #Projective: the transformation is stored as a (Dim+1)^2 matrix
-  *                             without any assumption.
-  * \tparam _Options has the same meaning as in class Matrix. It allows to specify DontAlign and/or RowMajor.
-  *                  These Options are passed directly to the underlying matrix type.
-  *
-  * The homography is internally represented and stored by a matrix which
-  * is available through the matrix() method. To understand the behavior of
-  * this class you have to think a Transform object as its internal
-  * matrix representation. The chosen convention is right multiply:
-  *
-  * \code v' = T * v \endcode
-  *
-  * Therefore, an affine transformation matrix M is shaped like this:
-  *
-  * \f$ \left( \begin{array}{cc}
-  * linear & translation\\
-  * 0 ... 0 & 1
-  * \end{array} \right) \f$
-  *
-  * Note that for a projective transformation the last row can be anything,
-  * and then the interpretation of different parts might be sightly different.
-  *
-  * However, unlike a plain matrix, the Transform class provides many features
-  * simplifying both its assembly and usage. In particular, it can be composed
-  * with any other transformations (Transform,Translation,RotationBase,DiagonalMatrix)
-  * and can be directly used to transform implicit homogeneous vectors. All these
-  * operations are handled via the operator*. For the composition of transformations,
-  * its principle consists to first convert the right/left hand sides of the product
-  * to a compatible (Dim+1)^2 matrix and then perform a pure matrix product.
-  * Of course, internally, operator* tries to perform the minimal number of operations
-  * according to the nature of each terms. Likewise, when applying the transform
-  * to points, the latters are automatically promoted to homogeneous vectors
-  * before doing the matrix product. The conventions to homogeneous representations
-  * are performed as follow:
-  *
-  * \b Translation t (Dim)x(1):
-  * \f$ \left( \begin{array}{cc}
-  * I & t \\
-  * 0\,...\,0 & 1
-  * \end{array} \right) \f$
-  *
-  * \b Rotation R (Dim)x(Dim):
-  * \f$ \left( \begin{array}{cc}
-  * R & 0\\
-  * 0\,...\,0 & 1
-  * \end{array} \right) \f$
-  *<!--
-  * \b Linear \b Matrix L (Dim)x(Dim):
-  * \f$ \left( \begin{array}{cc}
-  * L & 0\\
-  * 0\,...\,0 & 1
-  * \end{array} \right) \f$
-  *
-  * \b Affine \b Matrix A (Dim)x(Dim+1):
-  * \f$ \left( \begin{array}{c}
-  * A\\
-  * 0\,...\,0\,1
-  * \end{array} \right) \f$
-  *-->
-  * \b Scaling \b DiagonalMatrix S (Dim)x(Dim):
-  * \f$ \left( \begin{array}{cc}
-  * S & 0\\
-  * 0\,...\,0 & 1
-  * \end{array} \right) \f$
-  *
-  * \b Column \b point v (Dim)x(1):
-  * \f$ \left( \begin{array}{c}
-  * v\\
-  * 1
-  * \end{array} \right) \f$
-  *
-  * \b Set \b of \b column \b points V1...Vn (Dim)x(n):
-  * \f$ \left( \begin{array}{ccc}
-  * v_1 & ... & v_n\\
-  * 1 & ... & 1
-  * \end{array} \right) \f$
-  *
-  * The concatenation of a Transform object with any kind of other transformation
-  * always returns a Transform object.
-  *
-  * A little exception to the "as pure matrix product" rule is the case of the
-  * transformation of non homogeneous vectors by an affine transformation. In
-  * that case the last matrix row can be ignored, and the product returns non
-  * homogeneous vectors.
-  *
-  * Since, for instance, a Dim x Dim matrix is interpreted as a linear transformation,
-  * it is not possible to directly transform Dim vectors stored in a Dim x Dim matrix.
-  * The solution is either to use a Dim x Dynamic matrix or explicitly request a
-  * vector transformation by making the vector homogeneous:
-  * \code
-  * m' = T * m.colwise().homogeneous();
-  * \endcode
-  * Note that there is zero overhead.
-  *
-  * Conversion methods from/to Qt's QMatrix and QTransform are available if the
-  * preprocessor token EIGEN_QT_SUPPORT is defined.
-  *
-  * This class can be extended with the help of the plugin mechanism described on the page
-  * \ref TopicCustomizing_Plugins by defining the preprocessor symbol \c EIGEN_TRANSFORM_PLUGIN.
-  *
-  * \sa class Matrix, class Quaternion
-  */
-template<typename _Scalar, int _Dim, int _Mode, int _Options>
-class Transform
-{
-public:
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
-  enum {
-    Mode = _Mode,
-    Options = _Options,
-    Dim = _Dim,     ///< space dimension in which the transformation holds
-    HDim = _Dim+1,  ///< size of a respective homogeneous vector
-    Rows = int(Mode)==(AffineCompact) ? Dim : HDim
-  };
-  /** the scalar type of the coefficients */
-  typedef _Scalar Scalar;
-  typedef Eigen::Index StorageIndex;
-  typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3
-  /** type of the matrix used to represent the transformation */
-  typedef typename internal::make_proper_matrix_type<Scalar,Rows,HDim,Options>::type MatrixType;
-  /** constified MatrixType */
-  typedef const MatrixType ConstMatrixType;
-  /** type of the matrix used to represent the linear part of the transformation */
-  typedef Matrix<Scalar,Dim,Dim,Options> LinearMatrixType;
-  /** type of read/write reference to the linear part of the transformation */
-  typedef Block<MatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> LinearPart;
-  /** type of read reference to the linear part of the transformation */
-  typedef const Block<ConstMatrixType,Dim,Dim,int(Mode)==(AffineCompact) && (Options&RowMajor)==0> ConstLinearPart;
-  /** type of read/write reference to the affine part of the transformation */
-  typedef typename internal::conditional<int(Mode)==int(AffineCompact),
-                              MatrixType&,
-                              Block<MatrixType,Dim,HDim> >::type AffinePart;
-  /** type of read reference to the affine part of the transformation */
-  typedef typename internal::conditional<int(Mode)==int(AffineCompact),
-                              const MatrixType&,
-                              const Block<const MatrixType,Dim,HDim> >::type ConstAffinePart;
-  /** type of a vector */
-  typedef Matrix<Scalar,Dim,1> VectorType;
-  /** type of a read/write reference to the translation part of the rotation */
-  typedef Block<MatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> TranslationPart;
-  /** type of a read reference to the translation part of the rotation */
-  typedef const Block<ConstMatrixType,Dim,1,!(internal::traits<MatrixType>::Flags & RowMajorBit)> ConstTranslationPart;
-  /** corresponding translation type */
-  typedef Translation<Scalar,Dim> TranslationType;
-  
-  // this intermediate enum is needed to avoid an ICE with gcc 3.4 and 4.0
-  enum { TransformTimeDiagonalMode = ((Mode==int(Isometry))?Affine:int(Mode)) };
-  /** The return type of the product between a diagonal matrix and a transform */
-  typedef Transform<Scalar,Dim,TransformTimeDiagonalMode> TransformTimeDiagonalReturnType;
-
-protected:
-
-  MatrixType m_matrix;
-
-public:
-
-  /** Default constructor without initialization of the meaningful coefficients.
-    * If Mode==Affine, then the last row is set to [0 ... 0 1] */
-  EIGEN_DEVICE_FUNC inline Transform()
-  {
-    check_template_params();
-    internal::transform_make_affine<(int(Mode)==Affine) ? Affine : AffineCompact>::run(m_matrix);
-  }
-
-  EIGEN_DEVICE_FUNC inline Transform(const Transform& other)
-  {
-    check_template_params();
-    m_matrix = other.m_matrix;
-  }
-
-  EIGEN_DEVICE_FUNC inline explicit Transform(const TranslationType& t)
-  {
-    check_template_params();
-    *this = t;
-  }
-  EIGEN_DEVICE_FUNC inline explicit Transform(const UniformScaling<Scalar>& s)
-  {
-    check_template_params();
-    *this = s;
-  }
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline explicit Transform(const RotationBase<Derived, Dim>& r)
-  {
-    check_template_params();
-    *this = r;
-  }
-
-  EIGEN_DEVICE_FUNC inline Transform& operator=(const Transform& other)
-  { m_matrix = other.m_matrix; return *this; }
-
-  typedef internal::transform_take_affine_part<Transform> take_affine_part;
-
-  /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC inline explicit Transform(const EigenBase<OtherDerived>& other)
-  {
-    EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
-      YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
-
-    check_template_params();
-    internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
-  }
-
-  /** Set \c *this from a Dim^2 or (Dim+1)^2 matrix. */
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC inline Transform& operator=(const EigenBase<OtherDerived>& other)
-  {
-    EIGEN_STATIC_ASSERT((internal::is_same<Scalar,typename OtherDerived::Scalar>::value),
-      YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY);
-
-    internal::transform_construct_from_matrix<OtherDerived,Mode,Options,Dim,HDim>::run(this, other.derived());
-    return *this;
-  }
-  
-  template<int OtherOptions>
-  EIGEN_DEVICE_FUNC inline Transform(const Transform<Scalar,Dim,Mode,OtherOptions>& other)
-  {
-    check_template_params();
-    // only the options change, we can directly copy the matrices
-    m_matrix = other.matrix();
-  }
-
-  template<int OtherMode,int OtherOptions>
-  EIGEN_DEVICE_FUNC inline Transform(const Transform<Scalar,Dim,OtherMode,OtherOptions>& other)
-  {
-    check_template_params();
-    // prevent conversions as:
-    // Affine | AffineCompact | Isometry = Projective
-    EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Projective), Mode==int(Projective)),
-                        YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
-
-    // prevent conversions as:
-    // Isometry = Affine | AffineCompact
-    EIGEN_STATIC_ASSERT(EIGEN_IMPLIES(OtherMode==int(Affine)||OtherMode==int(AffineCompact), Mode!=int(Isometry)),
-                        YOU_PERFORMED_AN_INVALID_TRANSFORMATION_CONVERSION)
-
-    enum { ModeIsAffineCompact = Mode == int(AffineCompact),
-           OtherModeIsAffineCompact = OtherMode == int(AffineCompact)
-    };
-
-    if(ModeIsAffineCompact == OtherModeIsAffineCompact)
-    {
-      // We need the block expression because the code is compiled for all
-      // combinations of transformations and will trigger a compile time error
-      // if one tries to assign the matrices directly
-      m_matrix.template block<Dim,Dim+1>(0,0) = other.matrix().template block<Dim,Dim+1>(0,0);
-      makeAffine();
-    }
-    else if(OtherModeIsAffineCompact)
-    {
-      typedef typename Transform<Scalar,Dim,OtherMode,OtherOptions>::MatrixType OtherMatrixType;
-      internal::transform_construct_from_matrix<OtherMatrixType,Mode,Options,Dim,HDim>::run(this, other.matrix());
-    }
-    else
-    {
-      // here we know that Mode == AffineCompact and OtherMode != AffineCompact.
-      // if OtherMode were Projective, the static assert above would already have caught it.
-      // So the only possibility is that OtherMode == Affine
-      linear() = other.linear();
-      translation() = other.translation();
-    }
-  }
-
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC Transform(const ReturnByValue<OtherDerived>& other)
-  {
-    check_template_params();
-    other.evalTo(*this);
-  }
-
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC Transform& operator=(const ReturnByValue<OtherDerived>& other)
-  {
-    other.evalTo(*this);
-    return *this;
-  }
-
-  #ifdef EIGEN_QT_SUPPORT
-  inline Transform(const QMatrix& other);
-  inline Transform& operator=(const QMatrix& other);
-  inline QMatrix toQMatrix(void) const;
-  inline Transform(const QTransform& other);
-  inline Transform& operator=(const QTransform& other);
-  inline QTransform toQTransform(void) const;
-  #endif
-  
-  EIGEN_DEVICE_FUNC Index rows() const { return int(Mode)==int(Projective) ? m_matrix.cols() : (m_matrix.cols()-1); }
-  EIGEN_DEVICE_FUNC Index cols() const { return m_matrix.cols(); }
-
-  /** shortcut for m_matrix(row,col);
-    * \sa MatrixBase::operator(Index,Index) const */
-  EIGEN_DEVICE_FUNC inline Scalar operator() (Index row, Index col) const { return m_matrix(row,col); }
-  /** shortcut for m_matrix(row,col);
-    * \sa MatrixBase::operator(Index,Index) */
-  EIGEN_DEVICE_FUNC inline Scalar& operator() (Index row, Index col) { return m_matrix(row,col); }
-
-  /** \returns a read-only expression of the transformation matrix */
-  EIGEN_DEVICE_FUNC inline const MatrixType& matrix() const { return m_matrix; }
-  /** \returns a writable expression of the transformation matrix */
-  EIGEN_DEVICE_FUNC inline MatrixType& matrix() { return m_matrix; }
-
-  /** \returns a read-only expression of the linear part of the transformation */
-  EIGEN_DEVICE_FUNC inline ConstLinearPart linear() const { return ConstLinearPart(m_matrix,0,0); }
-  /** \returns a writable expression of the linear part of the transformation */
-  EIGEN_DEVICE_FUNC inline LinearPart linear() { return LinearPart(m_matrix,0,0); }
-
-  /** \returns a read-only expression of the Dim x HDim affine part of the transformation */
-  EIGEN_DEVICE_FUNC inline ConstAffinePart affine() const { return take_affine_part::run(m_matrix); }
-  /** \returns a writable expression of the Dim x HDim affine part of the transformation */
-  EIGEN_DEVICE_FUNC inline AffinePart affine() { return take_affine_part::run(m_matrix); }
-
-  /** \returns a read-only expression of the translation vector of the transformation */
-  EIGEN_DEVICE_FUNC inline ConstTranslationPart translation() const { return ConstTranslationPart(m_matrix,0,Dim); }
-  /** \returns a writable expression of the translation vector of the transformation */
-  EIGEN_DEVICE_FUNC inline TranslationPart translation() { return TranslationPart(m_matrix,0,Dim); }
-
-  /** \returns an expression of the product between the transform \c *this and a matrix expression \a other.
-    *
-    * The right-hand-side \a other can be either:
-    * \li an homogeneous vector of size Dim+1,
-    * \li a set of homogeneous vectors of size Dim+1 x N,
-    * \li a transformation matrix of size Dim+1 x Dim+1.
-    *
-    * Moreover, if \c *this represents an affine transformation (i.e., Mode!=Projective), then \a other can also be:
-    * \li a point of size Dim (computes: \code this->linear() * other + this->translation()\endcode),
-    * \li a set of N points as a Dim x N matrix (computes: \code (this->linear() * other).colwise() + this->translation()\endcode),
-    *
-    * In all cases, the return type is a matrix or vector of same sizes as the right-hand-side \a other.
-    *
-    * If you want to interpret \a other as a linear or affine transformation, then first convert it to a Transform<> type,
-    * or do your own cooking.
-    *
-    * Finally, if you want to apply Affine transformations to vectors, then explicitly apply the linear part only:
-    * \code
-    * Affine3f A;
-    * Vector3f v1, v2;
-    * v2 = A.linear() * v1;
-    * \endcode
-    *
-    */
-  // note: this function is defined here because some compilers cannot find the respective declaration
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const typename internal::transform_right_product_impl<Transform, OtherDerived>::ResultType
-  operator * (const EigenBase<OtherDerived> &other) const
-  { return internal::transform_right_product_impl<Transform, OtherDerived>::run(*this,other.derived()); }
-
-  /** \returns the product expression of a transformation matrix \a a times a transform \a b
-    *
-    * The left hand side \a other can be either:
-    * \li a linear transformation matrix of size Dim x Dim,
-    * \li an affine transformation matrix of size Dim x Dim+1,
-    * \li a general transformation matrix of size Dim+1 x Dim+1.
-    */
-  template<typename OtherDerived> friend
-  EIGEN_DEVICE_FUNC inline const typename internal::transform_left_product_impl<OtherDerived,Mode,Options,_Dim,_Dim+1>::ResultType
-    operator * (const EigenBase<OtherDerived> &a, const Transform &b)
-  { return internal::transform_left_product_impl<OtherDerived,Mode,Options,Dim,HDim>::run(a.derived(),b); }
-
-  /** \returns The product expression of a transform \a a times a diagonal matrix \a b
-    *
-    * The rhs diagonal matrix is interpreted as an affine scaling transformation. The
-    * product results in a Transform of the same type (mode) as the lhs only if the lhs 
-    * mode is no isometry. In that case, the returned transform is an affinity.
-    */
-  template<typename DiagonalDerived>
-  EIGEN_DEVICE_FUNC inline const TransformTimeDiagonalReturnType
-    operator * (const DiagonalBase<DiagonalDerived> &b) const
-  {
-    TransformTimeDiagonalReturnType res(*this);
-    res.linearExt() *= b;
-    return res;
-  }
-
-  /** \returns The product expression of a diagonal matrix \a a times a transform \a b
-    *
-    * The lhs diagonal matrix is interpreted as an affine scaling transformation. The
-    * product results in a Transform of the same type (mode) as the lhs only if the lhs 
-    * mode is no isometry. In that case, the returned transform is an affinity.
-    */
-  template<typename DiagonalDerived>
-  EIGEN_DEVICE_FUNC friend inline TransformTimeDiagonalReturnType
-    operator * (const DiagonalBase<DiagonalDerived> &a, const Transform &b)
-  {
-    TransformTimeDiagonalReturnType res;
-    res.linear().noalias() = a*b.linear();
-    res.translation().noalias() = a*b.translation();
-    if (Mode!=int(AffineCompact))
-      res.matrix().row(Dim) = b.matrix().row(Dim);
-    return res;
-  }
-
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC inline Transform& operator*=(const EigenBase<OtherDerived>& other) { return *this = *this * other; }
-
-  /** Concatenates two transformations */
-  EIGEN_DEVICE_FUNC inline const Transform operator * (const Transform& other) const
-  {
-    return internal::transform_transform_product_impl<Transform,Transform>::run(*this,other);
-  }
-  
-  #if EIGEN_COMP_ICC
-private:
-  // this intermediate structure permits to workaround a bug in ICC 11:
-  //   error: template instantiation resulted in unexpected function type of "Eigen::Transform<double, 3, 32, 0>
-  //             (const Eigen::Transform<double, 3, 2, 0> &) const"
-  //  (the meaning of a name may have changed since the template declaration -- the type of the template is:
-  // "Eigen::internal::transform_transform_product_impl<Eigen::Transform<double, 3, 32, 0>,
-  //     Eigen::Transform<double, 3, Mode, Options>, <expression>>::ResultType (const Eigen::Transform<double, 3, Mode, Options> &) const")
-  // 
-  template<int OtherMode,int OtherOptions> struct icc_11_workaround
-  {
-    typedef internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> > ProductType;
-    typedef typename ProductType::ResultType ResultType;
-  };
-  
-public:
-  /** Concatenates two different transformations */
-  template<int OtherMode,int OtherOptions>
-  inline typename icc_11_workaround<OtherMode,OtherOptions>::ResultType
-    operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
-  {
-    typedef typename icc_11_workaround<OtherMode,OtherOptions>::ProductType ProductType;
-    return ProductType::run(*this,other);
-  }
-  #else
-  /** Concatenates two different transformations */
-  template<int OtherMode,int OtherOptions>
-  EIGEN_DEVICE_FUNC inline typename internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::ResultType
-    operator * (const Transform<Scalar,Dim,OtherMode,OtherOptions>& other) const
-  {
-    return internal::transform_transform_product_impl<Transform,Transform<Scalar,Dim,OtherMode,OtherOptions> >::run(*this,other);
-  }
-  #endif
-
-  /** \sa MatrixBase::setIdentity() */
-  EIGEN_DEVICE_FUNC void setIdentity() { m_matrix.setIdentity(); }
-
-  /**
-   * \brief Returns an identity transformation.
-   * \todo In the future this function should be returning a Transform expression.
-   */
-  EIGEN_DEVICE_FUNC static const Transform Identity()
-  {
-    return Transform(MatrixType::Identity());
-  }
-
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC 
-  inline Transform& scale(const MatrixBase<OtherDerived> &other);
-
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC
-  inline Transform& prescale(const MatrixBase<OtherDerived> &other);
-
-  EIGEN_DEVICE_FUNC inline Transform& scale(const Scalar& s);
-  EIGEN_DEVICE_FUNC inline Transform& prescale(const Scalar& s);
-
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC
-  inline Transform& translate(const MatrixBase<OtherDerived> &other);
-
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC
-  inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
-
-  template<typename RotationType>
-  EIGEN_DEVICE_FUNC
-  inline Transform& rotate(const RotationType& rotation);
-
-  template<typename RotationType>
-  EIGEN_DEVICE_FUNC
-  inline Transform& prerotate(const RotationType& rotation);
-
-  EIGEN_DEVICE_FUNC Transform& shear(const Scalar& sx, const Scalar& sy);
-  EIGEN_DEVICE_FUNC Transform& preshear(const Scalar& sx, const Scalar& sy);
-
-  EIGEN_DEVICE_FUNC inline Transform& operator=(const TranslationType& t);
-  
-  EIGEN_DEVICE_FUNC
-  inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
-  
-  EIGEN_DEVICE_FUNC inline Transform operator*(const TranslationType& t) const;
-
-  EIGEN_DEVICE_FUNC 
-  inline Transform& operator=(const UniformScaling<Scalar>& t);
-  
-  EIGEN_DEVICE_FUNC
-  inline Transform& operator*=(const UniformScaling<Scalar>& s) { return scale(s.factor()); }
-  
-  EIGEN_DEVICE_FUNC
-  inline TransformTimeDiagonalReturnType operator*(const UniformScaling<Scalar>& s) const
-  {
-    TransformTimeDiagonalReturnType res = *this;
-    res.scale(s.factor());
-    return res;
-  }
-
-  EIGEN_DEVICE_FUNC
-  inline Transform& operator*=(const DiagonalMatrix<Scalar,Dim>& s) { linearExt() *= s; return *this; }
-
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline Transform& operator=(const RotationBase<Derived,Dim>& r);
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
-
-  EIGEN_DEVICE_FUNC const LinearMatrixType rotation() const;
-  template<typename RotationMatrixType, typename ScalingMatrixType>
-  EIGEN_DEVICE_FUNC
-  void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
-  template<typename ScalingMatrixType, typename RotationMatrixType>
-  EIGEN_DEVICE_FUNC
-  void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
-
-  template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
-  EIGEN_DEVICE_FUNC
-  Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
-    const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
-
-  EIGEN_DEVICE_FUNC
-  inline Transform inverse(TransformTraits traits = (TransformTraits)Mode) const;
-
-  /** \returns a const pointer to the column major internal matrix */
-  EIGEN_DEVICE_FUNC const Scalar* data() const { return m_matrix.data(); }
-  /** \returns a non-const pointer to the column major internal matrix */
-  EIGEN_DEVICE_FUNC Scalar* data() { return m_matrix.data(); }
-
-  /** \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<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type cast() const
-  { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim,Mode,Options> >::type(*this); }
-
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType>
-  EIGEN_DEVICE_FUNC inline explicit Transform(const Transform<OtherScalarType,Dim,Mode,Options>& other)
-  {
-    check_template_params();
-    m_matrix = other.matrix().template cast<Scalar>();
-  }
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  EIGEN_DEVICE_FUNC bool isApprox(const Transform& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
-  { return m_matrix.isApprox(other.m_matrix, prec); }
-
-  /** Sets the last row to [0 ... 0 1]
-    */
-  EIGEN_DEVICE_FUNC void makeAffine()
-  {
-    internal::transform_make_affine<int(Mode)>::run(m_matrix);
-  }
-
-  /** \internal
-    * \returns the Dim x Dim linear part if the transformation is affine,
-    *          and the HDim x Dim part for projective transformations.
-    */
-  EIGEN_DEVICE_FUNC inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt()
-  { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
-  /** \internal
-    * \returns the Dim x Dim linear part if the transformation is affine,
-    *          and the HDim x Dim part for projective transformations.
-    */
-  EIGEN_DEVICE_FUNC inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,Dim> linearExt() const
-  { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,Dim>(0,0); }
-
-  /** \internal
-    * \returns the translation part if the transformation is affine,
-    *          and the last column for projective transformations.
-    */
-  EIGEN_DEVICE_FUNC inline Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt()
-  { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
-  /** \internal
-    * \returns the translation part if the transformation is affine,
-    *          and the last column for projective transformations.
-    */
-  EIGEN_DEVICE_FUNC inline const Block<MatrixType,int(Mode)==int(Projective)?HDim:Dim,1> translationExt() const
-  { return m_matrix.template block<int(Mode)==int(Projective)?HDim:Dim,1>(0,Dim); }
-
-
-  #ifdef EIGEN_TRANSFORM_PLUGIN
-  #include EIGEN_TRANSFORM_PLUGIN
-  #endif
-  
-protected:
-  #ifndef EIGEN_PARSED_BY_DOXYGEN
-    EIGEN_DEVICE_FUNC static EIGEN_STRONG_INLINE void check_template_params()
-    {
-      EIGEN_STATIC_ASSERT((Options & (DontAlign|RowMajor)) == Options, INVALID_MATRIX_TEMPLATE_PARAMETERS)
-    }
-  #endif
-
-};
-
-/** \ingroup Geometry_Module */
-typedef Transform<float,2,Isometry> Isometry2f;
-/** \ingroup Geometry_Module */
-typedef Transform<float,3,Isometry> Isometry3f;
-/** \ingroup Geometry_Module */
-typedef Transform<double,2,Isometry> Isometry2d;
-/** \ingroup Geometry_Module */
-typedef Transform<double,3,Isometry> Isometry3d;
-
-/** \ingroup Geometry_Module */
-typedef Transform<float,2,Affine> Affine2f;
-/** \ingroup Geometry_Module */
-typedef Transform<float,3,Affine> Affine3f;
-/** \ingroup Geometry_Module */
-typedef Transform<double,2,Affine> Affine2d;
-/** \ingroup Geometry_Module */
-typedef Transform<double,3,Affine> Affine3d;
-
-/** \ingroup Geometry_Module */
-typedef Transform<float,2,AffineCompact> AffineCompact2f;
-/** \ingroup Geometry_Module */
-typedef Transform<float,3,AffineCompact> AffineCompact3f;
-/** \ingroup Geometry_Module */
-typedef Transform<double,2,AffineCompact> AffineCompact2d;
-/** \ingroup Geometry_Module */
-typedef Transform<double,3,AffineCompact> AffineCompact3d;
-
-/** \ingroup Geometry_Module */
-typedef Transform<float,2,Projective> Projective2f;
-/** \ingroup Geometry_Module */
-typedef Transform<float,3,Projective> Projective3f;
-/** \ingroup Geometry_Module */
-typedef Transform<double,2,Projective> Projective2d;
-/** \ingroup Geometry_Module */
-typedef Transform<double,3,Projective> Projective3d;
-
-/**************************
-*** Optional QT support ***
-**************************/
-
-#ifdef EIGEN_QT_SUPPORT
-/** Initializes \c *this from a QMatrix assuming the dimension is 2.
-  *
-  * This function is available only if the token EIGEN_QT_SUPPORT is defined.
-  */
-template<typename Scalar, int Dim, int Mode,int Options>
-Transform<Scalar,Dim,Mode,Options>::Transform(const QMatrix& other)
-{
-  check_template_params();
-  *this = other;
-}
-
-/** Set \c *this from a QMatrix assuming the dimension is 2.
-  *
-  * This function is available only if the token EIGEN_QT_SUPPORT is defined.
-  */
-template<typename Scalar, int Dim, int Mode,int Options>
-Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QMatrix& other)
-{
-  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
-  if (Mode == int(AffineCompact))
-    m_matrix << other.m11(), other.m21(), other.dx(),
-                other.m12(), other.m22(), other.dy();
-  else
-    m_matrix << other.m11(), other.m21(), other.dx(),
-                other.m12(), other.m22(), other.dy(),
-                0, 0, 1;
-  return *this;
-}
-
-/** \returns a QMatrix from \c *this assuming the dimension is 2.
-  *
-  * \warning this conversion might loss data if \c *this is not affine
-  *
-  * This function is available only if the token EIGEN_QT_SUPPORT is defined.
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-QMatrix Transform<Scalar,Dim,Mode,Options>::toQMatrix(void) const
-{
-  check_template_params();
-  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
-  return QMatrix(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
-                 m_matrix.coeff(0,1), m_matrix.coeff(1,1),
-                 m_matrix.coeff(0,2), m_matrix.coeff(1,2));
-}
-
-/** Initializes \c *this from a QTransform assuming the dimension is 2.
-  *
-  * This function is available only if the token EIGEN_QT_SUPPORT is defined.
-  */
-template<typename Scalar, int Dim, int Mode,int Options>
-Transform<Scalar,Dim,Mode,Options>::Transform(const QTransform& other)
-{
-  check_template_params();
-  *this = other;
-}
-
-/** Set \c *this from a QTransform assuming the dimension is 2.
-  *
-  * This function is available only if the token EIGEN_QT_SUPPORT is defined.
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const QTransform& other)
-{
-  check_template_params();
-  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
-  if (Mode == int(AffineCompact))
-    m_matrix << other.m11(), other.m21(), other.dx(),
-                other.m12(), other.m22(), other.dy();
-  else
-    m_matrix << other.m11(), other.m21(), other.dx(),
-                other.m12(), other.m22(), other.dy(),
-                other.m13(), other.m23(), other.m33();
-  return *this;
-}
-
-/** \returns a QTransform from \c *this assuming the dimension is 2.
-  *
-  * This function is available only if the token EIGEN_QT_SUPPORT is defined.
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-QTransform Transform<Scalar,Dim,Mode,Options>::toQTransform(void) const
-{
-  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
-  if (Mode == int(AffineCompact))
-    return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0),
-                      m_matrix.coeff(0,1), m_matrix.coeff(1,1),
-                      m_matrix.coeff(0,2), m_matrix.coeff(1,2));
-  else
-    return QTransform(m_matrix.coeff(0,0), m_matrix.coeff(1,0), m_matrix.coeff(2,0),
-                      m_matrix.coeff(0,1), m_matrix.coeff(1,1), m_matrix.coeff(2,1),
-                      m_matrix.coeff(0,2), m_matrix.coeff(1,2), m_matrix.coeff(2,2));
-}
-#endif
-
-/*********************
-*** Procedural API ***
-*********************/
-
-/** Applies on the right the non uniform scale transformation represented
-  * by the vector \a other to \c *this and returns a reference to \c *this.
-  * \sa prescale()
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::scale(const MatrixBase<OtherDerived> &other)
-{
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
-  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
-  linearExt().noalias() = (linearExt() * other.asDiagonal());
-  return *this;
-}
-
-/** Applies on the right a uniform scale of a factor \a c to \c *this
-  * and returns a reference to \c *this.
-  * \sa prescale(Scalar)
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::scale(const Scalar& s)
-{
-  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
-  linearExt() *= s;
-  return *this;
-}
-
-/** Applies on the left the non uniform scale transformation represented
-  * by the vector \a other to \c *this and returns a reference to \c *this.
-  * \sa scale()
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::prescale(const MatrixBase<OtherDerived> &other)
-{
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
-  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
-  affine().noalias() = (other.asDiagonal() * affine());
-  return *this;
-}
-
-/** Applies on the left a uniform scale of a factor \a c to \c *this
-  * and returns a reference to \c *this.
-  * \sa scale(Scalar)
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::prescale(const Scalar& s)
-{
-  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
-  m_matrix.template topRows<Dim>() *= s;
-  return *this;
-}
-
-/** Applies on the right the translation matrix represented by the vector \a other
-  * to \c *this and returns a reference to \c *this.
-  * \sa pretranslate()
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::translate(const MatrixBase<OtherDerived> &other)
-{
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
-  translationExt() += linearExt() * other;
-  return *this;
-}
-
-/** Applies on the left the translation matrix represented by the vector \a other
-  * to \c *this and returns a reference to \c *this.
-  * \sa translate()
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::pretranslate(const MatrixBase<OtherDerived> &other)
-{
-  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
-  if(int(Mode)==int(Projective))
-    affine() += other * m_matrix.row(Dim);
-  else
-    translation() += other;
-  return *this;
-}
-
-/** Applies on the right the rotation represented by the rotation \a rotation
-  * to \c *this and returns a reference to \c *this.
-  *
-  * The template parameter \a RotationType is the type of the rotation which
-  * must be known by internal::toRotationMatrix<>.
-  *
-  * Natively supported types includes:
-  *   - any scalar (2D),
-  *   - a Dim x Dim matrix expression,
-  *   - a Quaternion (3D),
-  *   - a AngleAxis (3D)
-  *
-  * This mechanism is easily extendable to support user types such as Euler angles,
-  * or a pair of Quaternion for 4D rotations.
-  *
-  * \sa rotate(Scalar), class Quaternion, class AngleAxis, prerotate(RotationType)
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename RotationType>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::rotate(const RotationType& rotation)
-{
-  linearExt() *= internal::toRotationMatrix<Scalar,Dim>(rotation);
-  return *this;
-}
-
-/** Applies on the left the rotation represented by the rotation \a rotation
-  * to \c *this and returns a reference to \c *this.
-  *
-  * See rotate() for further details.
-  *
-  * \sa rotate()
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename RotationType>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::prerotate(const RotationType& rotation)
-{
-  m_matrix.template block<Dim,HDim>(0,0) = internal::toRotationMatrix<Scalar,Dim>(rotation)
-                                         * m_matrix.template block<Dim,HDim>(0,0);
-  return *this;
-}
-
-/** Applies on the right the shear transformation represented
-  * by the vector \a other to \c *this and returns a reference to \c *this.
-  * \warning 2D only.
-  * \sa preshear()
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::shear(const Scalar& sx, const Scalar& sy)
-{
-  EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
-  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
-  VectorType tmp = linear().col(0)*sy + linear().col(1);
-  linear() << linear().col(0) + linear().col(1)*sx, tmp;
-  return *this;
-}
-
-/** Applies on the left the shear transformation represented
-  * by the vector \a other to \c *this and returns a reference to \c *this.
-  * \warning 2D only.
-  * \sa shear()
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::preshear(const Scalar& sx, const Scalar& sy)
-{
-  EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
-  EIGEN_STATIC_ASSERT(Mode!=int(Isometry), THIS_METHOD_IS_ONLY_FOR_SPECIFIC_TRANSFORMATIONS)
-  m_matrix.template block<Dim,HDim>(0,0) = LinearMatrixType(1, sx, sy, 1) * m_matrix.template block<Dim,HDim>(0,0);
-  return *this;
-}
-
-/******************************************************
-*** Scaling, Translation and Rotation compatibility ***
-******************************************************/
-
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const TranslationType& t)
-{
-  linear().setIdentity();
-  translation() = t.vector();
-  makeAffine();
-  return *this;
-}
-
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const TranslationType& t) const
-{
-  Transform res = *this;
-  res.translate(t.vector());
-  return res;
-}
-
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const UniformScaling<Scalar>& s)
-{
-  m_matrix.setZero();
-  linear().diagonal().fill(s.factor());
-  makeAffine();
-  return *this;
-}
-
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename Derived>
-EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options>& Transform<Scalar,Dim,Mode,Options>::operator=(const RotationBase<Derived,Dim>& r)
-{
-  linear() = internal::toRotationMatrix<Scalar,Dim>(r);
-  translation().setZero();
-  makeAffine();
-  return *this;
-}
-
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename Derived>
-EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode,Options> Transform<Scalar,Dim,Mode,Options>::operator*(const RotationBase<Derived,Dim>& r) const
-{
-  Transform res = *this;
-  res.rotate(r.derived());
-  return res;
-}
-
-/************************
-*** Special functions ***
-************************/
-
-/** \returns the rotation part of the transformation
-  *
-  *
-  * \svd_module
-  *
-  * \sa computeRotationScaling(), computeScalingRotation(), class SVD
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC const typename Transform<Scalar,Dim,Mode,Options>::LinearMatrixType
-Transform<Scalar,Dim,Mode,Options>::rotation() const
-{
-  LinearMatrixType result;
-  computeRotationScaling(&result, (LinearMatrixType*)0);
-  return result;
-}
-
-
-/** decomposes the linear part of the transformation as a product rotation x scaling, the scaling being
-  * not necessarily positive.
-  *
-  * If either pointer is zero, the corresponding computation is skipped.
-  *
-  *
-  *
-  * \svd_module
-  *
-  * \sa computeScalingRotation(), rotation(), class SVD
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename RotationMatrixType, typename ScalingMatrixType>
-EIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const
-{
-  JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU | ComputeFullV);
-
-  Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
-  VectorType sv(svd.singularValues());
-  sv.coeffRef(0) *= x;
-  if(scaling) scaling->lazyAssign(svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint());
-  if(rotation)
-  {
-    LinearMatrixType m(svd.matrixU());
-    m.col(0) /= x;
-    rotation->lazyAssign(m * svd.matrixV().adjoint());
-  }
-}
-
-/** decomposes the linear part of the transformation as a product scaling x rotation, the scaling being
-  * not necessarily positive.
-  *
-  * If either pointer is zero, the corresponding computation is skipped.
-  *
-  *
-  *
-  * \svd_module
-  *
-  * \sa computeRotationScaling(), rotation(), class SVD
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename ScalingMatrixType, typename RotationMatrixType>
-EIGEN_DEVICE_FUNC void Transform<Scalar,Dim,Mode,Options>::computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const
-{
-  JacobiSVD<LinearMatrixType> svd(linear(), ComputeFullU | ComputeFullV);
-
-  Scalar x = (svd.matrixU() * svd.matrixV().adjoint()).determinant(); // so x has absolute value 1
-  VectorType sv(svd.singularValues());
-  sv.coeffRef(0) *= x;
-  if(scaling) scaling->lazyAssign(svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint());
-  if(rotation)
-  {
-    LinearMatrixType m(svd.matrixU());
-    m.col(0) /= x;
-    rotation->lazyAssign(m * svd.matrixV().adjoint());
-  }
-}
-
-/** Convenient method to set \c *this from a position, orientation and scale
-  * of a 3D object.
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>&
-Transform<Scalar,Dim,Mode,Options>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
-  const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
-{
-  linear() = internal::toRotationMatrix<Scalar,Dim>(orientation);
-  linear() *= scale.asDiagonal();
-  translation() = position;
-  makeAffine();
-  return *this;
-}
-
-namespace internal {
-
-template<int Mode>
-struct transform_make_affine
-{
-  template<typename MatrixType>
-  EIGEN_DEVICE_FUNC static void run(MatrixType &mat)
-  {
-    static const int Dim = MatrixType::ColsAtCompileTime-1;
-    mat.template block<1,Dim>(Dim,0).setZero();
-    mat.coeffRef(Dim,Dim) = typename MatrixType::Scalar(1);
-  }
-};
-
-template<>
-struct transform_make_affine<AffineCompact>
-{
-  template<typename MatrixType> EIGEN_DEVICE_FUNC static void run(MatrixType &) { }
-};
-    
-// selector needed to avoid taking the inverse of a 3x4 matrix
-template<typename TransformType, int Mode=TransformType::Mode>
-struct projective_transform_inverse
-{
-  EIGEN_DEVICE_FUNC static inline void run(const TransformType&, TransformType&)
-  {}
-};
-
-template<typename TransformType>
-struct projective_transform_inverse<TransformType, Projective>
-{
-  EIGEN_DEVICE_FUNC static inline void run(const TransformType& m, TransformType& res)
-  {
-    res.matrix() = m.matrix().inverse();
-  }
-};
-
-} // end namespace internal
-
-
-/**
-  *
-  * \returns the inverse transformation according to some given knowledge
-  * on \c *this.
-  *
-  * \param hint allows to optimize the inversion process when the transformation
-  * is known to be not a general transformation (optional). The possible values are:
-  *  - #Projective if the transformation is not necessarily affine, i.e., if the
-  *    last row is not guaranteed to be [0 ... 0 1]
-  *  - #Affine if the last row can be assumed to be [0 ... 0 1]
-  *  - #Isometry if the transformation is only a concatenations of translations
-  *    and rotations.
-  *  The default is the template class parameter \c Mode.
-  *
-  * \warning unless \a traits is always set to NoShear or NoScaling, this function
-  * requires the generic inverse method of MatrixBase defined in the LU module. If
-  * you forget to include this module, then you will get hard to debug linking errors.
-  *
-  * \sa MatrixBase::inverse()
-  */
-template<typename Scalar, int Dim, int Mode, int Options>
-EIGEN_DEVICE_FUNC Transform<Scalar,Dim,Mode,Options>
-Transform<Scalar,Dim,Mode,Options>::inverse(TransformTraits hint) const
-{
-  Transform res;
-  if (hint == Projective)
-  {
-    internal::projective_transform_inverse<Transform>::run(*this, res);
-  }
-  else
-  {
-    if (hint == Isometry)
-    {
-      res.matrix().template topLeftCorner<Dim,Dim>() = linear().transpose();
-    }
-    else if(hint&Affine)
-    {
-      res.matrix().template topLeftCorner<Dim,Dim>() = linear().inverse();
-    }
-    else
-    {
-      eigen_assert(false && "Invalid transform traits in Transform::Inverse");
-    }
-    // translation and remaining parts
-    res.matrix().template topRightCorner<Dim,1>()
-      = - res.matrix().template topLeftCorner<Dim,Dim>() * translation();
-    res.makeAffine(); // we do need this, because in the beginning res is uninitialized
-  }
-  return res;
-}
-
-namespace internal {
-
-/*****************************************************
-*** Specializations of take affine part            ***
-*****************************************************/
-
-template<typename TransformType> struct transform_take_affine_part {
-  typedef typename TransformType::MatrixType MatrixType;
-  typedef typename TransformType::AffinePart AffinePart;
-  typedef typename TransformType::ConstAffinePart ConstAffinePart;
-  static inline AffinePart run(MatrixType& m)
-  { return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
-  static inline ConstAffinePart run(const MatrixType& m)
-  { return m.template block<TransformType::Dim,TransformType::HDim>(0,0); }
-};
-
-template<typename Scalar, int Dim, int Options>
-struct transform_take_affine_part<Transform<Scalar,Dim,AffineCompact, Options> > {
-  typedef typename Transform<Scalar,Dim,AffineCompact,Options>::MatrixType MatrixType;
-  static inline MatrixType& run(MatrixType& m) { return m; }
-  static inline const MatrixType& run(const MatrixType& m) { return m; }
-};
-
-/*****************************************************
-*** Specializations of construct from matrix       ***
-*****************************************************/
-
-template<typename Other, int Mode, int Options, int Dim, int HDim>
-struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,Dim>
-{
-  static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
-  {
-    transform->linear() = other;
-    transform->translation().setZero();
-    transform->makeAffine();
-  }
-};
-
-template<typename Other, int Mode, int Options, int Dim, int HDim>
-struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, Dim,HDim>
-{
-  static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
-  {
-    transform->affine() = other;
-    transform->makeAffine();
-  }
-};
-
-template<typename Other, int Mode, int Options, int Dim, int HDim>
-struct transform_construct_from_matrix<Other, Mode,Options,Dim,HDim, HDim,HDim>
-{
-  static inline void run(Transform<typename Other::Scalar,Dim,Mode,Options> *transform, const Other& other)
-  { transform->matrix() = other; }
-};
-
-template<typename Other, int Options, int Dim, int HDim>
-struct transform_construct_from_matrix<Other, AffineCompact,Options,Dim,HDim, HDim,HDim>
-{
-  static inline void run(Transform<typename Other::Scalar,Dim,AffineCompact,Options> *transform, const Other& other)
-  { transform->matrix() = other.template block<Dim,HDim>(0,0); }
-};
-
-/**********************************************************
-***   Specializations of operator* with rhs EigenBase   ***
-**********************************************************/
-
-template<int LhsMode,int RhsMode>
-struct transform_product_result
-{
-  enum 
-  { 
-    Mode =
-      (LhsMode == (int)Projective    || RhsMode == (int)Projective    ) ? Projective :
-      (LhsMode == (int)Affine        || RhsMode == (int)Affine        ) ? Affine :
-      (LhsMode == (int)AffineCompact || RhsMode == (int)AffineCompact ) ? AffineCompact :
-      (LhsMode == (int)Isometry      || RhsMode == (int)Isometry      ) ? Isometry : Projective
-  };
-};
-
-template< typename TransformType, typename MatrixType, int RhsCols>
-struct transform_right_product_impl< TransformType, MatrixType, 0, RhsCols>
-{
-  typedef typename MatrixType::PlainObject ResultType;
-
-  static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
-  {
-    return T.matrix() * other;
-  }
-};
-
-template< typename TransformType, typename MatrixType, int RhsCols>
-struct transform_right_product_impl< TransformType, MatrixType, 1, RhsCols>
-{
-  enum { 
-    Dim = TransformType::Dim, 
-    HDim = TransformType::HDim,
-    OtherRows = MatrixType::RowsAtCompileTime,
-    OtherCols = MatrixType::ColsAtCompileTime
-  };
-
-  typedef typename MatrixType::PlainObject ResultType;
-
-  static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
-  {
-    EIGEN_STATIC_ASSERT(OtherRows==HDim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
-
-    typedef Block<ResultType, Dim, OtherCols, int(MatrixType::RowsAtCompileTime)==Dim> TopLeftLhs;
-
-    ResultType res(other.rows(),other.cols());
-    TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() = T.affine() * other;
-    res.row(OtherRows-1) = other.row(OtherRows-1);
-    
-    return res;
-  }
-};
-
-template< typename TransformType, typename MatrixType, int RhsCols>
-struct transform_right_product_impl< TransformType, MatrixType, 2, RhsCols>
-{
-  enum { 
-    Dim = TransformType::Dim, 
-    HDim = TransformType::HDim,
-    OtherRows = MatrixType::RowsAtCompileTime,
-    OtherCols = MatrixType::ColsAtCompileTime
-  };
-
-  typedef typename MatrixType::PlainObject ResultType;
-
-  static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
-  {
-    EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
-
-    typedef Block<ResultType, Dim, OtherCols, true> TopLeftLhs;
-    ResultType res(Replicate<typename TransformType::ConstTranslationPart, 1, OtherCols>(T.translation(),1,other.cols()));
-    TopLeftLhs(res, 0, 0, Dim, other.cols()).noalias() += T.linear() * other;
-
-    return res;
-  }
-};
-
-template< typename TransformType, typename MatrixType >
-struct transform_right_product_impl< TransformType, MatrixType, 2, 1> // rhs is a vector of size Dim
-{
-  typedef typename TransformType::MatrixType TransformMatrix;
-  enum {
-    Dim = TransformType::Dim,
-    HDim = TransformType::HDim,
-    OtherRows = MatrixType::RowsAtCompileTime,
-    WorkingRows = EIGEN_PLAIN_ENUM_MIN(TransformMatrix::RowsAtCompileTime,HDim)
-  };
-
-  typedef typename MatrixType::PlainObject ResultType;
-
-  static EIGEN_STRONG_INLINE ResultType run(const TransformType& T, const MatrixType& other)
-  {
-    EIGEN_STATIC_ASSERT(OtherRows==Dim, YOU_MIXED_MATRICES_OF_DIFFERENT_SIZES);
-
-    Matrix<typename ResultType::Scalar, Dim+1, 1> rhs;
-    rhs.template head<Dim>() = other; rhs[Dim] = typename ResultType::Scalar(1);
-    Matrix<typename ResultType::Scalar, WorkingRows, 1> res(T.matrix() * rhs);
-    return res.template head<Dim>();
-  }
-};
-
-/**********************************************************
-***   Specializations of operator* with lhs EigenBase   ***
-**********************************************************/
-
-// generic HDim x HDim matrix * T => Projective
-template<typename Other,int Mode, int Options, int Dim, int HDim>
-struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, HDim,HDim>
-{
-  typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
-  typedef typename TransformType::MatrixType MatrixType;
-  typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
-  static ResultType run(const Other& other,const TransformType& tr)
-  { return ResultType(other * tr.matrix()); }
-};
-
-// generic HDim x HDim matrix * AffineCompact => Projective
-template<typename Other, int Options, int Dim, int HDim>
-struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, HDim,HDim>
-{
-  typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
-  typedef typename TransformType::MatrixType MatrixType;
-  typedef Transform<typename Other::Scalar,Dim,Projective,Options> ResultType;
-  static ResultType run(const Other& other,const TransformType& tr)
-  {
-    ResultType res;
-    res.matrix().noalias() = other.template block<HDim,Dim>(0,0) * tr.matrix();
-    res.matrix().col(Dim) += other.col(Dim);
-    return res;
-  }
-};
-
-// affine matrix * T
-template<typename Other,int Mode, int Options, int Dim, int HDim>
-struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,HDim>
-{
-  typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
-  typedef typename TransformType::MatrixType MatrixType;
-  typedef TransformType ResultType;
-  static ResultType run(const Other& other,const TransformType& tr)
-  {
-    ResultType res;
-    res.affine().noalias() = other * tr.matrix();
-    res.matrix().row(Dim) = tr.matrix().row(Dim);
-    return res;
-  }
-};
-
-// affine matrix * AffineCompact
-template<typename Other, int Options, int Dim, int HDim>
-struct transform_left_product_impl<Other,AffineCompact,Options,Dim,HDim, Dim,HDim>
-{
-  typedef Transform<typename Other::Scalar,Dim,AffineCompact,Options> TransformType;
-  typedef typename TransformType::MatrixType MatrixType;
-  typedef TransformType ResultType;
-  static ResultType run(const Other& other,const TransformType& tr)
-  {
-    ResultType res;
-    res.matrix().noalias() = other.template block<Dim,Dim>(0,0) * tr.matrix();
-    res.translation() += other.col(Dim);
-    return res;
-  }
-};
-
-// linear matrix * T
-template<typename Other,int Mode, int Options, int Dim, int HDim>
-struct transform_left_product_impl<Other,Mode,Options,Dim,HDim, Dim,Dim>
-{
-  typedef Transform<typename Other::Scalar,Dim,Mode,Options> TransformType;
-  typedef typename TransformType::MatrixType MatrixType;
-  typedef TransformType ResultType;
-  static ResultType run(const Other& other, const TransformType& tr)
-  {
-    TransformType res;
-    if(Mode!=int(AffineCompact))
-      res.matrix().row(Dim) = tr.matrix().row(Dim);
-    res.matrix().template topRows<Dim>().noalias()
-      = other * tr.matrix().template topRows<Dim>();
-    return res;
-  }
-};
-
-/**********************************************************
-*** Specializations of operator* with another Transform ***
-**********************************************************/
-
-template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
-struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,false >
-{
-  enum { ResultMode = transform_product_result<LhsMode,RhsMode>::Mode };
-  typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
-  typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
-  typedef Transform<Scalar,Dim,ResultMode,LhsOptions> ResultType;
-  static ResultType run(const Lhs& lhs, const Rhs& rhs)
-  {
-    ResultType res;
-    res.linear() = lhs.linear() * rhs.linear();
-    res.translation() = lhs.linear() * rhs.translation() + lhs.translation();
-    res.makeAffine();
-    return res;
-  }
-};
-
-template<typename Scalar, int Dim, int LhsMode, int LhsOptions, int RhsMode, int RhsOptions>
-struct transform_transform_product_impl<Transform<Scalar,Dim,LhsMode,LhsOptions>,Transform<Scalar,Dim,RhsMode,RhsOptions>,true >
-{
-  typedef Transform<Scalar,Dim,LhsMode,LhsOptions> Lhs;
-  typedef Transform<Scalar,Dim,RhsMode,RhsOptions> Rhs;
-  typedef Transform<Scalar,Dim,Projective> ResultType;
-  static ResultType run(const Lhs& lhs, const Rhs& rhs)
-  {
-    return ResultType( lhs.matrix() * rhs.matrix() );
-  }
-};
-
-template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
-struct transform_transform_product_impl<Transform<Scalar,Dim,AffineCompact,LhsOptions>,Transform<Scalar,Dim,Projective,RhsOptions>,true >
-{
-  typedef Transform<Scalar,Dim,AffineCompact,LhsOptions> Lhs;
-  typedef Transform<Scalar,Dim,Projective,RhsOptions> Rhs;
-  typedef Transform<Scalar,Dim,Projective> ResultType;
-  static ResultType run(const Lhs& lhs, const Rhs& rhs)
-  {
-    ResultType res;
-    res.matrix().template topRows<Dim>() = lhs.matrix() * rhs.matrix();
-    res.matrix().row(Dim) = rhs.matrix().row(Dim);
-    return res;
-  }
-};
-
-template<typename Scalar, int Dim, int LhsOptions, int RhsOptions>
-struct transform_transform_product_impl<Transform<Scalar,Dim,Projective,LhsOptions>,Transform<Scalar,Dim,AffineCompact,RhsOptions>,true >
-{
-  typedef Transform<Scalar,Dim,Projective,LhsOptions> Lhs;
-  typedef Transform<Scalar,Dim,AffineCompact,RhsOptions> Rhs;
-  typedef Transform<Scalar,Dim,Projective> ResultType;
-  static ResultType run(const Lhs& lhs, const Rhs& rhs)
-  {
-    ResultType res(lhs.matrix().template leftCols<Dim>() * rhs.matrix());
-    res.matrix().col(Dim) += lhs.matrix().col(Dim);
-    return res;
-  }
-};
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_TRANSFORM_H
diff --git a/eigen/Eigen/src/Geometry/Translation.h b/eigen/Eigen/src/Geometry/Translation.h
deleted file mode 100644
index 51d9a82..0000000
--- a/eigen/Eigen/src/Geometry/Translation.h
+++ /dev/null
@@ -1,208 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.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_TRANSLATION_H
-#define EIGEN_TRANSLATION_H
-
-namespace Eigen { 
-
-/** \geometry_module \ingroup Geometry_Module
-  *
-  * \class Translation
-  *
-  * \brief Represents a translation transformation
-  *
-  * \tparam _Scalar the scalar type, i.e., the type of the coefficients.
-  * \tparam _Dim the  dimension of the space, can be a compile time value or Dynamic
-  *
-  * \note This class is not aimed to be used to store a translation transformation,
-  * but rather to make easier the constructions and updates of Transform objects.
-  *
-  * \sa class Scaling, class Transform
-  */
-template<typename _Scalar, int _Dim>
-class Translation
-{
-public:
-  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
-  /** dimension of the space */
-  enum { Dim = _Dim };
-  /** the scalar type of the coefficients */
-  typedef _Scalar Scalar;
-  /** corresponding vector type */
-  typedef Matrix<Scalar,Dim,1> VectorType;
-  /** corresponding linear transformation matrix type */
-  typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
-  /** corresponding affine transformation type */
-  typedef Transform<Scalar,Dim,Affine> AffineTransformType;
-  /** corresponding isometric transformation type */
-  typedef Transform<Scalar,Dim,Isometry> IsometryTransformType;
-
-protected:
-
-  VectorType m_coeffs;
-
-public:
-
-  /** Default constructor without initialization. */
-  EIGEN_DEVICE_FUNC Translation() {}
-  /**  */
-  EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy)
-  {
-    eigen_assert(Dim==2);
-    m_coeffs.x() = sx;
-    m_coeffs.y() = sy;
-  }
-  /**  */
-  EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
-  {
-    eigen_assert(Dim==3);
-    m_coeffs.x() = sx;
-    m_coeffs.y() = sy;
-    m_coeffs.z() = sz;
-  }
-  /** Constructs and initialize the translation transformation from a vector of translation coefficients */
-  EIGEN_DEVICE_FUNC explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
-
-  /** \brief Retruns the x-translation by value. **/
-  EIGEN_DEVICE_FUNC inline Scalar x() const { return m_coeffs.x(); }
-  /** \brief Retruns the y-translation by value. **/
-  EIGEN_DEVICE_FUNC inline Scalar y() const { return m_coeffs.y(); }
-  /** \brief Retruns the z-translation by value. **/
-  EIGEN_DEVICE_FUNC inline Scalar z() const { return m_coeffs.z(); }
-
-  /** \brief Retruns the x-translation as a reference. **/
-  EIGEN_DEVICE_FUNC inline Scalar& x() { return m_coeffs.x(); }
-  /** \brief Retruns the y-translation as a reference. **/
-  EIGEN_DEVICE_FUNC inline Scalar& y() { return m_coeffs.y(); }
-  /** \brief Retruns the z-translation as a reference. **/
-  EIGEN_DEVICE_FUNC inline Scalar& z() { return m_coeffs.z(); }
-
-  EIGEN_DEVICE_FUNC const VectorType& vector() const { return m_coeffs; }
-  EIGEN_DEVICE_FUNC VectorType& vector() { return m_coeffs; }
-
-  EIGEN_DEVICE_FUNC const VectorType& translation() const { return m_coeffs; }
-  EIGEN_DEVICE_FUNC VectorType& translation() { return m_coeffs; }
-
-  /** Concatenates two translation */
-  EIGEN_DEVICE_FUNC inline Translation operator* (const Translation& other) const
-  { return Translation(m_coeffs + other.m_coeffs); }
-
-  /** Concatenates a translation and a uniform scaling */
-  EIGEN_DEVICE_FUNC inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const;
-
-  /** Concatenates a translation and a linear transformation */
-  template<typename OtherDerived>
-  EIGEN_DEVICE_FUNC inline AffineTransformType operator* (const EigenBase<OtherDerived>& linear) const;
-
-  /** Concatenates a translation and a rotation */
-  template<typename Derived>
-  EIGEN_DEVICE_FUNC inline IsometryTransformType operator*(const RotationBase<Derived,Dim>& r) const
-  { return *this * IsometryTransformType(r); }
-
-  /** \returns the concatenation of a linear transformation \a l with the translation \a t */
-  // its a nightmare to define a templated friend function outside its declaration
-  template<typename OtherDerived> friend
-  EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear, const Translation& t)
-  {
-    AffineTransformType res;
-    res.matrix().setZero();
-    res.linear() = linear.derived();
-    res.translation() = linear.derived() * t.m_coeffs;
-    res.matrix().row(Dim).setZero();
-    res(Dim,Dim) = Scalar(1);
-    return res;
-  }
-
-  /** Concatenates a translation and a transformation */
-  template<int Mode, int Options>
-  EIGEN_DEVICE_FUNC inline Transform<Scalar,Dim,Mode> operator* (const Transform<Scalar,Dim,Mode,Options>& t) const
-  {
-    Transform<Scalar,Dim,Mode> res = t;
-    res.pretranslate(m_coeffs);
-    return res;
-  }
-
-  /** Applies translation to vector */
-  template<typename Derived>
-  inline typename internal::enable_if<Derived::IsVectorAtCompileTime,VectorType>::type
-  operator* (const MatrixBase<Derived>& vec) const
-  { return m_coeffs + vec.derived(); }
-
-  /** \returns the inverse translation (opposite) */
-  Translation inverse() const { return Translation(-m_coeffs); }
-
-  Translation& operator=(const Translation& other)
-  {
-    m_coeffs = other.m_coeffs;
-    return *this;
-  }
-
-  static const Translation Identity() { return Translation(VectorType::Zero()); }
-
-  /** \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<Translation,Translation<NewScalarType,Dim> >::type cast() const
-  { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
-
-  /** Copy constructor with scalar type conversion */
-  template<typename OtherScalarType>
-  EIGEN_DEVICE_FUNC inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
-  { m_coeffs = other.vector().template cast<Scalar>(); }
-
-  /** \returns \c true if \c *this is approximately equal to \a other, within the precision
-    * determined by \a prec.
-    *
-    * \sa MatrixBase::isApprox() */
-  EIGEN_DEVICE_FUNC bool isApprox(const Translation& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
-  { return m_coeffs.isApprox(other.m_coeffs, prec); }
-
-};
-
-/** \addtogroup Geometry_Module */
-//@{
-typedef Translation<float, 2> Translation2f;
-typedef Translation<double,2> Translation2d;
-typedef Translation<float, 3> Translation3f;
-typedef Translation<double,3> Translation3d;
-//@}
-
-template<typename Scalar, int Dim>
-EIGEN_DEVICE_FUNC inline typename Translation<Scalar,Dim>::AffineTransformType
-Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const
-{
-  AffineTransformType res;
-  res.matrix().setZero();
-  res.linear().diagonal().fill(other.factor());
-  res.translation() = m_coeffs;
-  res(Dim,Dim) = Scalar(1);
-  return res;
-}
-
-template<typename Scalar, int Dim>
-template<typename OtherDerived>
-EIGEN_DEVICE_FUNC inline typename Translation<Scalar,Dim>::AffineTransformType
-Translation<Scalar,Dim>::operator* (const EigenBase<OtherDerived>& linear) const
-{
-  AffineTransformType res;
-  res.matrix().setZero();
-  res.linear() = linear.derived();
-  res.translation() = m_coeffs;
-  res.matrix().row(Dim).setZero();
-  res(Dim,Dim) = Scalar(1);
-  return res;
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_TRANSLATION_H
diff --git a/eigen/Eigen/src/Geometry/Umeyama.h b/eigen/Eigen/src/Geometry/Umeyama.h
deleted file mode 100644
index 7e933fc..0000000
--- a/eigen/Eigen/src/Geometry/Umeyama.h
+++ /dev/null
@@ -1,166 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2009 Hauke Heibel <hauke.heibel@gmail.com>
-//
-// 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_UMEYAMA_H
-#define EIGEN_UMEYAMA_H
-
-// This file requires the user to include 
-// * Eigen/Core
-// * Eigen/LU 
-// * Eigen/SVD
-// * Eigen/Array
-
-namespace Eigen { 
-
-#ifndef EIGEN_PARSED_BY_DOXYGEN
-
-// These helpers are required since it allows to use mixed types as parameters
-// for the Umeyama. The problem with mixed parameters is that the return type
-// cannot trivially be deduced when float and double types are mixed.
-namespace internal {
-
-// Compile time return type deduction for different MatrixBase types.
-// Different means here different alignment and parameters but the same underlying
-// real scalar type.
-template<typename MatrixType, typename OtherMatrixType>
-struct umeyama_transform_matrix_type
-{
-  enum {
-    MinRowsAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(MatrixType::RowsAtCompileTime, OtherMatrixType::RowsAtCompileTime),
-
-    // When possible we want to choose some small fixed size value since the result
-    // is likely to fit on the stack. So here, EIGEN_SIZE_MIN_PREFER_DYNAMIC is not what we want.
-    HomogeneousDimension = int(MinRowsAtCompileTime) == Dynamic ? Dynamic : int(MinRowsAtCompileTime)+1
-  };
-
-  typedef Matrix<typename traits<MatrixType>::Scalar,
-    HomogeneousDimension,
-    HomogeneousDimension,
-    AutoAlign | (traits<MatrixType>::Flags & RowMajorBit ? RowMajor : ColMajor),
-    HomogeneousDimension,
-    HomogeneousDimension
-  > type;
-};
-
-}
-
-#endif
-
-/**
-* \geometry_module \ingroup Geometry_Module
-*
-* \brief Returns the transformation between two point sets.
-*
-* The algorithm is based on:
-* "Least-squares estimation of transformation parameters between two point patterns",
-* Shinji Umeyama, PAMI 1991, DOI: 10.1109/34.88573
-*
-* It estimates parameters \f$ c, \mathbf{R}, \f$ and \f$ \mathbf{t} \f$ such that
-* \f{align*}
-*   \frac{1}{n} \sum_{i=1}^n \vert\vert y_i - (c\mathbf{R}x_i + \mathbf{t}) \vert\vert_2^2
-* \f}
-* is minimized.
-*
-* The algorithm is based on the analysis of the covariance matrix
-* \f$ \Sigma_{\mathbf{x}\mathbf{y}} \in \mathbb{R}^{d \times d} \f$
-* of the input point sets \f$ \mathbf{x} \f$ and \f$ \mathbf{y} \f$ where 
-* \f$d\f$ is corresponding to the dimension (which is typically small).
-* The analysis is involving the SVD having a complexity of \f$O(d^3)\f$
-* though the actual computational effort lies in the covariance
-* matrix computation which has an asymptotic lower bound of \f$O(dm)\f$ when 
-* the input point sets have dimension \f$d \times m\f$.
-*
-* Currently the method is working only for floating point matrices.
-*
-* \todo Should the return type of umeyama() become a Transform?
-*
-* \param src Source points \f$ \mathbf{x} = \left( x_1, \hdots, x_n \right) \f$.
-* \param dst Destination points \f$ \mathbf{y} = \left( y_1, \hdots, y_n \right) \f$.
-* \param with_scaling Sets \f$ c=1 \f$ when <code>false</code> is passed.
-* \return The homogeneous transformation 
-* \f{align*}
-*   T = \begin{bmatrix} c\mathbf{R} & \mathbf{t} \\ \mathbf{0} & 1 \end{bmatrix}
-* \f}
-* minimizing the resudiual above. This transformation is always returned as an 
-* Eigen::Matrix.
-*/
-template <typename Derived, typename OtherDerived>
-typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type
-umeyama(const MatrixBase<Derived>& src, const MatrixBase<OtherDerived>& dst, bool with_scaling = true)
-{
-  typedef typename internal::umeyama_transform_matrix_type<Derived, OtherDerived>::type TransformationMatrixType;
-  typedef typename internal::traits<TransformationMatrixType>::Scalar Scalar;
-  typedef typename NumTraits<Scalar>::Real RealScalar;
-
-  EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsComplex, NUMERIC_TYPE_MUST_BE_REAL)
-  EIGEN_STATIC_ASSERT((internal::is_same<Scalar, typename internal::traits<OtherDerived>::Scalar>::value),
-    YOU_MIXED_DIFFERENT_NUMERIC_TYPES__YOU_NEED_TO_USE_THE_CAST_METHOD_OF_MATRIXBASE_TO_CAST_NUMERIC_TYPES_EXPLICITLY)
-
-  enum { Dimension = EIGEN_SIZE_MIN_PREFER_DYNAMIC(Derived::RowsAtCompileTime, OtherDerived::RowsAtCompileTime) };
-
-  typedef Matrix<Scalar, Dimension, 1> VectorType;
-  typedef Matrix<Scalar, Dimension, Dimension> MatrixType;
-  typedef typename internal::plain_matrix_type_row_major<Derived>::type RowMajorMatrixType;
-
-  const Index m = src.rows(); // dimension
-  const Index n = src.cols(); // number of measurements
-
-  // required for demeaning ...
-  const RealScalar one_over_n = RealScalar(1) / static_cast<RealScalar>(n);
-
-  // computation of mean
-  const VectorType src_mean = src.rowwise().sum() * one_over_n;
-  const VectorType dst_mean = dst.rowwise().sum() * one_over_n;
-
-  // demeaning of src and dst points
-  const RowMajorMatrixType src_demean = src.colwise() - src_mean;
-  const RowMajorMatrixType dst_demean = dst.colwise() - dst_mean;
-
-  // Eq. (36)-(37)
-  const Scalar src_var = src_demean.rowwise().squaredNorm().sum() * one_over_n;
-
-  // Eq. (38)
-  const MatrixType sigma = one_over_n * dst_demean * src_demean.transpose();
-
-  JacobiSVD<MatrixType> svd(sigma, ComputeFullU | ComputeFullV);
-
-  // Initialize the resulting transformation with an identity matrix...
-  TransformationMatrixType Rt = TransformationMatrixType::Identity(m+1,m+1);
-
-  // Eq. (39)
-  VectorType S = VectorType::Ones(m);
-
-  if  ( svd.matrixU().determinant() * svd.matrixV().determinant() < 0 )
-    S(m-1) = -1;
-
-  // Eq. (40) and (43)
-  Rt.block(0,0,m,m).noalias() = svd.matrixU() * S.asDiagonal() * svd.matrixV().transpose();
-
-  if (with_scaling)
-  {
-    // Eq. (42)
-    const Scalar c = Scalar(1)/src_var * svd.singularValues().dot(S);
-
-    // Eq. (41)
-    Rt.col(m).head(m) = dst_mean;
-    Rt.col(m).head(m).noalias() -= c*Rt.topLeftCorner(m,m)*src_mean;
-    Rt.block(0,0,m,m) *= c;
-  }
-  else
-  {
-    Rt.col(m).head(m) = dst_mean;
-    Rt.col(m).head(m).noalias() -= Rt.topLeftCorner(m,m)*src_mean;
-  }
-
-  return Rt;
-}
-
-} // end namespace Eigen
-
-#endif // EIGEN_UMEYAMA_H
diff --git a/eigen/Eigen/src/Geometry/arch/Geometry_SSE.h b/eigen/Eigen/src/Geometry/arch/Geometry_SSE.h
deleted file mode 100644
index f68cab5..0000000
--- a/eigen/Eigen/src/Geometry/arch/Geometry_SSE.h
+++ /dev/null
@@ -1,161 +0,0 @@
-// This file is part of Eigen, a lightweight C++ template library
-// for linear algebra.
-//
-// Copyright (C) 2009 Rohit Garg <rpg.314@gmail.com>
-// Copyright (C) 2009-2010 Gael Guennebaud <gael.guennebaud@inria.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_GEOMETRY_SSE_H
-#define EIGEN_GEOMETRY_SSE_H
-
-namespace Eigen { 
-
-namespace internal {
-
-template<class Derived, class OtherDerived>
-struct quat_product<Architecture::SSE, Derived, OtherDerived, float>
-{
-  enum {
-    AAlignment = traits<Derived>::Alignment,
-    BAlignment = traits<OtherDerived>::Alignment,
-    ResAlignment = traits<Quaternion<float> >::Alignment
-  };
-  static inline Quaternion<float> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
-  {
-    Quaternion<float> res;
-    const __m128 mask = _mm_setr_ps(0.f,0.f,0.f,-0.f);
-    __m128 a = _a.coeffs().template packet<AAlignment>(0);
-    __m128 b = _b.coeffs().template packet<BAlignment>(0);
-    __m128 s1 = _mm_mul_ps(vec4f_swizzle1(a,1,2,0,2),vec4f_swizzle1(b,2,0,1,2));
-    __m128 s2 = _mm_mul_ps(vec4f_swizzle1(a,3,3,3,1),vec4f_swizzle1(b,0,1,2,1));
-    pstoret<float,Packet4f,ResAlignment>(
-              &res.x(),
-              _mm_add_ps(_mm_sub_ps(_mm_mul_ps(a,vec4f_swizzle1(b,3,3,3,3)),
-                                    _mm_mul_ps(vec4f_swizzle1(a,2,0,1,0),
-                                               vec4f_swizzle1(b,1,2,0,0))),
-                         _mm_xor_ps(mask,_mm_add_ps(s1,s2))));
-    
-    return res;
-  }
-};
-
-template<class Derived>
-struct quat_conj<Architecture::SSE, Derived, float>
-{
-  enum {
-    ResAlignment = traits<Quaternion<float> >::Alignment
-  };
-  static inline Quaternion<float> run(const QuaternionBase<Derived>& q)
-  {
-    Quaternion<float> res;
-    const __m128 mask = _mm_setr_ps(-0.f,-0.f,-0.f,0.f);
-    pstoret<float,Packet4f,ResAlignment>(&res.x(), _mm_xor_ps(mask, q.coeffs().template packet<traits<Derived>::Alignment>(0)));
-    return res;
-  }
-};
-
-
-template<typename VectorLhs,typename VectorRhs>
-struct cross3_impl<Architecture::SSE,VectorLhs,VectorRhs,float,true>
-{
-  enum {
-    ResAlignment = traits<typename plain_matrix_type<VectorLhs>::type>::Alignment
-  };
-  static inline typename plain_matrix_type<VectorLhs>::type
-  run(const VectorLhs& lhs, const VectorRhs& rhs)
-  {
-    __m128 a = lhs.template packet<traits<VectorLhs>::Alignment>(0);
-    __m128 b = rhs.template packet<traits<VectorRhs>::Alignment>(0);
-    __m128 mul1=_mm_mul_ps(vec4f_swizzle1(a,1,2,0,3),vec4f_swizzle1(b,2,0,1,3));
-    __m128 mul2=_mm_mul_ps(vec4f_swizzle1(a,2,0,1,3),vec4f_swizzle1(b,1,2,0,3));
-    typename plain_matrix_type<VectorLhs>::type res;
-    pstoret<float,Packet4f,ResAlignment>(&res.x(),_mm_sub_ps(mul1,mul2));
-    return res;
-  }
-};
-
-
-
-
-template<class Derived, class OtherDerived>
-struct quat_product<Architecture::SSE, Derived, OtherDerived, double>
-{
-  enum {
-    BAlignment = traits<OtherDerived>::Alignment,
-    ResAlignment = traits<Quaternion<double> >::Alignment
-  };
-
-  static inline Quaternion<double> run(const QuaternionBase<Derived>& _a, const QuaternionBase<OtherDerived>& _b)
-  {
-  const Packet2d mask = _mm_castsi128_pd(_mm_set_epi32(0x0,0x0,0x80000000,0x0));
-
-  Quaternion<double> res;
-
-  const double* a = _a.coeffs().data();
-  Packet2d b_xy = _b.coeffs().template packet<BAlignment>(0);
-  Packet2d b_zw = _b.coeffs().template packet<BAlignment>(2);
-  Packet2d a_xx = pset1<Packet2d>(a[0]);
-  Packet2d a_yy = pset1<Packet2d>(a[1]);
-  Packet2d a_zz = pset1<Packet2d>(a[2]);
-  Packet2d a_ww = pset1<Packet2d>(a[3]);
-
-  // two temporaries:
-  Packet2d t1, t2;
-
-  /*
-   * t1 = ww*xy + yy*zw
-   * t2 = zz*xy - xx*zw
-   * res.xy = t1 +/- swap(t2)
-   */
-  t1 = padd(pmul(a_ww, b_xy), pmul(a_yy, b_zw));
-  t2 = psub(pmul(a_zz, b_xy), pmul(a_xx, b_zw));
-#ifdef EIGEN_VECTORIZE_SSE3
-  EIGEN_UNUSED_VARIABLE(mask)
-  pstoret<double,Packet2d,ResAlignment>(&res.x(), _mm_addsub_pd(t1, preverse(t2)));
-#else
-  pstoret<double,Packet2d,ResAlignment>(&res.x(), padd(t1, pxor(mask,preverse(t2))));
-#endif
-  
-  /*
-   * t1 = ww*zw - yy*xy
-   * t2 = zz*zw + xx*xy
-   * res.zw = t1 -/+ swap(t2) = swap( swap(t1) +/- t2)
-   */
-  t1 = psub(pmul(a_ww, b_zw), pmul(a_yy, b_xy));
-  t2 = padd(pmul(a_zz, b_zw), pmul(a_xx, b_xy));
-#ifdef EIGEN_VECTORIZE_SSE3
-  EIGEN_UNUSED_VARIABLE(mask)
-  pstoret<double,Packet2d,ResAlignment>(&res.z(), preverse(_mm_addsub_pd(preverse(t1), t2)));
-#else
-  pstoret<double,Packet2d,ResAlignment>(&res.z(), psub(t1, pxor(mask,preverse(t2))));
-#endif
-
-  return res;
-}
-};
-
-template<class Derived>
-struct quat_conj<Architecture::SSE, Derived, double>
-{
-  enum {
-    ResAlignment = traits<Quaternion<double> >::Alignment
-  };
-  static inline Quaternion<double> run(const QuaternionBase<Derived>& q)
-  {
-    Quaternion<double> res;
-    const __m128d mask0 = _mm_setr_pd(-0.,-0.);
-    const __m128d mask2 = _mm_setr_pd(-0.,0.);
-    pstoret<double,Packet2d,ResAlignment>(&res.x(), _mm_xor_pd(mask0, q.coeffs().template packet<traits<Derived>::Alignment>(0)));
-    pstoret<double,Packet2d,ResAlignment>(&res.z(), _mm_xor_pd(mask2, q.coeffs().template packet<traits<Derived>::Alignment>(2)));
-    return res;
-  }
-};
-
-} // end namespace internal
-
-} // end namespace Eigen
-
-#endif // EIGEN_GEOMETRY_SSE_H