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diff --git a/eigen/Eigen/src/Eigen2Support/Geometry/Transform.h b/eigen/Eigen/src/Eigen2Support/Geometry/Transform.h
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+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
+// Copyright (C) 2009 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/.
+
+// no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway
+
+namespace Eigen { 
+
+// Note that we have to pass Dim and HDim because it is not allowed to use a template
+// parameter to define a template specialization. To be more precise, in the following
+// specializations, it is not allowed to use Dim+1 instead of HDim.
+template< typename Other,
+          int Dim,
+          int HDim,
+          int OtherRows=Other::RowsAtCompileTime,
+          int OtherCols=Other::ColsAtCompileTime>
+struct ei_transform_product_impl;
+
+/** \geometry_module \ingroup Geometry_Module
+  *
+  * \class Transform
+  *
+  * \brief Represents an homogeneous transformation in a N dimensional space
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients
+  * \param _Dim the dimension of the space
+  *
+  * The homography is internally represented and stored as a (Dim+1)^2 matrix which
+  * is available through the matrix() method.
+  *
+  * Conversion methods from/to Qt's QMatrix and QTransform are available if the
+  * preprocessor token EIGEN_QT_SUPPORT is defined.
+  *
+  * \sa class Matrix, class Quaternion
+  */
+template<typename _Scalar, int _Dim>
+class Transform
+{
+public:
+  EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim==Dynamic ? Dynamic : (_Dim+1)*(_Dim+1))
+  enum {
+    Dim = _Dim,     ///< space dimension in which the transformation holds
+    HDim = _Dim+1   ///< size of a respective homogeneous vector
+  };
+  /** the scalar type of the coefficients */
+  typedef _Scalar Scalar;
+  /** type of the matrix used to represent the transformation */
+  typedef Matrix<Scalar,HDim,HDim> MatrixType;
+  /** type of the matrix used to represent the linear part of the transformation */
+  typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
+  /** type of read/write reference to the linear part of the transformation */
+  typedef Block<MatrixType,Dim,Dim> LinearPart;
+  /** type of read/write reference to the linear part of the transformation */
+  typedef const Block<const MatrixType,Dim,Dim> ConstLinearPart;
+  /** 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> TranslationPart;
+  /** type of a read/write reference to the translation part of the rotation */
+  typedef const Block<const MatrixType,Dim,1> ConstTranslationPart;
+  /** corresponding translation type */
+  typedef Translation<Scalar,Dim> TranslationType;
+  /** corresponding scaling transformation type */
+  typedef Scaling<Scalar,Dim> ScalingType;
+
+protected:
+
+  MatrixType m_matrix;
+
+public:
+
+  /** Default constructor without initialization of the coefficients. */
+  inline Transform() { }
+
+  inline Transform(const Transform& other)
+  {
+    m_matrix = other.m_matrix;
+  }
+
+  inline explicit Transform(const TranslationType& t) { *this = t; }
+  inline explicit Transform(const ScalingType& s) { *this = s; }
+  template<typename Derived>
+  inline explicit Transform(const RotationBase<Derived, Dim>& r) { *this = r; }
+
+  inline Transform& operator=(const Transform& other)
+  { m_matrix = other.m_matrix; return *this; }
+
+  template<typename OtherDerived, bool BigMatrix> // MSVC 2005 will commit suicide if BigMatrix has a default value
+  struct construct_from_matrix
+  {
+    static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
+    {
+      transform->matrix() = other;
+    }
+  };
+
+  template<typename OtherDerived> struct construct_from_matrix<OtherDerived, true>
+  {
+    static inline void run(Transform *transform, const MatrixBase<OtherDerived>& other)
+    {
+      transform->linear() = other;
+      transform->translation().setZero();
+      transform->matrix()(Dim,Dim) = Scalar(1);
+      transform->matrix().template block<1,Dim>(Dim,0).setZero();
+    }
+  };
+
+  /** Constructs and initializes a transformation from a Dim^2 or a (Dim+1)^2 matrix. */
+  template<typename OtherDerived>
+  inline explicit Transform(const MatrixBase<OtherDerived>& other)
+  {
+    construct_from_matrix<OtherDerived, int(OtherDerived::RowsAtCompileTime) == Dim>::run(this, other);
+  }
+
+  /** Set \c *this from a (Dim+1)^2 matrix. */
+  template<typename OtherDerived>
+  inline Transform& operator=(const MatrixBase<OtherDerived>& other)
+  { m_matrix = other; 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
+
+  /** shortcut for m_matrix(row,col);
+    * \sa MatrixBase::operaror(int,int) const */
+  inline Scalar operator() (int row, int col) const { return m_matrix(row,col); }
+  /** shortcut for m_matrix(row,col);
+    * \sa MatrixBase::operaror(int,int) */
+  inline Scalar& operator() (int row, int col) { return m_matrix(row,col); }
+
+  /** \returns a read-only expression of the transformation matrix */
+  inline const MatrixType& matrix() const { return m_matrix; }
+  /** \returns a writable expression of the transformation matrix */
+  inline MatrixType& matrix() { return m_matrix; }
+
+  /** \returns a read-only expression of the linear (linear) part of the transformation */
+  inline ConstLinearPart linear() const { return m_matrix.template block<Dim,Dim>(0,0); }
+  /** \returns a writable expression of the linear (linear) part of the transformation */
+  inline LinearPart linear() { return m_matrix.template block<Dim,Dim>(0,0); }
+
+  /** \returns a read-only expression of the translation vector of the transformation */
+  inline ConstTranslationPart translation() const { return m_matrix.template block<Dim,1>(0,Dim); }
+  /** \returns a writable expression of the translation vector of the transformation */
+  inline TranslationPart translation() { return m_matrix.template block<Dim,1>(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 might be either:
+  * \li a vector of size Dim,
+  * \li an homogeneous vector of size Dim+1,
+  * \li a transformation matrix of size Dim+1 x Dim+1.
+  */
+  // note: this function is defined here because some compilers cannot find the respective declaration
+  template<typename OtherDerived>
+  inline const typename ei_transform_product_impl<OtherDerived,_Dim,_Dim+1>::ResultType
+  operator * (const MatrixBase<OtherDerived> &other) const
+  { return ei_transform_product_impl<OtherDerived,Dim,HDim>::run(*this,other.derived()); }
+
+  /** \returns the product expression of a transformation matrix \a a times a transform \a b
+    * The transformation matrix \a a must have a Dim+1 x Dim+1 sizes. */
+  template<typename OtherDerived>
+  friend inline const typename ProductReturnType<OtherDerived,MatrixType>::Type
+  operator * (const MatrixBase<OtherDerived> &a, const Transform &b)
+  { return a.derived() * b.matrix(); }
+
+  /** Contatenates two transformations */
+  inline const Transform
+  operator * (const Transform& other) const
+  { return Transform(m_matrix * other.matrix()); }
+
+  /** \sa MatrixBase::setIdentity() */
+  void setIdentity() { m_matrix.setIdentity(); }
+  static const typename MatrixType::IdentityReturnType Identity()
+  {
+    return MatrixType::Identity();
+  }
+
+  template<typename OtherDerived>
+  inline Transform& scale(const MatrixBase<OtherDerived> &other);
+
+  template<typename OtherDerived>
+  inline Transform& prescale(const MatrixBase<OtherDerived> &other);
+
+  inline Transform& scale(Scalar s);
+  inline Transform& prescale(Scalar s);
+
+  template<typename OtherDerived>
+  inline Transform& translate(const MatrixBase<OtherDerived> &other);
+
+  template<typename OtherDerived>
+  inline Transform& pretranslate(const MatrixBase<OtherDerived> &other);
+
+  template<typename RotationType>
+  inline Transform& rotate(const RotationType& rotation);
+
+  template<typename RotationType>
+  inline Transform& prerotate(const RotationType& rotation);
+
+  Transform& shear(Scalar sx, Scalar sy);
+  Transform& preshear(Scalar sx, Scalar sy);
+
+  inline Transform& operator=(const TranslationType& t);
+  inline Transform& operator*=(const TranslationType& t) { return translate(t.vector()); }
+  inline Transform operator*(const TranslationType& t) const;
+
+  inline Transform& operator=(const ScalingType& t);
+  inline Transform& operator*=(const ScalingType& s) { return scale(s.coeffs()); }
+  inline Transform operator*(const ScalingType& s) const;
+  friend inline Transform operator*(const LinearMatrixType& mat, const Transform& t)
+  {
+    Transform res = t;
+    res.matrix().row(Dim) = t.matrix().row(Dim);
+    res.matrix().template block<Dim,HDim>(0,0) = (mat * t.matrix().template block<Dim,HDim>(0,0)).lazy();
+    return res;
+  }
+
+  template<typename Derived>
+  inline Transform& operator=(const RotationBase<Derived,Dim>& r);
+  template<typename Derived>
+  inline Transform& operator*=(const RotationBase<Derived,Dim>& r) { return rotate(r.toRotationMatrix()); }
+  template<typename Derived>
+  inline Transform operator*(const RotationBase<Derived,Dim>& r) const;
+
+  LinearMatrixType rotation() const;
+  template<typename RotationMatrixType, typename ScalingMatrixType>
+  void computeRotationScaling(RotationMatrixType *rotation, ScalingMatrixType *scaling) const;
+  template<typename ScalingMatrixType, typename RotationMatrixType>
+  void computeScalingRotation(ScalingMatrixType *scaling, RotationMatrixType *rotation) const;
+
+  template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+  Transform& fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+    const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale);
+
+  inline const MatrixType inverse(TransformTraits traits = Affine) const;
+
+  /** \returns a const pointer to the column major internal matrix */
+  const Scalar* data() const { return m_matrix.data(); }
+  /** \returns a non-const pointer to the column major internal matrix */
+  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>
+  inline typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type cast() const
+  { return typename internal::cast_return_type<Transform,Transform<NewScalarType,Dim> >::type(*this); }
+
+  /** Copy constructor with scalar type conversion */
+  template<typename OtherScalarType>
+  inline explicit Transform(const Transform<OtherScalarType,Dim>& other)
+  { 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() */
+  bool isApprox(const Transform& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
+  { return m_matrix.isApprox(other.m_matrix, prec); }
+
+  #ifdef EIGEN_TRANSFORM_PLUGIN
+  #include EIGEN_TRANSFORM_PLUGIN
+  #endif
+
+protected:
+
+};
+
+/** \ingroup Geometry_Module */
+typedef Transform<float,2> Transform2f;
+/** \ingroup Geometry_Module */
+typedef Transform<float,3> Transform3f;
+/** \ingroup Geometry_Module */
+typedef Transform<double,2> Transform2d;
+/** \ingroup Geometry_Module */
+typedef Transform<double,3> Transform3d;
+
+/**************************
+*** Optional QT support ***
+**************************/
+
+#ifdef EIGEN_QT_SUPPORT
+/** Initialises \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>
+Transform<Scalar,Dim>::Transform(const QMatrix& other)
+{
+  *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>
+Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QMatrix& other)
+{
+  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+  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 convertion 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>
+QMatrix Transform<Scalar,Dim>::toQMatrix(void) const
+{
+  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));
+}
+
+/** Initialises \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>
+Transform<Scalar,Dim>::Transform(const QTransform& other)
+{
+  *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>
+Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const QTransform& other)
+{
+  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+  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>
+QTransform Transform<Scalar,Dim>::toQTransform(void) const
+{
+  EIGEN_STATIC_ASSERT(Dim==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+  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>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::scale(const MatrixBase<OtherDerived> &other)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+  linear() = (linear() * other.asDiagonal()).lazy();
+  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>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::scale(Scalar s)
+{
+  linear() *= 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>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::prescale(const MatrixBase<OtherDerived> &other)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+  m_matrix.template block<Dim,HDim>(0,0) = (other.asDiagonal() * m_matrix.template block<Dim,HDim>(0,0)).lazy();
+  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>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::prescale(Scalar s)
+{
+  m_matrix.template corner<Dim,HDim>(TopLeft) *= 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>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::translate(const MatrixBase<OtherDerived> &other)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+  translation() += linear() * 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>
+template<typename OtherDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::pretranslate(const MatrixBase<OtherDerived> &other)
+{
+  EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(OtherDerived,int(Dim))
+  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 ei_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>
+template<typename RotationType>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::rotate(const RotationType& rotation)
+{
+  linear() *= ei_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>
+template<typename RotationType>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::prerotate(const RotationType& rotation)
+{
+  m_matrix.template block<Dim,HDim>(0,0) = ei_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>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::shear(Scalar sx, Scalar sy)
+{
+  EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+  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>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::preshear(Scalar sx, Scalar sy)
+{
+  EIGEN_STATIC_ASSERT(int(Dim)==2, YOU_MADE_A_PROGRAMMING_MISTAKE)
+  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>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const TranslationType& t)
+{
+  linear().setIdentity();
+  translation() = t.vector();
+  m_matrix.template block<1,Dim>(Dim,0).setZero();
+  m_matrix(Dim,Dim) = Scalar(1);
+  return *this;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const TranslationType& t) const
+{
+  Transform res = *this;
+  res.translate(t.vector());
+  return res;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const ScalingType& s)
+{
+  m_matrix.setZero();
+  linear().diagonal() = s.coeffs();
+  m_matrix.coeffRef(Dim,Dim) = Scalar(1);
+  return *this;
+}
+
+template<typename Scalar, int Dim>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::operator*(const ScalingType& s) const
+{
+  Transform res = *this;
+  res.scale(s.coeffs());
+  return res;
+}
+
+template<typename Scalar, int Dim>
+template<typename Derived>
+inline Transform<Scalar,Dim>& Transform<Scalar,Dim>::operator=(const RotationBase<Derived,Dim>& r)
+{
+  linear() = ei_toRotationMatrix<Scalar,Dim>(r);
+  translation().setZero();
+  m_matrix.template block<1,Dim>(Dim,0).setZero();
+  m_matrix.coeffRef(Dim,Dim) = Scalar(1);
+  return *this;
+}
+
+template<typename Scalar, int Dim>
+template<typename Derived>
+inline Transform<Scalar,Dim> Transform<Scalar,Dim>::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
+  * \nonstableyet
+  *
+  * \svd_module
+  *
+  * \sa computeRotationScaling(), computeScalingRotation(), class SVD
+  */
+template<typename Scalar, int Dim>
+typename Transform<Scalar,Dim>::LinearMatrixType
+Transform<Scalar,Dim>::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.
+  *
+  * \nonstableyet
+  *
+  * \svd_module
+  *
+  * \sa computeScalingRotation(), rotation(), class SVD
+  */
+template<typename Scalar, int Dim>
+template<typename RotationMatrixType, typename ScalingMatrixType>
+void Transform<Scalar,Dim>::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
+  Matrix<Scalar, Dim, 1> sv(svd.singularValues());
+  sv.coeffRef(0) *= x;
+  if(scaling)
+  {
+    scaling->noalias() = svd.matrixV() * sv.asDiagonal() * svd.matrixV().adjoint();
+  }
+  if(rotation)
+  {
+    LinearMatrixType m(svd.matrixU());
+    m.col(0) /= x;
+    rotation->noalias() = m * svd.matrixV().adjoint();
+  }
+}
+
+/** 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.
+  *
+  * \nonstableyet
+  *
+  * \svd_module
+  *
+  * \sa computeRotationScaling(), rotation(), class SVD
+  */
+template<typename Scalar, int Dim>
+template<typename ScalingMatrixType, typename RotationMatrixType>
+void Transform<Scalar,Dim>::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
+  Matrix<Scalar, Dim, 1> sv(svd.singularValues());
+  sv.coeffRef(0) *= x;
+  if(scaling)
+  {
+    scaling->noalias() = svd.matrixU() * sv.asDiagonal() * svd.matrixU().adjoint();
+  }
+  if(rotation)
+  {
+    LinearMatrixType m(svd.matrixU());
+    m.col(0) /= x;
+    rotation->noalias() = 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>
+template<typename PositionDerived, typename OrientationType, typename ScaleDerived>
+Transform<Scalar,Dim>&
+Transform<Scalar,Dim>::fromPositionOrientationScale(const MatrixBase<PositionDerived> &position,
+  const OrientationType& orientation, const MatrixBase<ScaleDerived> &scale)
+{
+  linear() = ei_toRotationMatrix<Scalar,Dim>(orientation);
+  linear() *= scale.asDiagonal();
+  translation() = position;
+  m_matrix.template block<1,Dim>(Dim,0).setZero();
+  m_matrix(Dim,Dim) = Scalar(1);
+  return *this;
+}
+
+/** \nonstableyet
+  *
+  * \returns the inverse transformation matrix according to some given knowledge
+  * on \c *this.
+  *
+  * \param traits allows to optimize the inversion process when the transformion
+  * is known to be not a general transformation. 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 is the default, the last row is assumed to be [0 ... 0 1]
+  *  - Isometry if the transformation is only a concatenations of translations
+  *    and rotations.
+  *
+  * \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>
+inline const typename Transform<Scalar,Dim>::MatrixType
+Transform<Scalar,Dim>::inverse(TransformTraits traits) const
+{
+  if (traits == Projective)
+  {
+    return m_matrix.inverse();
+  }
+  else
+  {
+    MatrixType res;
+    if (traits == Affine)
+    {
+      res.template corner<Dim,Dim>(TopLeft) = linear().inverse();
+    }
+    else if (traits == Isometry)
+    {
+      res.template corner<Dim,Dim>(TopLeft) = linear().transpose();
+    }
+    else
+    {
+      ei_assert("invalid traits value in Transform::inverse()");
+    }
+    // translation and remaining parts
+    res.template corner<Dim,1>(TopRight) = - res.template corner<Dim,Dim>(TopLeft) * translation();
+    res.template corner<1,Dim>(BottomLeft).setZero();
+    res.coeffRef(Dim,Dim) = Scalar(1);
+    return res;
+  }
+}
+
+/*****************************************************
+*** Specializations of operator* with a MatrixBase ***
+*****************************************************/
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, HDim,HDim>
+{
+  typedef Transform<typename Other::Scalar,Dim> TransformType;
+  typedef typename TransformType::MatrixType MatrixType;
+  typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+  static ResultType run(const TransformType& tr, const Other& other)
+  { return tr.matrix() * other; }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, Dim,Dim>
+{
+  typedef Transform<typename Other::Scalar,Dim> TransformType;
+  typedef typename TransformType::MatrixType MatrixType;
+  typedef TransformType ResultType;
+  static ResultType run(const TransformType& tr, const Other& other)
+  {
+    TransformType res;
+    res.translation() = tr.translation();
+    res.matrix().row(Dim) = tr.matrix().row(Dim);
+    res.linear() = (tr.linear() * other).lazy();
+    return res;
+  }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, HDim,1>
+{
+  typedef Transform<typename Other::Scalar,Dim> TransformType;
+  typedef typename TransformType::MatrixType MatrixType;
+  typedef typename ProductReturnType<MatrixType,Other>::Type ResultType;
+  static ResultType run(const TransformType& tr, const Other& other)
+  { return tr.matrix() * other; }
+};
+
+template<typename Other, int Dim, int HDim>
+struct ei_transform_product_impl<Other,Dim,HDim, Dim,1>
+{
+  typedef typename Other::Scalar Scalar;
+  typedef Transform<Scalar,Dim> TransformType;
+  typedef Matrix<Scalar,Dim,1> ResultType;
+  static ResultType run(const TransformType& tr, const Other& other)
+  { return ((tr.linear() * other) + tr.translation())
+          * (Scalar(1) / ( (tr.matrix().template block<1,Dim>(Dim,0) * other).coeff(0) + tr.matrix().coeff(Dim,Dim))); }
+};
+
+} // end namespace Eigen