don't index Eigen

1 files changed, 0 insertions, 1542 deletions

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