text: // 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
  