Translation.h

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra.
00003 //
00004 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
00005 //
00006 // This Source Code Form is subject to the terms of the Mozilla
00007 // Public License v. 2.0. If a copy of the MPL was not distributed
00008 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
00009 
00010 #ifndef EIGEN_TRANSLATION_H
00011 #define EIGEN_TRANSLATION_H
00012 
00013 namespace Eigen { 
00014 
00015 /** \geometry_module \ingroup Geometry_Module
00016   *
00017   * \class Translation
00018   *
00019   * \brief Represents a translation transformation
00020   *
00021   * \param _Scalar the scalar type, i.e., the type of the coefficients.
00022   * \param _Dim the  dimension of the space, can be a compile time value or Dynamic
00023   *
00024   * \note This class is not aimed to be used to store a translation transformation,
00025   * but rather to make easier the constructions and updates of Transform objects.
00026   *
00027   * \sa class Scaling, class Transform
00028   */
00029 template<typename _Scalar, int _Dim>
00030 class Translation 
00031 {
00032 public:
00033   EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
00034   /** dimension of the space */
00035   enum { Dim = _Dim };
00036   /** the scalar type of the coefficients */
00037   typedef _Scalar Scalar;
00038   /** corresponding vector type */
00039   typedef Matrix<Scalar,Dim,1>  VectorType;
00040   /** corresponding linear transformation matrix type */
00041   typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
00042   /** corresponding affine transformation type */
00043   typedef Transform<Scalar,Dim,Affine>  AffineTransformType;
00044   /** corresponding isometric transformation type */
00045   typedef Transform<Scalar,Dim,Isometry>  IsometryTransformType;
00046 
00047 protected:
00048 
00049   VectorType  m_coeffs;
00050 
00051 public:
00052 
00053   /** Default constructor without initialization. */
00054   Translation() {}
00055   /**  */
00056   inline Translation(const Scalar& sx, const Scalar& sy)
00057   {
00058     eigen_assert(Dim==2);
00059     m_coeffs.x() = sx;
00060     m_coeffs.y() = sy;
00061   }
00062   /**  */
00063   inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
00064   {
00065     eigen_assert(Dim==3);
00066     m_coeffs.x() = sx;
00067     m_coeffs.y() = sy;
00068     m_coeffs.z() = sz;
00069   }
00070   /** Constructs and initialize the translation transformation from a vector of translation coefficients */
00071   explicit inline Translation(const VectorType & vector) : m_coeffs(vector) {}
00072 
00073   /** \brief Retruns the x-translation by value. **/
00074   inline Scalar x() const { return m_coeffs.x(); }
00075   /** \brief Retruns the y-translation by value. **/
00076   inline Scalar y() const { return m_coeffs.y(); }
00077   /** \brief Retruns the z-translation by value. **/
00078   inline Scalar z() const { return m_coeffs.z(); }
00079 
00080   /** \brief Retruns the x-translation as a reference. **/
00081   inline Scalar& x() { return m_coeffs.x(); }
00082   /** \brief Retruns the y-translation as a reference. **/
00083   inline Scalar& y() { return m_coeffs.y(); }
00084   /** \brief Retruns the z-translation as a reference. **/
00085   inline Scalar& z() { return m_coeffs.z(); }
00086 
00087   const VectorType& vector() const { return m_coeffs; }
00088   VectorType& vector() { return m_coeffs; }
00089 
00090   const VectorType& translation() const { return m_coeffs; }
00091   VectorType& translation() { return m_coeffs; }
00092 
00093   /** Concatenates two translation */
00094   inline Translation  operator* (const Translation & other) const
00095   { return Translation(m_coeffs + other.m_coeffs); }
00096 
00097   /** Concatenates a translation and a uniform scaling */
00098   inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const;
00099 
00100   /** Concatenates a translation and a linear transformation */
00101   template<typename OtherDerived>
00102   inline AffineTransformType operator* (const EigenBase<OtherDerived>& linear) const;
00103 
00104   /** Concatenates a translation and a rotation */
00105   template<typename Derived>
00106   inline IsometryTransformType  operator*(const RotationBase<Derived,Dim>& r) const
00107   { return *this * IsometryTransformType(r); }
00108 
00109   /** \returns the concatenation of a linear transformation \a l with the translation \a t */
00110   // its a nightmare to define a templated friend function outside its declaration
00111   template<typename OtherDerived> friend
00112   inline AffineTransformType  operator*(const EigenBase<OtherDerived>& linear, const Translation & t)
00113   {
00114     AffineTransformType  res;
00115     res.matrix ().setZero();
00116     res.linear () = linear.derived ();
00117     res.translation () = linear.derived () * t.m_coeffs;
00118     res.matrix ().row(Dim).setZero();
00119     res(Dim,Dim) = Scalar(1);
00120     return res;
00121   }
00122 
00123   /** Concatenates a translation and a transformation */
00124   template<int Mode, int Options>
00125   inline Transform<Scalar,Dim,Mode>  operator* (const Transform<Scalar,Dim,Mode,Options> & t) const
00126   {
00127     Transform<Scalar,Dim,Mode>  res = t;
00128     res.pretranslate(m_coeffs);
00129     return res;
00130   }
00131 
00132   /** Applies translation to vector */
00133   inline VectorType  operator* (const VectorType & other) const
00134   { return m_coeffs + other; }
00135 
00136   /** \returns the inverse translation (opposite) */
00137   Translation  inverse () const { return Translation(-m_coeffs); }
00138 
00139   Translation & operator=(const Translation & other)
00140   {
00141     m_coeffs = other.m_coeffs;
00142     return *this;
00143   }
00144 
00145   static const Translation Identity() { return Translation(VectorType::Zero()); }
00146 
00147   /** \returns \c *this with scalar type casted to \a NewScalarType
00148     *
00149     * Note that if \a NewScalarType is equal to the current scalar type of \c *this
00150     * then this function smartly returns a const reference to \c *this.
00151     */
00152   template<typename NewScalarType>
00153   inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast () const
00154   { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
00155 
00156   /** Copy constructor with scalar type conversion */
00157   template<typename OtherScalarType>
00158   inline explicit Translation(const Translation<OtherScalarType,Dim> & other)
00159   { m_coeffs = other.vector().template cast<Scalar>(); }
00160 
00161   /** \returns \c true if \c *this is approximately equal to \a other, within the precision
00162     * determined by \a prec.
00163     *
00164     * \sa MatrixBase::isApprox() */
00165   bool isApprox (const Translation & other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
00166   { return m_coeffs.isApprox(other.m_coeffs, prec); }
00167 
00168 };
00169 
00170 /** \addtogroup Geometry_Module */
00171 //@{
00172 typedef Translation<float, 2> Translation2f;
00173 typedef Translation<double,2> Translation2d;
00174 typedef Translation<float, 3> Translation3f;
00175 typedef Translation<double,3> Translation3d;
00176 //@}
00177 
00178 template<typename Scalar, int Dim>
00179 inline typename Translation<Scalar,Dim>::AffineTransformType
00180 Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const
00181 {
00182   AffineTransformType  res;
00183   res.matrix ().setZero();
00184   res.linear ().diagonal().fill(other.factor());
00185   res.translation () = m_coeffs;
00186   res(Dim,Dim) = Scalar(1);
00187   return res;
00188 }
00189 
00190 template<typename Scalar, int Dim>
00191 template<typename OtherDerived>
00192 inline typename Translation<Scalar,Dim>::AffineTransformType 
00193 Translation<Scalar,Dim>::operator* (const EigenBase<OtherDerived>& linear) const
00194 {
00195   AffineTransformType  res;
00196   res.matrix ().setZero();
00197   res.linear () = linear.derived ();
00198   res.translation () = m_coeffs;
00199   res.matrix ().row(Dim).setZero();
00200   res(Dim,Dim) = Scalar(1);
00201   return res;
00202 }
00203 
00204 } // end namespace Eigen
00205 
00206 #endif // EIGEN_TRANSLATION_H