1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #ifndef EIGEN_TRANSLATION_H 11 #define EIGEN_TRANSLATION_H 12 13 namespace Eigen { 14 15 /** \geometry_module \ingroup Geometry_Module 16 * 17 * \class Translation 18 * 19 * \brief Represents a translation transformation 20 * 21 * \param _Scalar the scalar type, i.e., the type of the coefficients. 22 * \param _Dim the dimension of the space, can be a compile time value or Dynamic 23 * 24 * \note This class is not aimed to be used to store a translation transformation, 25 * but rather to make easier the constructions and updates of Transform objects. 26 * 27 * \sa class Scaling, class Transform 28 */ 29 template<typename _Scalar, int _Dim> 30 class Translation 31 { 32 public: 33 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim) 34 /** dimension of the space */ 35 enum { Dim = _Dim }; 36 /** the scalar type of the coefficients */ 37 typedef _Scalar Scalar; 38 /** corresponding vector type */ 39 typedef Matrix<Scalar,Dim,1> VectorType; 40 /** corresponding linear transformation matrix type */ 41 typedef Matrix<Scalar,Dim,Dim> LinearMatrixType; 42 /** corresponding affine transformation type */ 43 typedef Transform<Scalar,Dim,Affine> AffineTransformType; 44 /** corresponding isometric transformation type */ 45 typedef Transform<Scalar,Dim,Isometry> IsometryTransformType; 46 47 protected: 48 49 VectorType m_coeffs; 50 51 public: 52 53 /** Default constructor without initialization. */ Translation()54 Translation() {} 55 /** */ Translation(const Scalar & sx,const Scalar & sy)56 inline Translation(const Scalar& sx, const Scalar& sy) 57 { 58 eigen_assert(Dim==2); 59 m_coeffs.x() = sx; 60 m_coeffs.y() = sy; 61 } 62 /** */ Translation(const Scalar & sx,const Scalar & sy,const Scalar & sz)63 inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz) 64 { 65 eigen_assert(Dim==3); 66 m_coeffs.x() = sx; 67 m_coeffs.y() = sy; 68 m_coeffs.z() = sz; 69 } 70 /** Constructs and initialize the translation transformation from a vector of translation coefficients */ Translation(const VectorType & vector)71 explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {} 72 73 /** \brief Retruns the x-translation by value. **/ x()74 inline Scalar x() const { return m_coeffs.x(); } 75 /** \brief Retruns the y-translation by value. **/ y()76 inline Scalar y() const { return m_coeffs.y(); } 77 /** \brief Retruns the z-translation by value. **/ z()78 inline Scalar z() const { return m_coeffs.z(); } 79 80 /** \brief Retruns the x-translation as a reference. **/ x()81 inline Scalar& x() { return m_coeffs.x(); } 82 /** \brief Retruns the y-translation as a reference. **/ y()83 inline Scalar& y() { return m_coeffs.y(); } 84 /** \brief Retruns the z-translation as a reference. **/ z()85 inline Scalar& z() { return m_coeffs.z(); } 86 vector()87 const VectorType& vector() const { return m_coeffs; } vector()88 VectorType& vector() { return m_coeffs; } 89 translation()90 const VectorType& translation() const { return m_coeffs; } translation()91 VectorType& translation() { return m_coeffs; } 92 93 /** Concatenates two translation */ 94 inline Translation operator* (const Translation& other) const 95 { return Translation(m_coeffs + other.m_coeffs); } 96 97 /** Concatenates a translation and a uniform scaling */ 98 inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const; 99 100 /** Concatenates a translation and a linear transformation */ 101 template<typename OtherDerived> 102 inline AffineTransformType operator* (const EigenBase<OtherDerived>& linear) const; 103 104 /** Concatenates a translation and a rotation */ 105 template<typename Derived> 106 inline IsometryTransformType operator*(const RotationBase<Derived,Dim>& r) const 107 { return *this * IsometryTransformType(r); } 108 109 /** \returns the concatenation of a linear transformation \a l with the translation \a t */ 110 // its a nightmare to define a templated friend function outside its declaration 111 template<typename OtherDerived> friend 112 inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear, const Translation& t) 113 { 114 AffineTransformType res; 115 res.matrix().setZero(); 116 res.linear() = linear.derived(); 117 res.translation() = linear.derived() * t.m_coeffs; 118 res.matrix().row(Dim).setZero(); 119 res(Dim,Dim) = Scalar(1); 120 return res; 121 } 122 123 /** Concatenates a translation and a transformation */ 124 template<int Mode, int Options> 125 inline Transform<Scalar,Dim,Mode> operator* (const Transform<Scalar,Dim,Mode,Options>& t) const 126 { 127 Transform<Scalar,Dim,Mode> res = t; 128 res.pretranslate(m_coeffs); 129 return res; 130 } 131 132 /** Applies translation to vector */ 133 inline VectorType operator* (const VectorType& other) const 134 { return m_coeffs + other; } 135 136 /** \returns the inverse translation (opposite) */ inverse()137 Translation inverse() const { return Translation(-m_coeffs); } 138 139 Translation& operator=(const Translation& other) 140 { 141 m_coeffs = other.m_coeffs; 142 return *this; 143 } 144 Identity()145 static const Translation Identity() { return Translation(VectorType::Zero()); } 146 147 /** \returns \c *this with scalar type casted to \a NewScalarType 148 * 149 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 150 * then this function smartly returns a const reference to \c *this. 151 */ 152 template<typename NewScalarType> cast()153 inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const 154 { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); } 155 156 /** Copy constructor with scalar type conversion */ 157 template<typename OtherScalarType> Translation(const Translation<OtherScalarType,Dim> & other)158 inline explicit Translation(const Translation<OtherScalarType,Dim>& other) 159 { m_coeffs = other.vector().template cast<Scalar>(); } 160 161 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 162 * determined by \a prec. 163 * 164 * \sa MatrixBase::isApprox() */ 165 bool isApprox(const Translation& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const 166 { return m_coeffs.isApprox(other.m_coeffs, prec); } 167 168 }; 169 170 /** \addtogroup Geometry_Module */ 171 //@{ 172 typedef Translation<float, 2> Translation2f; 173 typedef Translation<double,2> Translation2d; 174 typedef Translation<float, 3> Translation3f; 175 typedef Translation<double,3> Translation3d; 176 //@} 177 178 template<typename Scalar, int Dim> 179 inline typename Translation<Scalar,Dim>::AffineTransformType 180 Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const 181 { 182 AffineTransformType res; 183 res.matrix().setZero(); 184 res.linear().diagonal().fill(other.factor()); 185 res.translation() = m_coeffs; 186 res(Dim,Dim) = Scalar(1); 187 return res; 188 } 189 190 template<typename Scalar, int Dim> 191 template<typename OtherDerived> 192 inline typename Translation<Scalar,Dim>::AffineTransformType 193 Translation<Scalar,Dim>::operator* (const EigenBase<OtherDerived>& linear) const 194 { 195 AffineTransformType res; 196 res.matrix().setZero(); 197 res.linear() = linear.derived(); 198 res.translation() = m_coeffs; 199 res.matrix().row(Dim).setZero(); 200 res(Dim,Dim) = Scalar(1); 201 return res; 202 } 203 204 } // end namespace Eigen 205 206 #endif // EIGEN_TRANSLATION_H 207