1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. Eigen itself is part of the KDE project. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <g.gael (at) free.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 // no include guard, we'll include this twice from All.h from Eigen2Support, and it's internal anyway 11 12 namespace Eigen { 13 14 /** \geometry_module \ingroup Geometry_Module 15 * 16 * \class Translation 17 * 18 * \brief Represents a translation transformation 19 * 20 * \param _Scalar the scalar type, i.e., the type of the coefficients. 21 * \param _Dim the dimension of the space, can be a compile time value or Dynamic 22 * 23 * \note This class is not aimed to be used to store a translation transformation, 24 * but rather to make easier the constructions and updates of Transform objects. 25 * 26 * \sa class Scaling, class Transform 27 */ 28 template<typename _Scalar, int _Dim> 29 class Translation 30 { 31 public: 32 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim) 33 /** dimension of the space */ 34 enum { Dim = _Dim }; 35 /** the scalar type of the coefficients */ 36 typedef _Scalar Scalar; 37 /** corresponding vector type */ 38 typedef Matrix<Scalar,Dim,1> VectorType; 39 /** corresponding linear transformation matrix type */ 40 typedef Matrix<Scalar,Dim,Dim> LinearMatrixType; 41 /** corresponding scaling transformation type */ 42 typedef Scaling<Scalar,Dim> ScalingType; 43 /** corresponding affine transformation type */ 44 typedef Transform<Scalar,Dim> TransformType; 45 46 protected: 47 48 VectorType m_coeffs; 49 50 public: 51 52 /** Default constructor without initialization. */ 53 Translation() {} 54 /** */ 55 inline Translation(const Scalar& sx, const Scalar& sy) 56 { 57 ei_assert(Dim==2); 58 m_coeffs.x() = sx; 59 m_coeffs.y() = sy; 60 } 61 /** */ 62 inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz) 63 { 64 ei_assert(Dim==3); 65 m_coeffs.x() = sx; 66 m_coeffs.y() = sy; 67 m_coeffs.z() = sz; 68 } 69 /** Constructs and initialize the scaling transformation from a vector of scaling coefficients */ 70 explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {} 71 72 const VectorType& vector() const { return m_coeffs; } 73 VectorType& vector() { return m_coeffs; } 74 75 /** Concatenates two translation */ 76 inline Translation operator* (const Translation& other) const 77 { return Translation(m_coeffs + other.m_coeffs); } 78 79 /** Concatenates a translation and a scaling */ 80 inline TransformType operator* (const ScalingType& other) const; 81 82 /** Concatenates a translation and a linear transformation */ 83 inline TransformType operator* (const LinearMatrixType& linear) const; 84 85 template<typename Derived> 86 inline TransformType operator*(const RotationBase<Derived,Dim>& r) const 87 { return *this * r.toRotationMatrix(); } 88 89 /** Concatenates a linear transformation and a translation */ 90 // its a nightmare to define a templated friend function outside its declaration 91 friend inline TransformType operator* (const LinearMatrixType& linear, const Translation& t) 92 { 93 TransformType res; 94 res.matrix().setZero(); 95 res.linear() = linear; 96 res.translation() = linear * t.m_coeffs; 97 res.matrix().row(Dim).setZero(); 98 res(Dim,Dim) = Scalar(1); 99 return res; 100 } 101 102 /** Concatenates a translation and an affine transformation */ 103 inline TransformType operator* (const TransformType& t) const; 104 105 /** Applies translation to vector */ 106 inline VectorType operator* (const VectorType& other) const 107 { return m_coeffs + other; } 108 109 /** \returns the inverse translation (opposite) */ 110 Translation inverse() const { return Translation(-m_coeffs); } 111 112 Translation& operator=(const Translation& other) 113 { 114 m_coeffs = other.m_coeffs; 115 return *this; 116 } 117 118 /** \returns \c *this with scalar type casted to \a NewScalarType 119 * 120 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 121 * then this function smartly returns a const reference to \c *this. 122 */ 123 template<typename NewScalarType> 124 inline typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const 125 { return typename internal::cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); } 126 127 /** Copy constructor with scalar type conversion */ 128 template<typename OtherScalarType> 129 inline explicit Translation(const Translation<OtherScalarType,Dim>& other) 130 { m_coeffs = other.vector().template cast<Scalar>(); } 131 132 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 133 * determined by \a prec. 134 * 135 * \sa MatrixBase::isApprox() */ 136 bool isApprox(const Translation& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const 137 { return m_coeffs.isApprox(other.m_coeffs, prec); } 138 139 }; 140 141 /** \addtogroup Geometry_Module */ 142 //@{ 143 typedef Translation<float, 2> Translation2f; 144 typedef Translation<double,2> Translation2d; 145 typedef Translation<float, 3> Translation3f; 146 typedef Translation<double,3> Translation3d; 147 //@} 148 149 150 template<typename Scalar, int Dim> 151 inline typename Translation<Scalar,Dim>::TransformType 152 Translation<Scalar,Dim>::operator* (const ScalingType& other) const 153 { 154 TransformType res; 155 res.matrix().setZero(); 156 res.linear().diagonal() = other.coeffs(); 157 res.translation() = m_coeffs; 158 res(Dim,Dim) = Scalar(1); 159 return res; 160 } 161 162 template<typename Scalar, int Dim> 163 inline typename Translation<Scalar,Dim>::TransformType 164 Translation<Scalar,Dim>::operator* (const LinearMatrixType& linear) const 165 { 166 TransformType res; 167 res.matrix().setZero(); 168 res.linear() = linear; 169 res.translation() = m_coeffs; 170 res.matrix().row(Dim).setZero(); 171 res(Dim,Dim) = Scalar(1); 172 return res; 173 } 174 175 template<typename Scalar, int Dim> 176 inline typename Translation<Scalar,Dim>::TransformType 177 Translation<Scalar,Dim>::operator* (const TransformType& t) const 178 { 179 TransformType res = t; 180 res.pretranslate(m_coeffs); 181 return res; 182 } 183 184 } // end namespace Eigen 185
