1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <g.gael@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. */
Translation()53   Translation() {}
54   /**  */
Translation(const Scalar & sx,const Scalar & sy)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   /**  */
Translation(const Scalar & sx,const Scalar & sy,const Scalar & sz)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 */
Translation(const VectorType & vector)70   explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
71 
vector()72   const VectorType& vector() const { return m_coeffs; }
vector()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) */
inverse()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>
cast()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>
Translation(const Translation<OtherScalarType,Dim> & other)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