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+// 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