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Edit File: ParametrizedLine.h

// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr> // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com> // // 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_PARAMETRIZEDLINE_H #define EIGEN_PARAMETRIZEDLINE_H namespace Eigen { /** \geometry_module \ingroup Geometry_Module * * \class ParametrizedLine * * \brief A parametrized line * * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$. * * \tparam _Scalar the scalar type, i.e., the type of the coefficients * \tparam _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. */ template <typename _Scalar, int _AmbientDim, int _Options> class ParametrizedLine { public: EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) enum { AmbientDimAtCompileTime = _AmbientDim, Options = _Options }; typedef _Scalar Scalar; typedef typename NumTraits<Scalar>::Real RealScalar; typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3 typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType; /** Default constructor without initialization */ EIGEN_DEVICE_FUNC inline ParametrizedLine() {} template<int OtherOptions> EIGEN_DEVICE_FUNC ParametrizedLine(const ParametrizedLine<Scalar,AmbientDimAtCompileTime,OtherOptions>& other) : m_origin(other.origin()), m_direction(other.direction()) {} /** Constructs a dynamic-size line with \a _dim the dimension * of the ambient space */ EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {} /** Initializes a parametrized line of direction \a direction and origin \a origin. * \warning the vector direction is assumed to be normalized. */ EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction) : m_origin(origin), m_direction(direction) {} template <int OtherOptions> EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane); /** Constructs a parametrized line going from \a p0 to \a p1. */ EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1) { return ParametrizedLine(p0, (p1-p0).normalized()); } EIGEN_DEVICE_FUNC ~ParametrizedLine() {} /** \returns the dimension in which the line holds */ EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); } EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; } EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; } EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; } EIGEN_DEVICE_FUNC VectorType& direction() { return m_direction; } /** \returns the squared distance of a point \a p to its projection onto the line \c *this. * \sa distance() */ EIGEN_DEVICE_FUNC RealScalar squaredDistance(const VectorType& p) const { VectorType diff = p - origin(); return (diff - direction().dot(diff) * direction()).squaredNorm(); } /** \returns the distance of a point \a p to its projection onto the line \c *this. * \sa squaredDistance() */ EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const { EIGEN_USING_STD(sqrt) return sqrt(squaredDistance(p)); } /** \returns the projection of a point \a p onto the line \c *this. */ EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const { return origin() + direction().dot(p-origin()) * direction(); } EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const; template <int OtherOptions> EIGEN_DEVICE_FUNC Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const; template <int OtherOptions> EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const; template <int OtherOptions> EIGEN_DEVICE_FUNC VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const; /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this. * * \param mat the Dim x Dim transformation matrix * \param traits specifies whether the matrix \a mat represents an #Isometry * or a more generic #Affine transformation. The default is #Affine. */ template<typename XprType> EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine) { if (traits==Affine) direction() = (mat * direction()).normalized(); else if (traits==Isometry) direction() = mat * direction(); else { eigen_assert(0 && "invalid traits value in ParametrizedLine::transform()"); } origin() = mat * origin(); return *this; } /** Applies the transformation \a t to \c *this and returns a reference to \c *this. * * \param t the transformation of dimension Dim * \param traits specifies whether the transformation \a t represents an #Isometry * or a more generic #Affine transformation. The default is #Affine. * Other kind of transformations are not supported. */ template<int TrOptions> EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const Transform<Scalar,AmbientDimAtCompileTime,Affine,TrOptions>& t, TransformTraits traits = Affine) { transform(t.linear(), traits); origin() += t.translation(); return *this; } /** \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<ParametrizedLine, ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const { return typename internal::cast_return_type<ParametrizedLine, ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this); } /** Copy constructor with scalar type conversion */ template<typename OtherScalarType,int OtherOptions> EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other) { m_origin = other.origin().template cast<Scalar>(); m_direction = other.direction().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 ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); } protected: VectorType m_origin, m_direction; }; /** Constructs a parametrized line from a 2D hyperplane * * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line */ template <typename _Scalar, int _AmbientDim, int _Options> template <int OtherOptions> EIGEN_DEVICE_FUNC inline ParametrizedLine<_Scalar, _AmbientDim,_Options>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim,OtherOptions>& hyperplane) { EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2) direction() = hyperplane.normal().unitOrthogonal(); origin() = -hyperplane.normal()*hyperplane.offset(); } /** \returns the point at \a t along this line */ template <typename _Scalar, int _AmbientDim, int _Options> EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType ParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt(const _Scalar& t) const { return origin() + (direction()*t); } /** \returns the parameter value of the intersection between \c *this and the given \a hyperplane */ template <typename _Scalar, int _AmbientDim, int _Options> template <int OtherOptions> EIGEN_DEVICE_FUNC inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const { return -(hyperplane.offset()+hyperplane.normal().dot(origin())) / hyperplane.normal().dot(direction()); } /** \deprecated use intersectionParameter() * \returns the parameter value of the intersection between \c *this and the given \a hyperplane */ template <typename _Scalar, int _AmbientDim, int _Options> template <int OtherOptions> EIGEN_DEVICE_FUNC inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const { return intersectionParameter(hyperplane); } /** \returns the point of the intersection between \c *this and the given hyperplane */ template <typename _Scalar, int _AmbientDim, int _Options> template <int OtherOptions> EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const { return pointAt(intersectionParameter(hyperplane)); } } // end namespace Eigen #endif // EIGEN_PARAMETRIZEDLINE_H