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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>
- // 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_MATH(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;
- /** \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
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