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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$.
+  *
+  * \param _Scalar the scalar type, i.e., the type of the coefficients
+  * \param _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 DenseIndex Index;
+  typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType;
+
+  /** Default constructor without initialization */
+  inline ParametrizedLine() {}
+  
+  template<int OtherOptions>
+  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 */
+  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.
+    */
+  ParametrizedLine(const VectorType& origin, const VectorType& direction)
+    : m_origin(origin), m_direction(direction) {}
+
+  template <int OtherOptions>
+  explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);
+
+  /** Constructs a parametrized line going from \a p0 to \a p1. */
+  static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
+  { return ParametrizedLine(p0, (p1-p0).normalized()); }
+
+  ~ParametrizedLine() {}
+
+  /** \returns the dimension in which the line holds */
+  inline Index dim() const { return m_direction.size(); }
+
+  const VectorType& origin() const { return m_origin; }
+  VectorType& origin() { return m_origin; }
+
+  const VectorType& direction() const { return m_direction; }
+  VectorType& direction() { return m_direction; }
+
+  /** \returns the squared distance of a point \a p to its projection onto the line \c *this.
+    * \sa distance()
+    */
+  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()
+    */
+  RealScalar distance(const VectorType& p) const { using std::sqrt; return sqrt(squaredDistance(p)); }
+
+  /** \returns the projection of a point \a p onto the line \c *this. */
+  VectorType projection(const VectorType& p) const
+  { return origin() + direction().dot(p-origin()) * direction(); }
+
+  VectorType pointAt(const Scalar& t) const;
+  
+  template <int OtherOptions>
+  Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
+ 
+  template <int OtherOptions>
+  Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
+  
+  template <int OtherOptions>
+  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>
+  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>
+  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() */
+  bool isApprox(const ParametrizedLine& other, 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>
+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>
+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>
+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>
+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>
+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