1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) inria.fr> 5 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1 (at) gmail.com> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #ifndef EIGEN_PARAMETRIZEDLINE_H 12 #define EIGEN_PARAMETRIZEDLINE_H 13 14 namespace Eigen { 15 16 /** \geometry_module \ingroup Geometry_Module 17 * 18 * \class ParametrizedLine 19 * 20 * \brief A parametrized line 21 * 22 * A parametrized line is defined by an origin point \f$ \mathbf{o} \f$ and a unit 23 * direction vector \f$ \mathbf{d} \f$ such that the line corresponds to 24 * the set \f$ l(t) = \mathbf{o} + t \mathbf{d} \f$, \f$ t \in \mathbf{R} \f$. 25 * 26 * \param _Scalar the scalar type, i.e., the type of the coefficients 27 * \param _AmbientDim the dimension of the ambient space, can be a compile time value or Dynamic. 28 */ 29 template <typename _Scalar, int _AmbientDim, int _Options> 30 class ParametrizedLine 31 { 32 public: 33 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_AmbientDim) 34 enum { 35 AmbientDimAtCompileTime = _AmbientDim, 36 Options = _Options 37 }; 38 typedef _Scalar Scalar; 39 typedef typename NumTraits<Scalar>::Real RealScalar; 40 typedef DenseIndex Index; 41 typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType; 42 43 /** Default constructor without initialization */ 44 inline explicit ParametrizedLine() {} 45 46 template<int OtherOptions> 47 ParametrizedLine(const ParametrizedLine<Scalar,AmbientDimAtCompileTime,OtherOptions>& other) 48 : m_origin(other.origin()), m_direction(other.direction()) 49 {} 50 51 /** Constructs a dynamic-size line with \a _dim the dimension 52 * of the ambient space */ 53 inline explicit ParametrizedLine(Index _dim) : m_origin(_dim), m_direction(_dim) {} 54 55 /** Initializes a parametrized line of direction \a direction and origin \a origin. 56 * \warning the vector direction is assumed to be normalized. 57 */ 58 ParametrizedLine(const VectorType& origin, const VectorType& direction) 59 : m_origin(origin), m_direction(direction) {} 60 61 template <int OtherOptions> 62 explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane); 63 64 /** Constructs a parametrized line going from \a p0 to \a p1. */ 65 static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1) 66 { return ParametrizedLine(p0, (p1-p0).normalized()); } 67 68 ~ParametrizedLine() {} 69 70 /** \returns the dimension in which the line holds */ 71 inline Index dim() const { return m_direction.size(); } 72 73 const VectorType& origin() const { return m_origin; } 74 VectorType& origin() { return m_origin; } 75 76 const VectorType& direction() const { return m_direction; } 77 VectorType& direction() { return m_direction; } 78 79 /** \returns the squared distance of a point \a p to its projection onto the line \c *this. 80 * \sa distance() 81 */ 82 RealScalar squaredDistance(const VectorType& p) const 83 { 84 VectorType diff = p - origin(); 85 return (diff - direction().dot(diff) * direction()).squaredNorm(); 86 } 87 /** \returns the distance of a point \a p to its projection onto the line \c *this. 88 * \sa squaredDistance() 89 */ 90 RealScalar distance(const VectorType& p) const { return internal::sqrt(squaredDistance(p)); } 91 92 /** \returns the projection of a point \a p onto the line \c *this. */ 93 VectorType projection(const VectorType& p) const 94 { return origin() + direction().dot(p-origin()) * direction(); } 95 96 VectorType pointAt( Scalar t ) const; 97 98 template <int OtherOptions> 99 Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const; 100 101 template <int OtherOptions> 102 Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const; 103 104 template <int OtherOptions> 105 VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const; 106 107 /** \returns \c *this with scalar type casted to \a NewScalarType 108 * 109 * Note that if \a NewScalarType is equal to the current scalar type of \c *this 110 * then this function smartly returns a const reference to \c *this. 111 */ 112 template<typename NewScalarType> 113 inline typename internal::cast_return_type<ParametrizedLine, 114 ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const 115 { 116 return typename internal::cast_return_type<ParametrizedLine, 117 ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this); 118 } 119 120 /** Copy constructor with scalar type conversion */ 121 template<typename OtherScalarType,int OtherOptions> 122 inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other) 123 { 124 m_origin = other.origin().template cast<Scalar>(); 125 m_direction = other.direction().template cast<Scalar>(); 126 } 127 128 /** \returns \c true if \c *this is approximately equal to \a other, within the precision 129 * determined by \a prec. 130 * 131 * \sa MatrixBase::isApprox() */ 132 bool isApprox(const ParametrizedLine& other, typename NumTraits<Scalar>::Real prec = NumTraits<Scalar>::dummy_precision()) const 133 { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); } 134 135 protected: 136 137 VectorType m_origin, m_direction; 138 }; 139 140 /** Constructs a parametrized line from a 2D hyperplane 141 * 142 * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line 143 */ 144 template <typename _Scalar, int _AmbientDim, int _Options> 145 template <int OtherOptions> 146 inline ParametrizedLine<_Scalar, _AmbientDim,_Options>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim,OtherOptions>& hyperplane) 147 { 148 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2) 149 direction() = hyperplane.normal().unitOrthogonal(); 150 origin() = -hyperplane.normal()*hyperplane.offset(); 151 } 152 153 /** \returns the point at \a t along this line 154 */ 155 template <typename _Scalar, int _AmbientDim, int _Options> 156 inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType 157 ParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt( _Scalar t ) const 158 { 159 return origin() + (direction()*t); 160 } 161 162 /** \returns the parameter value of the intersection between \c *this and the given \a hyperplane 163 */ 164 template <typename _Scalar, int _AmbientDim, int _Options> 165 template <int OtherOptions> 166 inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const 167 { 168 return -(hyperplane.offset()+hyperplane.normal().dot(origin())) 169 / hyperplane.normal().dot(direction()); 170 } 171 172 173 /** \deprecated use intersectionParameter() 174 * \returns the parameter value of the intersection between \c *this and the given \a hyperplane 175 */ 176 template <typename _Scalar, int _AmbientDim, int _Options> 177 template <int OtherOptions> 178 inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const 179 { 180 return intersectionParameter(hyperplane); 181 } 182 183 /** \returns the point of the intersection between \c *this and the given hyperplane 184 */ 185 template <typename _Scalar, int _AmbientDim, int _Options> 186 template <int OtherOptions> 187 inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType 188 ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const 189 { 190 return pointAt(intersectionParameter(hyperplane)); 191 } 192 193 } // end namespace Eigen 194 195 #endif // EIGEN_PARAMETRIZEDLINE_H 196
