1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2008 Gael Guennebaud <[email protected]>
5 // Copyright (C) 2008 Benoit Jacob <[email protected]>
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 * \tparam _Scalar the scalar type, i.e., the type of the coefficients
27 * \tparam _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 Eigen::Index Index; ///< \deprecated since Eigen 3.3
41 typedef Matrix<Scalar,AmbientDimAtCompileTime,1,Options> VectorType;
42
43 /** Default constructor without initialization */
ParametrizedLine()44 EIGEN_DEVICE_FUNC inline ParametrizedLine() {}
45
46 template<int OtherOptions>
ParametrizedLine(const ParametrizedLine<Scalar,AmbientDimAtCompileTime,OtherOptions> & other)47 EIGEN_DEVICE_FUNC 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 */
ParametrizedLine(Index _dim)53 EIGEN_DEVICE_FUNC 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 */
ParametrizedLine(const VectorType & origin,const VectorType & direction)58 EIGEN_DEVICE_FUNC ParametrizedLine(const VectorType& origin, const VectorType& direction)
59 : m_origin(origin), m_direction(direction) {}
60
61 template <int OtherOptions>
62 EIGEN_DEVICE_FUNC explicit ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane);
63
64 /** Constructs a parametrized line going from \a p0 to \a p1. */
Through(const VectorType & p0,const VectorType & p1)65 EIGEN_DEVICE_FUNC static inline ParametrizedLine Through(const VectorType& p0, const VectorType& p1)
66 { return ParametrizedLine(p0, (p1-p0).normalized()); }
67
~ParametrizedLine()68 EIGEN_DEVICE_FUNC ~ParametrizedLine() {}
69
70 /** \returns the dimension in which the line holds */
dim()71 EIGEN_DEVICE_FUNC inline Index dim() const { return m_direction.size(); }
72
origin()73 EIGEN_DEVICE_FUNC const VectorType& origin() const { return m_origin; }
origin()74 EIGEN_DEVICE_FUNC VectorType& origin() { return m_origin; }
75
direction()76 EIGEN_DEVICE_FUNC const VectorType& direction() const { return m_direction; }
direction()77 EIGEN_DEVICE_FUNC 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 */
squaredDistance(const VectorType & p)82 EIGEN_DEVICE_FUNC 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 */
distance(const VectorType & p)90 EIGEN_DEVICE_FUNC RealScalar distance(const VectorType& p) const { EIGEN_USING_STD(sqrt) return sqrt(squaredDistance(p)); }
91
92 /** \returns the projection of a point \a p onto the line \c *this. */
projection(const VectorType & p)93 EIGEN_DEVICE_FUNC VectorType projection(const VectorType& p) const
94 { return origin() + direction().dot(p-origin()) * direction(); }
95
96 EIGEN_DEVICE_FUNC VectorType pointAt(const Scalar& t) const;
97
98 template <int OtherOptions>
99 EIGEN_DEVICE_FUNC Scalar intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
100
101 template <int OtherOptions>
102 EIGEN_DEVICE_FUNC Scalar intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
103
104 template <int OtherOptions>
105 EIGEN_DEVICE_FUNC VectorType intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const;
106
107 /** Applies the transformation matrix \a mat to \c *this and returns a reference to \c *this.
108 *
109 * \param mat the Dim x Dim transformation matrix
110 * \param traits specifies whether the matrix \a mat represents an #Isometry
111 * or a more generic #Affine transformation. The default is #Affine.
112 */
113 template<typename XprType>
114 EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const MatrixBase<XprType>& mat, TransformTraits traits = Affine)
115 {
116 if (traits==Affine)
117 direction() = (mat * direction()).normalized();
118 else if (traits==Isometry)
119 direction() = mat * direction();
120 else
121 {
122 eigen_assert(0 && "invalid traits value in ParametrizedLine::transform()");
123 }
124 origin() = mat * origin();
125 return *this;
126 }
127
128 /** Applies the transformation \a t to \c *this and returns a reference to \c *this.
129 *
130 * \param t the transformation of dimension Dim
131 * \param traits specifies whether the transformation \a t represents an #Isometry
132 * or a more generic #Affine transformation. The default is #Affine.
133 * Other kind of transformations are not supported.
134 */
135 template<int TrOptions>
136 EIGEN_DEVICE_FUNC inline ParametrizedLine& transform(const Transform<Scalar,AmbientDimAtCompileTime,Affine,TrOptions>& t,
137 TransformTraits traits = Affine)
138 {
139 transform(t.linear(), traits);
140 origin() += t.translation();
141 return *this;
142 }
143
144 /** \returns \c *this with scalar type casted to \a NewScalarType
145 *
146 * Note that if \a NewScalarType is equal to the current scalar type of \c *this
147 * then this function smartly returns a const reference to \c *this.
148 */
149 template<typename NewScalarType>
150 EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<ParametrizedLine,
cast()151 ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type cast() const
152 {
153 return typename internal::cast_return_type<ParametrizedLine,
154 ParametrizedLine<NewScalarType,AmbientDimAtCompileTime,Options> >::type(*this);
155 }
156
157 /** Copy constructor with scalar type conversion */
158 template<typename OtherScalarType,int OtherOptions>
ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions> & other)159 EIGEN_DEVICE_FUNC inline explicit ParametrizedLine(const ParametrizedLine<OtherScalarType,AmbientDimAtCompileTime,OtherOptions>& other)
160 {
161 m_origin = other.origin().template cast<Scalar>();
162 m_direction = other.direction().template cast<Scalar>();
163 }
164
165 /** \returns \c true if \c *this is approximately equal to \a other, within the precision
166 * determined by \a prec.
167 *
168 * \sa MatrixBase::isApprox() */
169 EIGEN_DEVICE_FUNC bool isApprox(const ParametrizedLine& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
170 { return m_origin.isApprox(other.m_origin, prec) && m_direction.isApprox(other.m_direction, prec); }
171
172 protected:
173
174 VectorType m_origin, m_direction;
175 };
176
177 /** Constructs a parametrized line from a 2D hyperplane
178 *
179 * \warning the ambient space must have dimension 2 such that the hyperplane actually describes a line
180 */
181 template <typename _Scalar, int _AmbientDim, int _Options>
182 template <int OtherOptions>
ParametrizedLine(const Hyperplane<_Scalar,_AmbientDim,OtherOptions> & hyperplane)183 EIGEN_DEVICE_FUNC inline ParametrizedLine<_Scalar, _AmbientDim,_Options>::ParametrizedLine(const Hyperplane<_Scalar, _AmbientDim,OtherOptions>& hyperplane)
184 {
185 EIGEN_STATIC_ASSERT_VECTOR_SPECIFIC_SIZE(VectorType, 2)
186 direction() = hyperplane.normal().unitOrthogonal();
187 origin() = -hyperplane.normal()*hyperplane.offset();
188 }
189
190 /** \returns the point at \a t along this line
191 */
192 template <typename _Scalar, int _AmbientDim, int _Options>
193 EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
pointAt(const _Scalar & t)194 ParametrizedLine<_Scalar, _AmbientDim,_Options>::pointAt(const _Scalar& t) const
195 {
196 return origin() + (direction()*t);
197 }
198
199 /** \returns the parameter value of the intersection between \c *this and the given \a hyperplane
200 */
201 template <typename _Scalar, int _AmbientDim, int _Options>
202 template <int OtherOptions>
intersectionParameter(const Hyperplane<_Scalar,_AmbientDim,OtherOptions> & hyperplane)203 EIGEN_DEVICE_FUNC inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionParameter(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
204 {
205 return -(hyperplane.offset()+hyperplane.normal().dot(origin()))
206 / hyperplane.normal().dot(direction());
207 }
208
209
210 /** \deprecated use intersectionParameter()
211 * \returns the parameter value of the intersection between \c *this and the given \a hyperplane
212 */
213 template <typename _Scalar, int _AmbientDim, int _Options>
214 template <int OtherOptions>
intersection(const Hyperplane<_Scalar,_AmbientDim,OtherOptions> & hyperplane)215 EIGEN_DEVICE_FUNC inline _Scalar ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersection(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
216 {
217 return intersectionParameter(hyperplane);
218 }
219
220 /** \returns the point of the intersection between \c *this and the given hyperplane
221 */
222 template <typename _Scalar, int _AmbientDim, int _Options>
223 template <int OtherOptions>
224 EIGEN_DEVICE_FUNC inline typename ParametrizedLine<_Scalar, _AmbientDim,_Options>::VectorType
intersectionPoint(const Hyperplane<_Scalar,_AmbientDim,OtherOptions> & hyperplane)225 ParametrizedLine<_Scalar, _AmbientDim,_Options>::intersectionPoint(const Hyperplane<_Scalar, _AmbientDim, OtherOptions>& hyperplane) const
226 {
227 return pointAt(intersectionParameter(hyperplane));
228 }
229
230 } // end namespace Eigen
231
232 #endif // EIGEN_PARAMETRIZEDLINE_H
233