1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
|
// 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>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
// License as published by the Free Software Foundation; either
// version 3 of the License, or (at your option) any later version.
//
// Alternatively, you can redistribute it and/or
// modify it under the terms of the GNU General Public License as
// published by the Free Software Foundation; either version 2 of
// the License, or (at your option) any later version.
//
// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU Lesser General Public
// License and a copy of the GNU General Public License along with
// Eigen. If not, see <http://www.gnu.org/licenses/>.
#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 explicit 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 { return internal::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
|
