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
|
// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <g.gael@free.fr>
//
// 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_TRANSLATION_H
#define EIGEN_TRANSLATION_H
/** \geometry_module \ingroup Geometry_Module
*
* \class Translation
*
* \brief Represents a translation transformation
*
* \param _Scalar the scalar type, i.e., the type of the coefficients.
* \param _Dim the dimension of the space, can be a compile time value or Dynamic
*
* \note This class is not aimed to be used to store a translation transformation,
* but rather to make easier the constructions and updates of Transform objects.
*
* \sa class Scaling, class Transform
*/
template<typename _Scalar, int _Dim>
class Translation
{
public:
EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar,_Dim)
/** dimension of the space */
enum { Dim = _Dim };
/** the scalar type of the coefficients */
typedef _Scalar Scalar;
/** corresponding vector type */
typedef Matrix<Scalar,Dim,1> VectorType;
/** corresponding linear transformation matrix type */
typedef Matrix<Scalar,Dim,Dim> LinearMatrixType;
/** corresponding affine transformation type */
typedef Transform<Scalar,Dim> AffineTransformType;
protected:
VectorType m_coeffs;
public:
/** Default constructor without initialization. */
Translation() {}
/** */
inline Translation(const Scalar& sx, const Scalar& sy)
{
ei_assert(Dim==2);
m_coeffs.x() = sx;
m_coeffs.y() = sy;
}
/** */
inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
{
ei_assert(Dim==3);
m_coeffs.x() = sx;
m_coeffs.y() = sy;
m_coeffs.z() = sz;
}
/** Constructs and initialize the translation transformation from a vector of translation coefficients */
explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}
const VectorType& vector() const { return m_coeffs; }
VectorType& vector() { return m_coeffs; }
/** Concatenates two translation */
inline Translation operator* (const Translation& other) const
{ return Translation(m_coeffs + other.m_coeffs); }
/** Concatenates a translation and a uniform scaling */
inline AffineTransformType operator* (const UniformScaling<Scalar>& other) const;
/** Concatenates a translation and a linear transformation */
template<typename OtherDerived>
inline AffineTransformType operator* (const AnyMatrixBase<OtherDerived>& linear) const;
/** Concatenates a translation and a rotation */
template<typename Derived>
inline AffineTransformType operator*(const RotationBase<Derived,Dim>& r) const
{ return *this * r.toRotationMatrix(); }
/** \returns the concatenation of a linear transformation \a l with the translation \a t */
// its a nightmare to define a templated friend function outside its declaration
template<typename OtherDerived> friend
inline AffineTransformType operator*(const AnyMatrixBase<OtherDerived>& linear, const Translation& t)
{
AffineTransformType res;
res.matrix().setZero();
res.linear() = linear.derived();
res.translation() = linear.derived() * t.m_coeffs;
res.matrix().row(Dim).setZero();
res(Dim,Dim) = Scalar(1);
return res;
}
/** Concatenates a translation and an affine transformation */
template<int Mode>
inline Transform<Scalar,Dim,Mode> operator* (const Transform<Scalar,Dim,Mode>& t) const
{
Transform<Scalar,Dim,Mode> res = t;
res.pretranslate(m_coeffs);
return res;
}
/** Applies translation to vector */
inline VectorType operator* (const VectorType& other) const
{ return m_coeffs + other; }
/** \returns the inverse translation (opposite) */
Translation inverse() const { return Translation(-m_coeffs); }
Translation& operator=(const Translation& other)
{
m_coeffs = other.m_coeffs;
return *this;
}
/** \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 ei_cast_return_type<Translation,Translation<NewScalarType,Dim> >::type cast() const
{ return typename ei_cast_return_type<Translation,Translation<NewScalarType,Dim> >::type(*this); }
/** Copy constructor with scalar type conversion */
template<typename OtherScalarType>
inline explicit Translation(const Translation<OtherScalarType,Dim>& other)
{ m_coeffs = other.vector().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 Translation& other, typename NumTraits<Scalar>::Real prec = precision<Scalar>()) const
{ return m_coeffs.isApprox(other.m_coeffs, prec); }
};
/** \addtogroup Geometry_Module */
//@{
typedef Translation<float, 2> Translation2f;
typedef Translation<double,2> Translation2d;
typedef Translation<float, 3> Translation3f;
typedef Translation<double,3> Translation3d;
//@}
template<typename Scalar, int Dim>
inline typename Translation<Scalar,Dim>::AffineTransformType
Translation<Scalar,Dim>::operator* (const UniformScaling<Scalar>& other) const
{
AffineTransformType res;
res.matrix().setZero();
res.linear().diagonal().fill(other.factor());
res.translation() = m_coeffs;
res(Dim,Dim) = Scalar(1);
return res;
}
template<typename Scalar, int Dim>
template<typename OtherDerived>
inline typename Translation<Scalar,Dim>::AffineTransformType
Translation<Scalar,Dim>::operator* (const AnyMatrixBase<OtherDerived>& linear) const
{
AffineTransformType res;
res.matrix().setZero();
res.linear() = linear.derived();
res.translation() = m_coeffs;
res.matrix().row(Dim).setZero();
res(Dim,Dim) = Scalar(1);
return res;
}
#endif // EIGEN_TRANSLATION_H
|
