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
|
// Copyright (c) 2018
// Utrecht University (The Netherlands),
// ETH Zurich (Switzerland),
// INRIA Sophia-Antipolis (France),
// Max-Planck-Institute Saarbruecken (Germany),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Cartesian_kernel/include/CGAL/Cartesian/Reflection_rep_2.h $
// $Id: include/CGAL/Cartesian/Reflection_rep_2.h b26b07a1242 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Maxime Gimeno
#ifndef CGAL_CARTESIAN_REFLECTION_REP_2_H
#define CGAL_CARTESIAN_REFLECTION_REP_2_H
#include <cmath>
namespace CGAL {
template < class R >
class Reflection_repC2: public Aff_transformation_rep_baseC2<R>
{
friend class Translation_repC2<R>;
friend class Rotation_repC2<R>;
friend class Scaling_repC2<R>;
friend class Aff_transformation_repC2<R>;
public:
typedef Aff_transformation_rep_baseC2<R> Aff_t_base;
typedef typename Aff_t_base::FT FT;
typedef typename Aff_t_base::Point_2 Point_2;
typedef typename Aff_t_base::Vector_2 Vector_2;
typedef typename Aff_t_base::Direction_2 Direction_2;
typedef typename CGAL::Line_2<R> Line_2;
typedef typename Aff_t_base::Aff_transformation_2 Aff_transformation_2;
typedef Aff_transformation_repC2<R> Transformation;
typedef Reflection_repC2<R> Reflection;
typedef Scaling_repC2<R> Scaling;
typedef Rotation_repC2<R> Rotation;
typedef Translation_repC2<R> Translation;
Reflection_repC2(const Line_2 &l)
{
if(l.a() == 0)
t = -Vector_2(0, l.c()/l.b());
else
t = -Vector_2(l.c()/l.a(),0);
Vector_2 l_to_v = l.to_vector();
FT scal = l_to_v.x(); //Projection of l_to_v on Ox. = |L|*cos(a)
FT det = l_to_v.y();// = |L|*sin(a)
sinus_ = 2*det*scal/l_to_v.squared_length(); //sin(2a) = 2*sin(a)*cos(a)
FT sq_cos = scal*scal/l_to_v.squared_length(); //cos(a)*cos(a)
cosinus_ = 2*sq_cos-1;
}
~Reflection_repC2()
{}
Point_2 transform(const Point_2 &p) const
{
return Point_2(
cosinus_*p.x()+sinus_*p.y()-cosinus_*t.x()-sinus_*t.y()+t.x(),
sinus_*p.x()-cosinus_*p.y()-sinus_*t.x()+cosinus_*t.y()+t.y());
}
Vector_2 transform(const Vector_2 &p) const
{
return Vector_2(
cosinus_*p.x()+sinus_*p.y()-cosinus_*t.x()-sinus_*t.y()+t.x(),
sinus_*p.x()-cosinus_*p.y()-sinus_*t.x()+cosinus_*t.y()+t.y());
}
Direction_2 transform(const Direction_2 &d) const
{
return transform(d.vector()).direction();
}
Aff_transformation_2 operator*(const Aff_t_base &t) const
{
return t.compose(*this);
}
Aff_transformation_2 compose(const Translation &tr) const
{
return Aff_transformation_2(cosinus_, sinus_, t13()+tr.translationvector_.x(),
sinus_, -cosinus_, t23()+tr.translationvector_.y());
}
Aff_transformation_2 compose(const Scaling &s) const
{
return Aff_transformation_2(s.scalefactor_ * cosinus_,
s.scalefactor_ * sinus_,
s.scalefactor_ * t13(),
s.scalefactor_ * sinus_,
-s.scalefactor_ * cosinus_,
s.scalefactor_ * t23());
}
Aff_transformation_2 compose(const Transformation &tr) const
{
return Aff_transformation_2(
tr.t11*cosinus_+tr.t12*sinus_,
tr.t11*sinus_-tr.t12*cosinus_,
tr.t11*t13()+tr.t12*t23()+tr.t13,
tr.t21*cosinus_+tr.t22*sinus_,
tr.t21*sinus_-tr.t22*cosinus_,
tr.t21*t13()+tr.t22*t23()+tr.t23);
}
Aff_transformation_2 compose(const Rotation &r) const
{
return Aff_transformation_2(
r.cosinus_*cosinus_-r.sinus_*sinus_,
r.cosinus_*sinus_+r.sinus_*cosinus_,
r.cosinus_*t13()
-r.sinus_*t23(),
r.sinus_*cosinus_+r.cosinus_*sinus_,
r.sinus_*sinus_-r.cosinus_*cosinus_,
r.sinus_*t13()
+r.cosinus_*t23());
}
Aff_transformation_2 compose(const Reflection &r) const
{
return Aff_transformation_2(
cosinus_*r.cosinus_+sinus_*r.sinus_,
r.cosinus_*sinus_-r.sinus_*cosinus_,
r.cosinus_*(t13()-r.t.x()) + r.sinus_*(t23()-r.t.y())+r.t.x(),
r.sinus_*cosinus_ - r.cosinus_*sinus_,
r.sinus_*sinus_+r.cosinus_*cosinus_,
r.sinus_*(t13()-r.t.x()) -r.cosinus_*(t23()-r.t.y())+r.t.y());
}
Aff_transformation_2 inverse() const
{
return Aff_transformation_2(cartesian(0,0), cartesian(0,1), cartesian(0,2),
cartesian(1,0), cartesian(1,1), cartesian(1,2));
}
bool is_even() const
{
return true;
}
virtual bool is_reflection() const
{
return true;
}
FT cartesian(int i, int j) const
{
switch (i)
{
case 0: switch (j)
{
case 0: return cosinus_;
case 1: return sinus_;
default: return FT(0);
}
case 1: switch (j)
{
case 0: return sinus_;
case 1: return -cosinus_;
default: return FT(0);
}
case 2: switch (j)
{
case 0: return FT(0);
case 1: return FT(0);
default: return FT(1);
}
}
return FT(0);
}
std::ostream &print(std::ostream &os) const
{
os << "Aff_transformationC2(" << sinus_ << ", " << cosinus_ << "; "<< t <<")";
return os;
}
//convevience functions for composition
FT t13()const
{
return FT(-cosinus_*t.x()-sinus_*t.y()+t.x());
}
FT t23()const
{
return FT(-sinus_*t.x()+cosinus_*t.y()+t.y());
}
private:
Vector_2 t;
FT sinus_, cosinus_;
};
} //namespace CGAL
#endif // CGAL_CARTESIAN_REFLECTION_REP_2_H
|
