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
|
// Copyright (c) 1999,2016
// 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/v6.0.1/Homogeneous_kernel/include/CGAL/Homogeneous/predicates_on_pointsH2.h $
// $Id: include/CGAL/Homogeneous/predicates_on_pointsH2.h 50cfbde3b84 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Stefan Schirra, Olivier Devillers, Mariette Yvinec
#ifndef CGAL_PREDICATES_ON_POINTSH2_H
#define CGAL_PREDICATES_ON_POINTSH2_H
#include <CGAL/Homogeneous/PointH2.h>
namespace CGAL {
template < class R>
CGAL_KERNEL_INLINE
bool
equal_xy(const PointH2<R>& p,
const PointH2<R>& q)
{
typedef typename R::RT RT;
// Using these references allows to spare calls to [pq].hw().
const RT& phw = p.hw();
const RT& qhw = q.hw();
return (p.hx()*qhw == q.hx()*phw) && (p.hy()*qhw == q.hy()*phw);
}
template <class R>
CGAL_KERNEL_MEDIUM_INLINE
Oriented_side
_where_wrt_L_wedge( const PointH2<R>& p, const PointH2<R>& q )
{
Sign xs = CGAL_NTS sign( q.hx()*p.hw() - p.hx()*q.hw() ); // sign( qx - px )
Sign ys = CGAL_NTS sign( q.hy()*p.hw() - p.hy()*q.hw() ); // sign( qy - py )
if (( xs == NEGATIVE ) || ( ys == NEGATIVE ))
return ON_NEGATIVE_SIDE;
if (( xs == POSITIVE ) && ( ys == POSITIVE ))
return ON_POSITIVE_SIDE;
return ON_ORIENTED_BOUNDARY;
}
template <class RT>
Comparison_result
compare_power_distanceH2(const RT& phx, const RT& phy, const RT& phw,
const Quotient<RT>& pwt,
const RT& qhx, const RT& qhy, const RT& qhw,
const Quotient<RT>& qwt,
const RT& rhx, const RT& rhy, const RT& rhw)
{
// returns SMALLER if r is closer to p w.r.t. the power metric
RT dphx = rhx * phw - phx * rhw;
RT dphy = rhy * phw - phy * rhw;
RT dqhx = rhx * qhw - qhx * rhw;
RT dqhy = rhy * qhw - qhy * rhw;
RT dphw = CGAL_NTS square(phw);
RT dqhw = CGAL_NTS square(qhw);
RT drhw = CGAL_NTS square(rhw);
RT npwt = pwt.numerator();
RT dpwt = pwt.denominator();
RT nqwt = qwt.numerator();
RT dqwt = qwt.denominator();
RT dh1 = (CGAL_NTS square(dphx) + CGAL_NTS square(dphy))*dpwt - npwt * dphw * drhw;
RT dh2 = (CGAL_NTS square(dqhx) + CGAL_NTS square(dqhy))*dqwt - nqwt * dqhw * drhw;
return CGAL_NTS compare(dh1 * dqhw * dqwt, dh2 * dphw * dpwt );
}
template <class RT>
Oriented_side
power_testH2( const RT &phx, const RT &phy, const RT &phw, const Quotient<RT> &pwt,
const RT &qhx, const RT &qhy, const RT &qhw, const Quotient<RT> &qwt,
const RT &rhx, const RT &rhy, const RT &rhw, const Quotient<RT> &rwt,
const RT &thx, const RT &thy, const RT &thw, const Quotient<RT> &twt)
{
RT npwt = pwt.numerator();
RT dpwt = pwt.denominator();
RT nqwt = qwt.numerator();
RT dqwt = qwt.denominator();
RT nrwt = rwt.numerator();
RT drwt = rwt.denominator();
RT ntwt = twt.numerator();
RT dtwt = twt.denominator();
RT dphx = phx*phw;
RT dphy = phy*phw;
RT dphw = CGAL_NTS square(phw);
RT dpz = (CGAL_NTS square(phx) + CGAL_NTS square(phy))*dpwt - npwt*dphw;
RT dqhx = qhx*qhw;
RT dqhy = qhy*qhw;
RT dqhw = CGAL_NTS square(qhw);
RT dqz = (CGAL_NTS square(qhx) + CGAL_NTS square(qhy))*dqwt - nqwt*dqhw;
RT drhx = rhx*rhw;
RT drhy = rhy*rhw;
RT drhw = CGAL_NTS square(rhw);
RT drz = (CGAL_NTS square(rhx) + CGAL_NTS square(rhy)) *drwt - nrwt*drhw;
RT dthx = thx*thw;
RT dthy = thy*thw;
RT dthw = CGAL_NTS square(thw);
RT dtz = (CGAL_NTS square(thx) + CGAL_NTS square(thy))*dtwt - ntwt*dthw;
dthx *= dtwt;
dthy *= dtwt;
dthw *= dtwt;
return sign_of_determinant(dphx, dphy, dpz, dphw,
dqhx, dqhy, dqz, dqhw,
drhx, drhy, drz, drhw,
dthx, dthy, dtz, dthw);
}
template <class RT>
Oriented_side
power_testH2( const RT &phx, const RT &phy, const RT &phw, const Quotient<RT> &pwt,
const RT &qhx, const RT &qhy, const RT &qhw, const Quotient<RT> &qwt,
const RT &thx, const RT &thy, const RT &thw, const Quotient<RT> &twt)
{
RT npwt = pwt.numerator();
RT dpwt = pwt.denominator();
RT nqwt = qwt.numerator();
RT dqwt = qwt.denominator();
RT ntwt = twt.numerator();
RT dtwt = twt.denominator();
// Test if we can project on the (x) axis. If not, then on the
// (y) axis
RT pa, qa, ta;
if (phx * qhw != qhx * phw )
{
pa = phx*phw;
qa = qhx*qhw;
ta = thx*thw;
}
else
{
pa = phy*phw;
qa = qhy*qhw;
ta = thy*thw;
}
RT dphw = CGAL_NTS square(phw);
RT dpz = (CGAL_NTS square(phx) + CGAL_NTS square(phy))*dpwt - npwt*dphw;
RT dqhw = CGAL_NTS square(qhw);
RT dqz = (CGAL_NTS square(qhx) + CGAL_NTS square(qhy))*dqwt - nqwt*dqhw;
RT dthw = CGAL_NTS square(thw);
RT dtz = (CGAL_NTS square(thx) + CGAL_NTS square(thy))*dtwt - ntwt*dthw;
pa *= dtwt;
qa *= dtwt;
ta *= dtwt;
return CGAL_NTS compare(pa, qa) * sign_of_determinant(pa, dpz, dphw,
qa, dqz, dqhw,
ta, dtz, dthw);
}
#if 0
// Unused, undocumented, un-functorized.
template < class R >
CGAL_KERNEL_MEDIUM_INLINE
Comparison_result
compare_deltax_deltay(const PointH2<R>& p,
const PointH2<R>& q,
const PointH2<R>& r,
const PointH2<R>& s)
{
return CGAL_NTS compare(
CGAL_NTS abs(p.hx()*q.hw() - q.hx()*p.hw()) * r.hw()*s.hw(),
CGAL_NTS abs(r.hy()*s.hw() - s.hy()*r.hw()) * p.hw()*q.hw());
}
#endif
} //namespace CGAL
#endif // CGAL_PREDICATES_ON_POINTSH2_H
|
