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
|
/*
* Sline.cc -- ePiX::Sline class (spherical arc)
*
* This file is part of ePiX, a preprocessor for creating high-quality
* line figures in LaTeX
*
* Version 1.2.17
* Last Change: June 30, 2017
*/
/*
* Copyright (C) 2017
* Andrew D. Hwang <ahwang -at- holycross -dot- edu>
* Department of Mathematics and Computer Science
* College of the Holy Cross
* Worcester, MA, 01610-2395, USA
*/
/*
* ePiX is free software; 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.
*
* ePiX 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 General Public
* License for more details.
*
* You should have received a copy of the GNU General Public License
* along with ePiX; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#include <cmath>
#include "constants.h"
#include "errors.h"
#include "triples.h"
#include "geometry.h"
#include "Sline.h"
namespace ePiX {
Sline::Sline(const P& tail, const P& head)
: m_tail(tail), m_head(head), m_malformed(false)
{
double mt(norm(tail)), mh(norm(head));
if (fabs(mt - 1) > EPIX_EPSILON)
{
epix_warning("First argument of Sline is not a unit vector");
if (EPIX_EPSILON < mt && mt < EPIX_INFTY)
m_tail *= 1.0/mt;
else
m_malformed = true;
}
if (fabs(mh - 1) > EPIX_EPSILON)
{
epix_warning("Second argument of Sline is not a unit vector");
if (EPIX_EPSILON < mh && mh < EPIX_INFTY)
m_head *= 1.0/mh;
else
m_malformed = true;
}
m_pole = m_tail * m_head;
double mp(norm(m_pole));
if (mp < EPIX_EPSILON)
{
epix_warning("Collinear arguments in Sline");
m_pole = P(0,0,0);
m_malformed = true;
}
else // well-formed; normalize pole
m_pole *= 1.0/mp;
} // end of Sline::Sline
bool Sline::malformed() const
{
return m_malformed;
}
P Sline::pole() const
{
if (m_malformed)
epix_warning("Pole of malformed Sline requested");
return m_pole;
}
double Sline::cosine() const
{
return (m_tail | m_head);
}
P Sline::operator * (const Sline& arg) const
{
if (m_malformed || arg.m_malformed)
{
epix_warning("Malformed argument(s) in Sline intersection");
return P(0,0,0);
}
else if (this -> collinear(arg))
{
epix_warning("Collinear argument(s) in Sline intersection");
return P(0,0,0);
}
// else
P val(m_pole * arg.m_pole);
val *= 1.0/norm(val);
if (0 < (m_tail | val))
return val;
else
return -val;
}
P Sline::reflect(const P& arg) const
{
return arg - 2*(m_pole | arg)*m_pole;
}
Sline Sline::reflect(const Sline& arg) const
{
return Sline(this -> reflect(arg.m_tail), this -> reflect(arg.m_head));
}
bool Sline::collinear(const Sline& arg) const
{
return m_malformed ||
arg.m_malformed ||
norm(m_pole * arg.m_pole) < EPIX_EPSILON;
}
bool Sline::cuts(const Sline& arg) const // we and arg cross
{
return ((m_tail | arg.m_pole)*(m_head | arg.m_pole) < 0 &&
(m_pole | arg.m_tail)*(m_pole | arg.m_head) < 0);
}
void Sline::draw() const
{
this -> draw_front();
this -> draw_back();
}
void Sline::draw_front() const // front arc
{
front_arc(m_tail, m_head);
}
void Sline::draw_back() const // back arc
{
back_arc(m_tail, m_head);
}
void Sline::draw_line() const
{
this -> line_back();
this -> line_front();
}
void Sline::line_front() const
{
front_line(m_tail, m_head);
}
void Sline::line_back() const // back line
{
back_line(m_tail, m_head);
}
} // end of namespace
|
