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
|
// -*- C++ -*-
/* Copyright (C) 1989-2020 Free Software Foundation, Inc.
Written by Gaius Mulley <gaius@glam.ac.uk>
using adjust_arc_center() from printer.cpp, written by James Clark.
This file is part of groff.
groff 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 3 of the License, or
(at your option) any later version.
groff 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 this program. If not, see <http://www.gnu.org/licenses/>. */
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
#include <stdio.h>
#include <math.h>
#undef MAX
#define MAX(a, b) (((a) > (b)) ? (a) : (b))
#undef MIN
#define MIN(a, b) (((a) < (b)) ? (a) : (b))
// This utility function adjusts the specified center of the
// arc so that it is equidistant between the specified start
// and end points. (p[0], p[1]) is a vector from the current
// point to the center; (p[2], p[3]) is a vector from the
// center to the end point. If the center can be adjusted,
// a vector from the current point to the adjusted center is
// stored in c[0], c[1] and 1 is returned. Otherwise 0 is
// returned.
#if 1
int adjust_arc_center(const int *p, double *c)
{
// We move the center along a line parallel to the line between
// the specified start point and end point so that the center
// is equidistant between the start and end point.
// It can be proved (using Lagrange multipliers) that this will
// give the point nearest to the specified center that is equidistant
// between the start and end point.
double x = p[0] + p[2]; // (x, y) is the end point
double y = p[1] + p[3];
double n = x*x + y*y;
if (n != 0) {
c[0]= double(p[0]);
c[1] = double(p[1]);
double k = .5 - (c[0]*x + c[1]*y)/n;
c[0] += k*x;
c[1] += k*y;
return 1;
}
else
return 0;
}
#else
int printer::adjust_arc_center(const int *p, double *c)
{
int x = p[0] + p[2]; // (x, y) is the end point
int y = p[1] + p[3];
// Start at the current point; go in the direction of the specified
// center point until we reach a point that is equidistant between
// the specified starting point and the specified end point. Place
// the center of the arc there.
double n = p[0]*double(x) + p[1]*double(y);
if (n > 0) {
double k = (double(x)*x + double(y)*y)/(2.0*n);
// (cx, cy) is our chosen center
c[0] = k*p[0];
c[1] = k*p[1];
return 1;
}
else {
// We would never reach such a point. So instead start at the
// specified end point of the arc. Go towards the specified
// center point until we reach a point that is equidistant between
// the specified start point and specified end point. Place
// the center of the arc there.
n = p[2]*double(x) + p[3]*double(y);
if (n > 0) {
double k = 1 - (double(x)*x + double(y)*y)/(2.0*n);
// (c[0], c[1]) is our chosen center
c[0] = p[0] + k*p[2];
c[1] = p[1] + k*p[3];
return 1;
}
else
return 0;
}
}
#endif
/*
* check_output_arc_limits - works out the smallest box that will encompass
* an arc defined by an origin (x, y) and two
* vectors (p0, p1) and (p2, p3).
* (x1, y1) -> start of arc
* (x1, y1) + (xv1, yv1) -> center of circle
* (x1, y1) + (xv1, yv1) + (xv2, yv2) -> end of arc
*
* Works out in which quadrant the arc starts and
* stops, and from this it determines the x, y
* max/min limits. The arc is drawn clockwise.
*/
void check_output_arc_limits(int x_1, int y_1,
int xv_1, int yv_1,
int xv_2, int yv_2,
double c_0, double c_1,
int *minx, int *maxx,
int *miny, int *maxy)
{
int radius = (int)sqrt(c_0 * c_0 + c_1 * c_1);
// clockwise direction
int xcenter = x_1 + xv_1;
int ycenter = y_1 + yv_1;
int xend = xcenter + xv_2;
int yend = ycenter + yv_2;
// for convenience, transform to counterclockwise direction,
// centered at the origin
int xs = xend - xcenter;
int ys = yend - ycenter;
int xe = x_1 - xcenter;
int ye = y_1 - ycenter;
*minx = *maxx = xs;
*miny = *maxy = ys;
if (xe > *maxx)
*maxx = xe;
else if (xe < *minx)
*minx = xe;
if (ye > *maxy)
*maxy = ye;
else if (ye < *miny)
*miny = ye;
int qs, qe; // quadrants 0..3
if (xs >= 0)
qs = (ys >= 0) ? 0 : 3;
else
qs = (ys >= 0) ? 1 : 2;
if (xe >= 0)
qe = (ye >= 0) ? 0 : 3;
else
qe = (ye >= 0) ? 1 : 2;
// make qs always smaller than qe
if ((qs > qe)
|| ((qs == qe) && (double(xs) * ye < double(xe) * ys)))
qe += 4;
for (int i = qs; i < qe; i++)
switch (i % 4) {
case 0:
*maxy = radius;
break;
case 1:
*minx = -radius;
break;
case 2:
*miny = -radius;
break;
case 3:
*maxx = radius;
break;
}
*minx += xcenter;
*maxx += xcenter;
*miny += ycenter;
*maxy += ycenter;
}
|
