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geom.c
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1/*
2 * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
3 * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
4 *
5 * Permission is hereby granted, free of charge, to any person obtaining a
6 * copy of this software and associated documentation files (the "Software"),
7 * to deal in the Software without restriction, including without limitation
8 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
9 * and/or sell copies of the Software, and to permit persons to whom the
10 * Software is furnished to do so, subject to the following conditions:
11 *
12 * The above copyright notice including the dates of first publication and
13 * either this permission notice or a reference to
14 * http://oss.sgi.com/projects/FreeB/
15 * shall be included in all copies or substantial portions of the Software.
16 *
17 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
18 * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
19 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
20 * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
21 * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
22 * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
23 * SOFTWARE.
24 *
25 * Except as contained in this notice, the name of Silicon Graphics, Inc.
26 * shall not be used in advertising or otherwise to promote the sale, use or
27 * other dealings in this Software without prior written authorization from
28 * Silicon Graphics, Inc.
29 */
30/*
31** Author: Eric Veach, July 1994.
32**
33*/
34
35#include "gluos.h"
36#include <assert.h>
37#include "mesh.h"
38#include "geom.h"
39
41{
42 /* Returns TRUE if u is lexicographically <= v. */
43
44 return VertLeq( u, v );
45}
46
48{
49 /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
50 * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
51 * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
52 * If uw is vertical (and thus passes thru v), the result is zero.
53 *
54 * The calculation is extremely accurate and stable, even when v
55 * is very close to u or w. In particular if we set v->t = 0 and
56 * let r be the negated result (this evaluates (uw)(v->s)), then
57 * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
58 */
59 GLdouble gapL, gapR;
60
61 assert( VertLeq( u, v ) && VertLeq( v, w ));
62
63 gapL = v->s - u->s;
64 gapR = w->s - v->s;
65
66 if( gapL + gapR > 0 ) {
67 if( gapL < gapR ) {
68 return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
69 } else {
70 return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
71 }
72 }
73 /* vertical line */
74 return 0;
75}
76
78{
79 /* Returns a number whose sign matches EdgeEval(u,v,w) but which
80 * is cheaper to evaluate. Returns > 0, == 0 , or < 0
81 * as v is above, on, or below the edge uw.
82 */
83 GLdouble gapL, gapR;
84
85 assert( VertLeq( u, v ) && VertLeq( v, w ));
86
87 gapL = v->s - u->s;
88 gapR = w->s - v->s;
89
90 if( gapL + gapR > 0 ) {
91 return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
92 }
93 /* vertical line */
94 return 0;
95}
96
97
98/***********************************************************************
99 * Define versions of EdgeSign, EdgeEval with s and t transposed.
100 */
101
103{
104 /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
105 * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
106 * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v.
107 * If uw is vertical (and thus passes thru v), the result is zero.
108 *
109 * The calculation is extremely accurate and stable, even when v
110 * is very close to u or w. In particular if we set v->s = 0 and
111 * let r be the negated result (this evaluates (uw)(v->t)), then
112 * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
113 */
114 GLdouble gapL, gapR;
115
116 assert( TransLeq( u, v ) && TransLeq( v, w ));
117
118 gapL = v->t - u->t;
119 gapR = w->t - v->t;
120
121 if( gapL + gapR > 0 ) {
122 if( gapL < gapR ) {
123 return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
124 } else {
125 return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
126 }
127 }
128 /* vertical line */
129 return 0;
130}
131
133{
134 /* Returns a number whose sign matches TransEval(u,v,w) but which
135 * is cheaper to evaluate. Returns > 0, == 0 , or < 0
136 * as v is above, on, or below the edge uw.
137 */
138 GLdouble gapL, gapR;
139
140 assert( TransLeq( u, v ) && TransLeq( v, w ));
141
142 gapL = v->t - u->t;
143 gapR = w->t - v->t;
144
145 if( gapL + gapR > 0 ) {
146 return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
147 }
148 /* vertical line */
149 return 0;
150}
151
152
154{
155 /* For almost-degenerate situations, the results are not reliable.
156 * Unless the floating-point arithmetic can be performed without
157 * rounding errors, *any* implementation will give incorrect results
158 * on some degenerate inputs, so the client must have some way to
159 * handle this situation.
160 */
161 return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0;
162}
163
164/* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
165 * or (x+y)/2 if a==b==0. It requires that a,b >= 0, and enforces
166 * this in the rare case that one argument is slightly negative.
167 * The implementation is extremely stable numerically.
168 * In particular it guarantees that the result r satisfies
169 * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
170 * even when a and b differ greatly in magnitude.
171 */
172#define RealInterpolate(a,x,b,y) \
173 (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b, \
174 ((a <= b) ? ((b == 0) ? ((x+y) / 2) \
175 : (x + (y-x) * (a/(a+b)))) \
176 : (y + (x-y) * (b/(a+b)))))
177
178#ifndef FOR_TRITE_TEST_PROGRAM
179#define Interpolate(a,x,b,y) RealInterpolate(a,x,b,y)
180#else
181
182/* Claim: the ONLY property the sweep algorithm relies on is that
183 * MIN(x,y) <= r <= MAX(x,y). This is a nasty way to test that.
184 */
185#include <stdlib.h>
186extern int RandomInterpolate;
187
189{
190printf("*********************%d\n",RandomInterpolate);
191 if( RandomInterpolate ) {
192 a = 1.2 * drand48() - 0.1;
193 a = (a < 0) ? 0 : ((a > 1) ? 1 : a);
194 b = 1.0 - a;
195 }
196 return RealInterpolate(a,x,b,y);
197}
198
199#endif
200
201#define Swap(a,b) do { GLUvertex *t = a; a = b; b = t; } while (0)
202
204 GLUvertex *o2, GLUvertex *d2,
205 GLUvertex *v )
206/* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
207 * The computed point is guaranteed to lie in the intersection of the
208 * bounding rectangles defined by each edge.
209 */
210{
211 GLdouble z1, z2;
212
213 /* This is certainly not the most efficient way to find the intersection
214 * of two line segments, but it is very numerically stable.
215 *
216 * Strategy: find the two middle vertices in the VertLeq ordering,
217 * and interpolate the intersection s-value from these. Then repeat
218 * using the TransLeq ordering to find the intersection t-value.
219 */
220
221 if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); }
222 if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); }
223 if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
224
225 if( ! VertLeq( o2, d1 )) {
226 /* Technically, no intersection -- do our best */
227 v->s = (o2->s + d1->s) / 2;
228 } else if( VertLeq( d1, d2 )) {
229 /* Interpolate between o2 and d1 */
230 z1 = EdgeEval( o1, o2, d1 );
231 z2 = EdgeEval( o2, d1, d2 );
232 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
233 v->s = Interpolate( z1, o2->s, z2, d1->s );
234 } else {
235 /* Interpolate between o2 and d2 */
236 z1 = EdgeSign( o1, o2, d1 );
237 z2 = -EdgeSign( o1, d2, d1 );
238 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
239 v->s = Interpolate( z1, o2->s, z2, d2->s );
240 }
241
242 /* Now repeat the process for t */
243
244 if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); }
245 if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); }
246 if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
247
248 if( ! TransLeq( o2, d1 )) {
249 /* Technically, no intersection -- do our best */
250 v->t = (o2->t + d1->t) / 2;
251 } else if( TransLeq( d1, d2 )) {
252 /* Interpolate between o2 and d1 */
253 z1 = TransEval( o1, o2, d1 );
254 z2 = TransEval( o2, d1, d2 );
255 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
256 v->t = Interpolate( z1, o2->t, z2, d1->t );
257 } else {
258 /* Interpolate between o2 and d2 */
259 z1 = TransSign( o1, o2, d1 );
260 z2 = -TransSign( o1, d2, d1 );
261 if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
262 v->t = Interpolate( z1, o2->t, z2, d2->t );
263 }
264}
double GLdouble
Definition: GL_glu.h:279
#define b(i)
Definition: RSha256.hxx:100
int __gl_vertCCW(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:153
GLdouble __gl_edgeSign(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:77
GLdouble __gl_transEval(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:102
#define RealInterpolate(a, x, b, y)
Definition: geom.c:172
GLdouble __gl_edgeEval(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:47
void __gl_edgeIntersect(GLUvertex *o1, GLUvertex *d1, GLUvertex *o2, GLUvertex *d2, GLUvertex *v)
Definition: geom.c:203
#define Interpolate(a, x, b, y)
Definition: geom.c:179
int __gl_vertLeq(GLUvertex *u, GLUvertex *v)
Definition: geom.c:40
GLdouble __gl_transSign(GLUvertex *u, GLUvertex *v, GLUvertex *w)
Definition: geom.c:132
#define Swap(a, b)
Definition: geom.c:201
#define VertLeq(u, v)
Definition: geom.h:50
#define TransEval(u, v, w)
Definition: geom.h:61
#define TransLeq(u, v)
Definition: geom.h:59
#define EdgeSign(u, v, w)
Definition: geom.h:55
#define TransSign(u, v, w)
Definition: geom.h:62
#define EdgeEval(u, v, w)
Definition: geom.h:54
Double_t y[n]
Definition: legend1.C:17
Double_t x[n]
Definition: legend1.C:17
GLdouble t
Definition: mesh.h:122
GLdouble s
Definition: mesh.h:122
auto * a
Definition: textangle.C:12