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
40int __gl_vertLeq( GLUvertex *u, GLUvertex *v )
41{
42  /* Returns TRUE if u is lexicographically <= v. */
43
44  return VertLeq( u, v );
45}
46
47GLdouble __gl_edgeEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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
77GLdouble __gl_edgeSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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
102GLdouble __gl_transEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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
132GLdouble __gl_transSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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
153int __gl_vertCCW( GLUvertex *u, GLUvertex *v, GLUvertex *w )
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
188GLdouble Interpolate( GLdouble a, GLdouble x, GLdouble b, GLdouble y)
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
203void __gl_edgeIntersect( GLUvertex *o1, GLUvertex *d1,
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}
265