1/*
2** License Applicability. Except to the extent portions of this file are
3** made subject to an alternative license as permitted in the SGI Free
4** Software License B, Version 1.1 (the "License"), the contents of this
5** file are subject only to the provisions of the License. You may not use
6** this file except in compliance with the License. You may obtain a copy
7** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
8** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
9**
10** http://oss.sgi.com/projects/FreeB
11**
12** Note that, as provided in the License, the Software is distributed on an
13** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
14** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
15** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
16** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
17**
18** Original Code. The Original Code is: OpenGL Sample Implementation,
19** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
20** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
21** Copyright in any portions created by third parties is as indicated
22** elsewhere herein. All Rights Reserved.
23**
24** Additional Notice Provisions: The application programming interfaces
25** established by SGI in conjunction with the Original Code are The
26** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
27** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
28** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
29** Window System(R) (Version 1.3), released October 19, 1998. This software
30** was created using the OpenGL(R) version 1.2.1 Sample Implementation
31** published by SGI, but has not been independently verified as being
32** compliant with the OpenGL(R) version 1.2.1 Specification.
33**
34*/
35/*
36** Author: Eric Veach, July 1994.
37**
38** $Date$ $Revision$
39** $Header: //depot/main/gfx/lib/glu/libtess/geom.c#5 $
40*/
41
42#include "gluos.h"
43#include <assert.h>
44#include "mesh.h"
45#include "geom.h"
46
47int __gl_vertLeq( GLUvertex *u, GLUvertex *v )
48{
49  /* Returns TRUE if u is lexicographically <= v. */
50
51  return VertLeq( u, v );
52}
53
54GLdouble __gl_edgeEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
55{
56  /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
57   * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
58   * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
59   * If uw is vertical (and thus passes thru v), the result is zero.
60   *
61   * The calculation is extremely accurate and stable, even when v
62   * is very close to u or w.  In particular if we set v->t = 0 and
63   * let r be the negated result (this evaluates (uw)(v->s)), then
64   * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
65   */
66  GLdouble gapL, gapR;
67
68  assert( VertLeq( u, v ) && VertLeq( v, w ));
69
70  gapL = v->s - u->s;
71  gapR = w->s - v->s;
72
73  if( gapL + gapR > 0 ) {
74    if( gapL < gapR ) {
75      return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
76    } else {
77      return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
78    }
79  }
80  /* vertical line */
81  return 0;
82}
83
84GLdouble __gl_edgeSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
85{
86  /* Returns a number whose sign matches EdgeEval(u,v,w) but which
87   * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
88   * as v is above, on, or below the edge uw.
89   */
90  GLdouble gapL, gapR;
91
92  assert( VertLeq( u, v ) && VertLeq( v, w ));
93
94  gapL = v->s - u->s;
95  gapR = w->s - v->s;
96
97  if( gapL + gapR > 0 ) {
98    return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
99  }
100  /* vertical line */
101  return 0;
102}
103
104
105/***********************************************************************
106 * Define versions of EdgeSign, EdgeEval with s and t transposed.
107 */
108
109GLdouble __gl_transEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
110{
111  /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
112   * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
113   * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v.
114   * If uw is vertical (and thus passes thru v), the result is zero.
115   *
116   * The calculation is extremely accurate and stable, even when v
117   * is very close to u or w.  In particular if we set v->s = 0 and
118   * let r be the negated result (this evaluates (uw)(v->t)), then
119   * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
120   */
121  GLdouble gapL, gapR;
122
123  assert( TransLeq( u, v ) && TransLeq( v, w ));
124
125  gapL = v->t - u->t;
126  gapR = w->t - v->t;
127
128  if( gapL + gapR > 0 ) {
129    if( gapL < gapR ) {
130      return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
131    } else {
132      return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
133    }
134  }
135  /* vertical line */
136  return 0;
137}
138
139GLdouble __gl_transSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
140{
141  /* Returns a number whose sign matches TransEval(u,v,w) but which
142   * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
143   * as v is above, on, or below the edge uw.
144   */
145  GLdouble gapL, gapR;
146
147  assert( TransLeq( u, v ) && TransLeq( v, w ));
148
149  gapL = v->t - u->t;
150  gapR = w->t - v->t;
151
152  if( gapL + gapR > 0 ) {
153    return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
154  }
155  /* vertical line */
156  return 0;
157}
158
159
160int __gl_vertCCW( GLUvertex *u, GLUvertex *v, GLUvertex *w )
161{
162  /* For almost-degenerate situations, the results are not reliable.
163   * Unless the floating-point arithmetic can be performed without
164   * rounding errors, *any* implementation will give incorrect results
165   * on some degenerate inputs, so the client must have some way to
166   * handle this situation.
167   */
168  return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0;
169}
170
171/* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
172 * or (x+y)/2 if a==b==0.  It requires that a,b >= 0, and enforces
173 * this in the rare case that one argument is slightly negative.
174 * The implementation is extremely stable numerically.
175 * In particular it guarantees that the result r satisfies
176 * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
177 * even when a and b differ greatly in magnitude.
178 */
179#define RealInterpolate(a,x,b,y)			\
180  (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b,		\
181  ((a <= b) ? ((b == 0) ? ((x+y) / 2)			\
182                        : (x + (y-x) * (a/(a+b))))	\
183            : (y + (x-y) * (b/(a+b)))))
184
185#ifndef FOR_TRITE_TEST_PROGRAM
186#define Interpolate(a,x,b,y)	RealInterpolate(a,x,b,y)
187#else
188
189/* Claim: the ONLY property the sweep algorithm relies on is that
190 * MIN(x,y) <= r <= MAX(x,y).  This is a nasty way to test that.
191 */
192#include <stdlib.h>
193extern int RandomInterpolate;
194
195GLdouble Interpolate( GLdouble a, GLdouble x, GLdouble b, GLdouble y)
196{
197printf("*********************%d\n",RandomInterpolate);
198  if( RandomInterpolate ) {
199    a = 1.2 * drand48() - 0.1;
200    a = (a < 0) ? 0 : ((a > 1) ? 1 : a);
201    b = 1.0 - a;
202  }
203  return RealInterpolate(a,x,b,y);
204}
205
206#endif
207
208#define Swap(a,b)	do { GLUvertex *t = a; a = b; b = t; } while(0)
209
210void __gl_edgeIntersect( GLUvertex *o1, GLUvertex *d1,
211			 GLUvertex *o2, GLUvertex *d2,
212			 GLUvertex *v )
213/* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
214 * The computed point is guaranteed to lie in the intersection of the
215 * bounding rectangles defined by each edge.
216 */
217{
218  GLdouble z1, z2;
219
220  /* This is certainly not the most efficient way to find the intersection
221   * of two line segments, but it is very numerically stable.
222   *
223   * Strategy: find the two middle vertices in the VertLeq ordering,
224   * and interpolate the intersection s-value from these.  Then repeat
225   * using the TransLeq ordering to find the intersection t-value.
226   */
227
228  if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); }
229  if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); }
230  if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
231
232  if( ! VertLeq( o2, d1 )) {
233    /* Technically, no intersection -- do our best */
234    v->s = (o2->s + d1->s) / 2;
235  } else if( VertLeq( d1, d2 )) {
236    /* Interpolate between o2 and d1 */
237    z1 = EdgeEval( o1, o2, d1 );
238    z2 = EdgeEval( o2, d1, d2 );
239    if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
240    v->s = Interpolate( z1, o2->s, z2, d1->s );
241  } else {
242    /* Interpolate between o2 and d2 */
243    z1 = EdgeSign( o1, o2, d1 );
244    z2 = -EdgeSign( o1, d2, d1 );
245    if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
246    v->s = Interpolate( z1, o2->s, z2, d2->s );
247  }
248
249  /* Now repeat the process for t */
250
251  if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); }
252  if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); }
253  if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
254
255  if( ! TransLeq( o2, d1 )) {
256    /* Technically, no intersection -- do our best */
257    v->t = (o2->t + d1->t) / 2;
258  } else if( TransLeq( d1, d2 )) {
259    /* Interpolate between o2 and d1 */
260    z1 = TransEval( o1, o2, d1 );
261    z2 = TransEval( o2, d1, d2 );
262    if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
263    v->t = Interpolate( z1, o2->t, z2, d1->t );
264  } else {
265    /* Interpolate between o2 and d2 */
266    z1 = TransSign( o1, o2, d1 );
267    z2 = -TransSign( o1, d2, d1 );
268    if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
269    v->t = Interpolate( z1, o2->t, z2, d2->t );
270  }
271}
272