src/glu/sgi/libtess/geom.c

   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 ** $Date: 2001/03/17 00:25:41 $ $Revision: 1.1 $
  34 ** $Header: /home/krh/git/sync/mesa-cvs-repo/Mesa/src/glu/sgi/libtess/geom.c,v 1.1 2001/03/17 00:25:41 brianp Exp $
  35 */
  36
  37 #include "gluos.h"
  38 #include <assert.h>
  39 #include "mesh.h"
  40 #include "geom.h"
  41
  42 int __gl_vertLeq( GLUvertex *u, GLUvertex *v )
  43 {
  44   /* Returns TRUE if u is lexicographically <= v. */
  45
  46   return VertLeq( u, v );
  47 }
  48
  49 GLdouble __gl_edgeEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
  50 {
  51   /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
  52    * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
  53    * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
  54    * If uw is vertical (and thus passes thru v), the result is zero.
  55    *
  56    * The calculation is extremely accurate and stable, even when v
  57    * is very close to u or w.  In particular if we set v->t = 0 and
  58    * let r be the negated result (this evaluates (uw)(v->s)), then
  59    * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
  60    */
  61   GLdouble gapL, gapR;
  62
  63   assert( VertLeq( u, v ) && VertLeq( v, w ));
  64
  65   gapL = v->s - u->s;
  66   gapR = w->s - v->s;
  67
  68   if( gapL + gapR > 0 ) {
  69     if( gapL < gapR ) {
  70       return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
  71     } else {
  72       return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
  73     }
  74   }
  75   /* vertical line */
  76   return 0;
  77 }
  78
  79 GLdouble __gl_edgeSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
  80 {
  81   /* Returns a number whose sign matches EdgeEval(u,v,w) but which
  82    * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
  83    * as v is above, on, or below the edge uw.
  84    */
  85   GLdouble gapL, gapR;
  86
  87   assert( VertLeq( u, v ) && VertLeq( v, w ));
  88
  89   gapL = v->s - u->s;
  90   gapR = w->s - v->s;
  91
  92   if( gapL + gapR > 0 ) {
  93     return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
  94   }
  95   /* vertical line */
  96   return 0;
  97 }
  98
  99
 100 /***********************************************************************
 101  * Define versions of EdgeSign, EdgeEval with s and t transposed.
 102  */
 103
 104 GLdouble __gl_transEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 105 {
 106   /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
 107    * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
 108    * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v.
 109    * If uw is vertical (and thus passes thru v), the result is zero.
 110    *
 111    * The calculation is extremely accurate and stable, even when v
 112    * is very close to u or w.  In particular if we set v->s = 0 and
 113    * let r be the negated result (this evaluates (uw)(v->t)), then
 114    * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
 115    */
 116   GLdouble gapL, gapR;
 117
 118   assert( TransLeq( u, v ) && TransLeq( v, w ));
 119
 120   gapL = v->t - u->t;
 121   gapR = w->t - v->t;
 122
 123   if( gapL + gapR > 0 ) {
 124     if( gapL < gapR ) {
 125       return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
 126     } else {
 127       return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
 128     }
 129   }
 130   /* vertical line */
 131   return 0;
 132 }
 133
 134 GLdouble __gl_transSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 135 {
 136   /* Returns a number whose sign matches TransEval(u,v,w) but which
 137    * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
 138    * as v is above, on, or below the edge uw.
 139    */
 140   GLdouble gapL, gapR;
 141
 142   assert( TransLeq( u, v ) && TransLeq( v, w ));
 143
 144   gapL = v->t - u->t;
 145   gapR = w->t - v->t;
 146
 147   if( gapL + gapR > 0 ) {
 148     return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
 149   }
 150   /* vertical line */
 151   return 0;
 152 }
 153
 154
 155 int __gl_vertCCW( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 156 {
 157   /* For almost-degenerate situations, the results are not reliable.
 158    * Unless the floating-point arithmetic can be performed without
 159    * rounding errors, *any* implementation will give incorrect results
 160    * on some degenerate inputs, so the client must have some way to
 161    * handle this situation.
 162    */
 163   return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0;
 164 }
 165
 166 /* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
 167  * or (x+y)/2 if a==b==0.  It requires that a,b >= 0, and enforces
 168  * this in the rare case that one argument is slightly negative.
 169  * The implementation is extremely stable numerically.
 170  * In particular it guarantees that the result r satisfies
 171  * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
 172  * even when a and b differ greatly in magnitude.
 173  */
 174 #define RealInterpolate(a,x,b,y)                        \
 175   (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b,            \
 176   ((a <= b) ? ((b == 0) ? ((x+y) / 2)                   \
 177                         : (x + (y-x) * (a/(a+b))))      \
 178             : (y + (x-y) * (b/(a+b)))))
 179
 180 #ifndef FOR_TRITE_TEST_PROGRAM
 181 #define Interpolate(a,x,b,y)    RealInterpolate(a,x,b,y)
 182 #else
 183
 184 /* Claim: the ONLY property the sweep algorithm relies on is that
 185  * MIN(x,y) <= r <= MAX(x,y).  This is a nasty way to test that.
 186  */
 187 #include <stdlib.h>
 188 extern int RandomInterpolate;
 189
 190 GLdouble Interpolate( GLdouble a, GLdouble x, GLdouble b, GLdouble y)
 191 {
 192 printf("*********************%d\n",RandomInterpolate);
 193   if( RandomInterpolate ) {
 194     a = 1.2 * drand48() - 0.1;
 195     a = (a < 0) ? 0 : ((a > 1) ? 1 : a);
 196     b = 1.0 - a;
 197   }
 198   return RealInterpolate(a,x,b,y);
 199 }
 200
 201 #endif
 202
 203 #define Swap(a,b)       if (1) { GLUvertex *t = a; a = b; b = t; } else
 204
 205 void __gl_edgeIntersect( GLUvertex *o1, GLUvertex *d1,
 206                          GLUvertex *o2, GLUvertex *d2,
 207                          GLUvertex *v )
 208 /* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
 209  * The computed point is guaranteed to lie in the intersection of the
 210  * bounding rectangles defined by each edge.
 211  */
 212 {
 213   GLdouble z1, z2;
 214
 215   /* This is certainly not the most efficient way to find the intersection
 216    * of two line segments, but it is very numerically stable.
 217    *
 218    * Strategy: find the two middle vertices in the VertLeq ordering,
 219    * and interpolate the intersection s-value from these.  Then repeat
 220    * using the TransLeq ordering to find the intersection t-value.
 221    */
 222
 223   if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); }
 224   if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); }
 225   if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
 226
 227   if( ! VertLeq( o2, d1 )) {
 228     /* Technically, no intersection -- do our best */
 229     v->s = (o2->s + d1->s) / 2;
 230   } else if( VertLeq( d1, d2 )) {
 231     /* Interpolate between o2 and d1 */
 232     z1 = EdgeEval( o1, o2, d1 );
 233     z2 = EdgeEval( o2, d1, d2 );
 234     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 235     v->s = Interpolate( z1, o2->s, z2, d1->s );
 236   } else {
 237     /* Interpolate between o2 and d2 */
 238     z1 = EdgeSign( o1, o2, d1 );
 239     z2 = -EdgeSign( o1, d2, d1 );
 240     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 241     v->s = Interpolate( z1, o2->s, z2, d2->s );
 242   }
 243
 244   /* Now repeat the process for t */
 245
 246   if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); }
 247   if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); }
 248   if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
 249
 250   if( ! TransLeq( o2, d1 )) {
 251     /* Technically, no intersection -- do our best */
 252     v->t = (o2->t + d1->t) / 2;
 253   } else if( TransLeq( d1, d2 )) {
 254     /* Interpolate between o2 and d1 */
 255     z1 = TransEval( o1, o2, d1 );
 256     z2 = TransEval( o2, d1, d2 );
 257     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 258     v->t = Interpolate( z1, o2->t, z2, d1->t );
 259   } else {
 260     /* Interpolate between o2 and d2 */
 261     z1 = TransSign( o1, o2, d1 );
 262     z2 = -TransSign( o1, d2, d1 );
 263     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 264     v->t = Interpolate( z1, o2->t, z2, d2->t );
 265   }
 266 }