src/glu/sgi/libtess/geom.c

   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 */
  39
  40 #include "gluos.h"
  41 #include <assert.h>
  42 #include "mesh.h"
  43 #include "geom.h"
  44
  45 int __gl_vertLeq( GLUvertex *u, GLUvertex *v )
  46 {
  47   /* Returns TRUE if u is lexicographically <= v. */
  48
  49   return VertLeq( u, v );
  50 }
  51
  52 GLdouble __gl_edgeEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
  53 {
  54   /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
  55    * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
  56    * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
  57    * If uw is vertical (and thus passes thru v), the result is zero.
  58    *
  59    * The calculation is extremely accurate and stable, even when v
  60    * is very close to u or w.  In particular if we set v->t = 0 and
  61    * let r be the negated result (this evaluates (uw)(v->s)), then
  62    * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
  63    */
  64   GLdouble gapL, gapR;
  65
  66   assert( VertLeq( u, v ) && VertLeq( v, w ));
  67
  68   gapL = v->s - u->s;
  69   gapR = w->s - v->s;
  70
  71   if( gapL + gapR > 0 ) {
  72     if( gapL < gapR ) {
  73       return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
  74     } else {
  75       return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
  76     }
  77   }
  78   /* vertical line */
  79   return 0;
  80 }
  81
  82 GLdouble __gl_edgeSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
  83 {
  84   /* Returns a number whose sign matches EdgeEval(u,v,w) but which
  85    * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
  86    * as v is above, on, or below the edge uw.
  87    */
  88   GLdouble gapL, gapR;
  89
  90   assert( VertLeq( u, v ) && VertLeq( v, w ));
  91
  92   gapL = v->s - u->s;
  93   gapR = w->s - v->s;
  94
  95   if( gapL + gapR > 0 ) {
  96     return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
  97   }
  98   /* vertical line */
  99   return 0;
 100 }
 101
 102
 103 /***********************************************************************
 104  * Define versions of EdgeSign, EdgeEval with s and t transposed.
 105  */
 106
 107 GLdouble __gl_transEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 108 {
 109   /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
 110    * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
 111    * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v.
 112    * If uw is vertical (and thus passes thru v), the result is zero.
 113    *
 114    * The calculation is extremely accurate and stable, even when v
 115    * is very close to u or w.  In particular if we set v->s = 0 and
 116    * let r be the negated result (this evaluates (uw)(v->t)), then
 117    * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
 118    */
 119   GLdouble gapL, gapR;
 120
 121   assert( TransLeq( u, v ) && TransLeq( v, w ));
 122
 123   gapL = v->t - u->t;
 124   gapR = w->t - v->t;
 125
 126   if( gapL + gapR > 0 ) {
 127     if( gapL < gapR ) {
 128       return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
 129     } else {
 130       return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
 131     }
 132   }
 133   /* vertical line */
 134   return 0;
 135 }
 136
 137 GLdouble __gl_transSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 138 {
 139   /* Returns a number whose sign matches TransEval(u,v,w) but which
 140    * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
 141    * as v is above, on, or below the edge uw.
 142    */
 143   GLdouble gapL, gapR;
 144
 145   assert( TransLeq( u, v ) && TransLeq( v, w ));
 146
 147   gapL = v->t - u->t;
 148   gapR = w->t - v->t;
 149
 150   if( gapL + gapR > 0 ) {
 151     return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
 152   }
 153   /* vertical line */
 154   return 0;
 155 }
 156
 157
 158 int __gl_vertCCW( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 159 {
 160   /* For almost-degenerate situations, the results are not reliable.
 161    * Unless the floating-point arithmetic can be performed without
 162    * rounding errors, *any* implementation will give incorrect results
 163    * on some degenerate inputs, so the client must have some way to
 164    * handle this situation.
 165    */
 166   return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0;
 167 }
 168
 169 /* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
 170  * or (x+y)/2 if a==b==0.  It requires that a,b >= 0, and enforces
 171  * this in the rare case that one argument is slightly negative.
 172  * The implementation is extremely stable numerically.
 173  * In particular it guarantees that the result r satisfies
 174  * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
 175  * even when a and b differ greatly in magnitude.
 176  */
 177 #define RealInterpolate(a,x,b,y)                        \
 178   (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b,            \
 179   ((a <= b) ? ((b == 0) ? ((x+y) / 2)                   \
 180                         : (x + (y-x) * (a/(a+b))))      \
 181             : (y + (x-y) * (b/(a+b)))))
 182
 183 #ifndef FOR_TRITE_TEST_PROGRAM
 184 #define Interpolate(a,x,b,y)    RealInterpolate(a,x,b,y)
 185 #else
 186
 187 /* Claim: the ONLY property the sweep algorithm relies on is that
 188  * MIN(x,y) <= r <= MAX(x,y).  This is a nasty way to test that.
 189  */
 190 #include <stdlib.h>
 191 extern int RandomInterpolate;
 192
 193 GLdouble Interpolate( GLdouble a, GLdouble x, GLdouble b, GLdouble y)
 194 {
 195 printf("*********************%d\n",RandomInterpolate);
 196   if( RandomInterpolate ) {
 197     a = 1.2 * drand48() - 0.1;
 198     a = (a < 0) ? 0 : ((a > 1) ? 1 : a);
 199     b = 1.0 - a;
 200   }
 201   return RealInterpolate(a,x,b,y);
 202 }
 203
 204 #endif
 205
 206 #define Swap(a,b)       if (1) { GLUvertex *t = a; a = b; b = t; } else
 207
 208 void __gl_edgeIntersect( GLUvertex *o1, GLUvertex *d1,
 209                          GLUvertex *o2, GLUvertex *d2,
 210                          GLUvertex *v )
 211 /* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
 212  * The computed point is guaranteed to lie in the intersection of the
 213  * bounding rectangles defined by each edge.
 214  */
 215 {
 216   GLdouble z1, z2;
 217
 218   /* This is certainly not the most efficient way to find the intersection
 219    * of two line segments, but it is very numerically stable.
 220    *
 221    * Strategy: find the two middle vertices in the VertLeq ordering,
 222    * and interpolate the intersection s-value from these.  Then repeat
 223    * using the TransLeq ordering to find the intersection t-value.
 224    */
 225
 226   if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); }
 227   if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); }
 228   if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
 229
 230   if( ! VertLeq( o2, d1 )) {
 231     /* Technically, no intersection -- do our best */
 232     v->s = (o2->s + d1->s) / 2;
 233   } else if( VertLeq( d1, d2 )) {
 234     /* Interpolate between o2 and d1 */
 235     z1 = EdgeEval( o1, o2, d1 );
 236     z2 = EdgeEval( o2, d1, d2 );
 237     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 238     v->s = Interpolate( z1, o2->s, z2, d1->s );
 239   } else {
 240     /* Interpolate between o2 and d2 */
 241     z1 = EdgeSign( o1, o2, d1 );
 242     z2 = -EdgeSign( o1, d2, d1 );
 243     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 244     v->s = Interpolate( z1, o2->s, z2, d2->s );
 245   }
 246
 247   /* Now repeat the process for t */
 248
 249   if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); }
 250   if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); }
 251   if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
 252
 253   if( ! TransLeq( o2, d1 )) {
 254     /* Technically, no intersection -- do our best */
 255     v->t = (o2->t + d1->t) / 2;
 256   } else if( TransLeq( d1, d2 )) {
 257     /* Interpolate between o2 and d1 */
 258     z1 = TransEval( o1, o2, d1 );
 259     z2 = TransEval( o2, d1, d2 );
 260     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 261     v->t = Interpolate( z1, o2->t, z2, d1->t );
 262   } else {
 263     /* Interpolate between o2 and d2 */
 264     z1 = TransSign( o1, o2, d1 );
 265     z2 = -TransSign( o1, d2, d1 );
 266     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 267     v->t = Interpolate( z1, o2->t, z2, d2->t );
 268   }
 269 }