dlls/glu32/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 */
  34
  35 #include <stdarg.h>
  36 #include <assert.h>
  37
  38 #include "windef.h"
  39 #include "winbase.h"
  40
  41 #include "tess.h"
  42
  43 int __gl_vertLeq( GLUvertex *u, GLUvertex *v )
  44 {
  45   /* Returns TRUE if u is lexicographically <= v. */
  46
  47   return VertLeq( u, v );
  48 }
  49
  50 GLdouble __gl_edgeEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
  51 {
  52   /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
  53    * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
  54    * Returns v->t - (uw)(v->s), i.e. the signed distance from uw to v.
  55    * If uw is vertical (and thus passes through v), the result is zero.
  56    *
  57    * The calculation is extremely accurate and stable, even when v
  58    * is very close to u or w.  In particular if we set v->t = 0 and
  59    * let r be the negated result (this evaluates (uw)(v->s)), then
  60    * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
  61    */
  62   GLdouble gapL, gapR;
  63
  64   assert( VertLeq( u, v ) && VertLeq( v, w ));
  65
  66   gapL = v->s - u->s;
  67   gapR = w->s - v->s;
  68
  69   if( gapL + gapR > 0 ) {
  70     if( gapL < gapR ) {
  71       return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
  72     } else {
  73       return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
  74     }
  75   }
  76   /* vertical line */
  77   return 0;
  78 }
  79
  80 GLdouble __gl_edgeSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
  81 {
  82   /* Returns a number whose sign matches EdgeEval(u,v,w) but which
  83    * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
  84    * as v is above, on, or below the edge uw.
  85    */
  86   GLdouble gapL, gapR;
  87
  88   assert( VertLeq( u, v ) && VertLeq( v, w ));
  89
  90   gapL = v->s - u->s;
  91   gapR = w->s - v->s;
  92
  93   if( gapL + gapR > 0 ) {
  94     return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
  95   }
  96   /* vertical line */
  97   return 0;
  98 }
  99
 100
 101 /***********************************************************************
 102  * Define versions of EdgeSign, EdgeEval with s and t transposed.
 103  */
 104
 105 GLdouble __gl_transEval( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 106 {
 107   /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
 108    * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
 109    * Returns v->s - (uw)(v->t), i.e. the signed distance from uw to v.
 110    * If uw is vertical (and thus passes through v), the result is zero.
 111    *
 112    * The calculation is extremely accurate and stable, even when v
 113    * is very close to u or w.  In particular if we set v->s = 0 and
 114    * let r be the negated result (this evaluates (uw)(v->t)), then
 115    * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
 116    */
 117   GLdouble gapL, gapR;
 118
 119   assert( TransLeq( u, v ) && TransLeq( v, w ));
 120
 121   gapL = v->t - u->t;
 122   gapR = w->t - v->t;
 123
 124   if( gapL + gapR > 0 ) {
 125     if( gapL < gapR ) {
 126       return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
 127     } else {
 128       return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
 129     }
 130   }
 131   /* vertical line */
 132   return 0;
 133 }
 134
 135 GLdouble __gl_transSign( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 136 {
 137   /* Returns a number whose sign matches TransEval(u,v,w) but which
 138    * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
 139    * as v is above, on, or below the edge uw.
 140    */
 141   GLdouble gapL, gapR;
 142
 143   assert( TransLeq( u, v ) && TransLeq( v, w ));
 144
 145   gapL = v->t - u->t;
 146   gapR = w->t - v->t;
 147
 148   if( gapL + gapR > 0 ) {
 149     return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
 150   }
 151   /* vertical line */
 152   return 0;
 153 }
 154
 155
 156 int __gl_vertCCW( GLUvertex *u, GLUvertex *v, GLUvertex *w )
 157 {
 158   /* For almost-degenerate situations, the results are not reliable.
 159    * Unless the floating-point arithmetic can be performed without
 160    * rounding errors, *any* implementation will give incorrect results
 161    * on some degenerate inputs, so the client must have some way to
 162    * handle this situation.
 163    */
 164   return (u->s*(v->t - w->t) + v->s*(w->t - u->t) + w->s*(u->t - v->t)) >= 0;
 165 }
 166
 167 /* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
 168  * or (x+y)/2 if a==b==0.  It requires that a,b >= 0, and enforces
 169  * this in the rare case that one argument is slightly negative.
 170  * The implementation is extremely stable numerically.
 171  * In particular it guarantees that the result r satisfies
 172  * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
 173  * even when a and b differ greatly in magnitude.
 174  */
 175 #define Interpolate(a,x,b,y)                            \
 176   (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b,            \
 177   ((a <= b) ? ((b == 0) ? ((x+y) / 2)                   \
 178                         : (x + (y-x) * (a/(a+b))))      \
 179             : (y + (x-y) * (b/(a+b)))))
 180
 181 #define Swap(a,b)       do { GLUvertex *t = a; a = b; b = t; } while (0)
 182
 183 void __gl_edgeIntersect( GLUvertex *o1, GLUvertex *d1,
 184                          GLUvertex *o2, GLUvertex *d2,
 185                          GLUvertex *v )
 186 /* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
 187  * The computed point is guaranteed to lie in the intersection of the
 188  * bounding rectangles defined by each edge.
 189  */
 190 {
 191   GLdouble z1, z2;
 192
 193   /* This is certainly not the most efficient way to find the intersection
 194    * of two line segments, but it is very numerically stable.
 195    *
 196    * Strategy: find the two middle vertices in the VertLeq ordering,
 197    * and interpolate the intersection s-value from these.  Then repeat
 198    * using the TransLeq ordering to find the intersection t-value.
 199    */
 200
 201   if( ! VertLeq( o1, d1 )) { Swap( o1, d1 ); }
 202   if( ! VertLeq( o2, d2 )) { Swap( o2, d2 ); }
 203   if( ! VertLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
 204
 205   if( ! VertLeq( o2, d1 )) {
 206     /* Technically, no intersection -- do our best */
 207     v->s = (o2->s + d1->s) / 2;
 208   } else if( VertLeq( d1, d2 )) {
 209     /* Interpolate between o2 and d1 */
 210     z1 = EdgeEval( o1, o2, d1 );
 211     z2 = EdgeEval( o2, d1, d2 );
 212     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 213     v->s = Interpolate( z1, o2->s, z2, d1->s );
 214   } else {
 215     /* Interpolate between o2 and d2 */
 216     z1 = EdgeSign( o1, o2, d1 );
 217     z2 = -EdgeSign( o1, d2, d1 );
 218     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 219     v->s = Interpolate( z1, o2->s, z2, d2->s );
 220   }
 221
 222   /* Now repeat the process for t */
 223
 224   if( ! TransLeq( o1, d1 )) { Swap( o1, d1 ); }
 225   if( ! TransLeq( o2, d2 )) { Swap( o2, d2 ); }
 226   if( ! TransLeq( o1, o2 )) { Swap( o1, o2 ); Swap( d1, d2 ); }
 227
 228   if( ! TransLeq( o2, d1 )) {
 229     /* Technically, no intersection -- do our best */
 230     v->t = (o2->t + d1->t) / 2;
 231   } else if( TransLeq( d1, d2 )) {
 232     /* Interpolate between o2 and d1 */
 233     z1 = TransEval( o1, o2, d1 );
 234     z2 = TransEval( o2, d1, d2 );
 235     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 236     v->t = Interpolate( z1, o2->t, z2, d1->t );
 237   } else {
 238     /* Interpolate between o2 and d2 */
 239     z1 = TransSign( o1, o2, d1 );
 240     z2 = -TransSign( o1, d2, d1 );
 241     if( z1+z2 < 0 ) { z1 = -z1; z2 = -z2; }
 242     v->t = Interpolate( z1, o2->t, z2, d2->t );
 243   }
 244 }