File indexing completed on 2024-04-21 14:46:23

 /*
 ** Author: Eric Veach, July 1994.
 **
 */
 
 #include "gluos.h"
 #include <assert.h>
 #include "mesh.h"
 #include "geom.h"
 
 int __gl_vertLeq(GLUvertex *u, GLUvertex *v)
 {
     /* Returns TRUE if u is lexicographically <= v. */
 
     return VertLeq(u, v);
 }
 
 GLdouble __gl_edgeEval(GLUvertex *u, GLUvertex *v, GLUvertex *w)
 {
     /* Given three vertices u,v,w such that VertLeq(u,v) && VertLeq(v,w),
    * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
    * Returns v->t - (uw)(v->s), ie. the signed distance from uw to v.
    * If uw is vertical (and thus passes thru v), the result is zero.
    *
    * The calculation is extremely accurate and stable, even when v
    * is very close to u or w.  In particular if we set v->t = 0 and
    * let r be the negated result (this evaluates (uw)(v->s)), then
    * r is guaranteed to satisfy MIN(u->t,w->t) <= r <= MAX(u->t,w->t).
    */
     GLdouble gapL, gapR;
 
     assert(VertLeq(u, v) && VertLeq(v, w));
 
     gapL = v->s - u->s;
     gapR = w->s - v->s;
 
     if (gapL + gapR > 0)
     {
         if (gapL < gapR)
         {
             return (v->t - u->t) + (u->t - w->t) * (gapL / (gapL + gapR));
         }
         else
         {
             return (v->t - w->t) + (w->t - u->t) * (gapR / (gapL + gapR));
         }
     }
     /* vertical line */
     return 0;
 }
 
 GLdouble __gl_edgeSign(GLUvertex *u, GLUvertex *v, GLUvertex *w)
 {
     /* Returns a number whose sign matches EdgeEval(u,v,w) but which
    * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
    * as v is above, on, or below the edge uw.
    */
     GLdouble gapL, gapR;
 
     assert(VertLeq(u, v) && VertLeq(v, w));
 
     gapL = v->s - u->s;
     gapR = w->s - v->s;
 
     if (gapL + gapR > 0)
     {
         return (v->t - w->t) * gapL + (v->t - u->t) * gapR;
     }
     /* vertical line */
     return 0;
 }
 
 /***********************************************************************
  * Define versions of EdgeSign, EdgeEval with s and t transposed.
  */
 
 GLdouble __gl_transEval(GLUvertex *u, GLUvertex *v, GLUvertex *w)
 {
     /* Given three vertices u,v,w such that TransLeq(u,v) && TransLeq(v,w),
    * evaluates the t-coord of the edge uw at the s-coord of the vertex v.
    * Returns v->s - (uw)(v->t), ie. the signed distance from uw to v.
    * If uw is vertical (and thus passes thru v), the result is zero.
    *
    * The calculation is extremely accurate and stable, even when v
    * is very close to u or w.  In particular if we set v->s = 0 and
    * let r be the negated result (this evaluates (uw)(v->t)), then
    * r is guaranteed to satisfy MIN(u->s,w->s) <= r <= MAX(u->s,w->s).
    */
     GLdouble gapL, gapR;
 
     assert(TransLeq(u, v) && TransLeq(v, w));
 
     gapL = v->t - u->t;
     gapR = w->t - v->t;
 
     if (gapL + gapR > 0)
     {
         if (gapL < gapR)
         {
             return (v->s - u->s) + (u->s - w->s) * (gapL / (gapL + gapR));
         }
         else
         {
             return (v->s - w->s) + (w->s - u->s) * (gapR / (gapL + gapR));
         }
     }
     /* vertical line */
     return 0;
 }
 
 GLdouble __gl_transSign(GLUvertex *u, GLUvertex *v, GLUvertex *w)
 {
     /* Returns a number whose sign matches TransEval(u,v,w) but which
    * is cheaper to evaluate.  Returns > 0, == 0 , or < 0
    * as v is above, on, or below the edge uw.
    */
     GLdouble gapL, gapR;
 
     assert(TransLeq(u, v) && TransLeq(v, w));
 
     gapL = v->t - u->t;
     gapR = w->t - v->t;
 
     if (gapL + gapR > 0)
     {
         return (v->s - w->s) * gapL + (v->s - u->s) * gapR;
     }
     /* vertical line */
     return 0;
 }
 
 int __gl_vertCCW(GLUvertex *u, GLUvertex *v, GLUvertex *w)
 {
     /* For almost-degenerate situations, the results are not reliable.
    * Unless the floating-point arithmetic can be performed without
    * rounding errors, *any* implementation will give incorrect results
    * on some degenerate inputs, so the client must have some way to
    * handle this situation.
    */
     return (u->s * (v->t - w->t) + v->s * (w->t - u->t) + w->s * (u->t - v->t)) >= 0;
 }
 
 /* Given parameters a,x,b,y returns the value (b*x+a*y)/(a+b),
  * or (x+y)/2 if a==b==0.  It requires that a,b >= 0, and enforces
  * this in the rare case that one argument is slightly negative.
  * The implementation is extremely stable numerically.
  * In particular it guarantees that the result r satisfies
  * MIN(x,y) <= r <= MAX(x,y), and the results are very accurate
  * even when a and b differ greatly in magnitude.
  */
 #define RealInterpolate(a, x, b, y)            \
     (a = (a < 0) ? 0 : a, b = (b < 0) ? 0 : b, \
      ((a <= b) ? ((b == 0) ? ((x + y) / 2) : (x + (y - x) * (a / (a + b)))) : (y + (x - y) * (b / (a + b)))))
 
 #ifndef FOR_TRITE_TEST_PROGRAM
 #define Interpolate(a, x, b, y) RealInterpolate(a, x, b, y)
 #else
 
 /* Claim: the ONLY property the sweep algorithm relies on is that
  * MIN(x,y) <= r <= MAX(x,y).  This is a nasty way to test that.
  */
 #include <stdlib.h>
 extern int RandomInterpolate;
 
 GLdouble Interpolate(GLdouble a, GLdouble x, GLdouble b, GLdouble y)
 {
     printf("*********************%d\n", RandomInterpolate);
     if (RandomInterpolate)
     {
         a = 1.2 * drand48() - 0.1;
         a = (a < 0) ? 0 : ((a > 1) ? 1 : a);
         b = 1.0 - a;
     }
     return RealInterpolate(a, x, b, y);
 }
 
 #endif
 
 #define Swap(a, b)        \
     do                    \
     {                     \
         GLUvertex *t = a; \
         a            = b; \
         b            = t; \
     } while (0)
 
 void __gl_edgeIntersect(GLUvertex *o1, GLUvertex *d1, GLUvertex *o2, GLUvertex *d2, GLUvertex *v)
 /* Given edges (o1,d1) and (o2,d2), compute their point of intersection.
  * The computed point is guaranteed to lie in the intersection of the
  * bounding rectangles defined by each edge.
  */
 {
     GLdouble z1, z2;
 
     /* This is certainly not the most efficient way to find the intersection
    * of two line segments, but it is very numerically stable.
    *
    * Strategy: find the two middle vertices in the VertLeq ordering,
    * and interpolate the intersection s-value from these.  Then repeat
    * using the TransLeq ordering to find the intersection t-value.
    */
 
     if (!VertLeq(o1, d1))
     {
         Swap(o1, d1);
     }
     if (!VertLeq(o2, d2))
     {
         Swap(o2, d2);
     }
     if (!VertLeq(o1, o2))
     {
         Swap(o1, o2);
         Swap(d1, d2);
     }
 
     if (!VertLeq(o2, d1))
     {
         /* Technically, no intersection -- do our best */
         v->s = (o2->s + d1->s) / 2;
     }
     else if (VertLeq(d1, d2))
     {
         /* Interpolate between o2 and d1 */
         z1 = EdgeEval(o1, o2, d1);
         z2 = EdgeEval(o2, d1, d2);
         if (z1 + z2 < 0)
         {
             z1 = -z1;
             z2 = -z2;
         }
         v->s = Interpolate(z1, o2->s, z2, d1->s);
     }
     else
     {
         /* Interpolate between o2 and d2 */
         z1 = EdgeSign(o1, o2, d1);
         z2 = -EdgeSign(o1, d2, d1);
         if (z1 + z2 < 0)
         {
             z1 = -z1;
             z2 = -z2;
         }
         v->s = Interpolate(z1, o2->s, z2, d2->s);
     }
 
     /* Now repeat the process for t */
 
     if (!TransLeq(o1, d1))
     {
         Swap(o1, d1);
     }
     if (!TransLeq(o2, d2))
     {
         Swap(o2, d2);
     }
     if (!TransLeq(o1, o2))
     {
         Swap(o1, o2);
         Swap(d1, d2);
     }
 
     if (!TransLeq(o2, d1))
     {
         /* Technically, no intersection -- do our best */
         v->t = (o2->t + d1->t) / 2;
     }
     else if (TransLeq(d1, d2))
     {
         /* Interpolate between o2 and d1 */
         z1 = TransEval(o1, o2, d1);
         z2 = TransEval(o2, d1, d2);
         if (z1 + z2 < 0)
         {
             z1 = -z1;
             z2 = -z2;
         }
         v->t = Interpolate(z1, o2->t, z2, d1->t);
     }
     else
     {
         /* Interpolate between o2 and d2 */
         z1 = TransSign(o1, o2, d1);
         z2 = -TransSign(o1, d2, d1);
         if (z1 + z2 < 0)
         {
             z1 = -z1;
             z2 = -z2;
         }
         v->t = Interpolate(z1, o2->t, z2, d2->t);
     }
 }