text: /*
  ** SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
  ** Copyright (C) [dates of first publication] Silicon Graphics, Inc.
  ** All Rights Reserved.
  **
  ** Permission is hereby granted, free of charge, to any person obtaining a copy
  ** of this software and associated documentation files (the "Software"), to deal
  ** in the Software without restriction, including without limitation the rights
  ** to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
  ** of the Software, and to permit persons to whom the Software is furnished to do so,
  ** subject to the following conditions:
  **
  ** The above copyright notice including the dates of first publication and either this
  ** permission notice or a reference to http://oss.sgi.com/projects/FreeB/ shall be
  ** included in all copies or substantial portions of the Software.
  **
  ** THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED,
  ** INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A
  ** PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL SILICON GRAPHICS, INC.
  ** BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
  ** TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE
  ** OR OTHER DEALINGS IN THE SOFTWARE.
  **
  ** Except as contained in this notice, the name of Silicon Graphics, Inc. shall not
  ** be used in advertising or otherwise to promote the sale, use or other dealings in
  ** this Software without prior written authorization from Silicon Graphics, Inc.
  */
  /*
  ** Author: Eric Veach, July 1994.
  */
  
  //#include "tesos.h"
  #include <assert.h>
  #include "mesh.h"
  #include "geom.h"
  
  int tesvertLeq( TESSvertex *u, TESSvertex *v )
  {
  	/* Returns TRUE if u is lexicographically <= v. */
  
  	return VertLeq( u, v );
  }
  
  TESSreal tesedgeEval( TESSvertex *u, TESSvertex *v, TESSvertex *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).
  	*/
  	TESSreal 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;
  }
  
  TESSreal tesedgeSign( TESSvertex *u, TESSvertex *v, TESSvertex *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.
  	*/
  	TESSreal 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.
  */
  
  TESSreal testransEval( TESSvertex *u, TESSvertex *v, TESSvertex *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).
  	*/
  	TESSreal 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;
  }
  
  TESSreal testransSign( TESSvertex *u, TESSvertex *v, TESSvertex *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.
  	*/
  	TESSreal 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 tesvertCCW( TESSvertex *u, TESSvertex *v, TESSvertex *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;
  
  double Interpolate( double a, double x, double b, double 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)	if (1) { TESSvertex *t = a; a = b; b = t; } else
  
  void tesedgeIntersect( TESSvertex *o1, TESSvertex *d1,
  					  TESSvertex *o2, TESSvertex *d2,
  					  TESSvertex *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.
  					  */
  {
  	TESSreal 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 );
  	}
  }
  