libtess2/Source/geom.c

/*
** 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"
#include <math.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 );
	}
}

TESSreal inCircle( TESSvertex *v, TESSvertex *v0, TESSvertex *v1, TESSvertex *v2 ) {
	TESSreal adx, ady, bdx, bdy, cdx, cdy;
	TESSreal abdet, bcdet, cadet;
	TESSreal alift, blift, clift;

	adx = v0->s - v->s;
	ady = v0->t - v->t;
	bdx = v1->s - v->s;
	bdy = v1->t - v->t;
	cdx = v2->s - v->s;
	cdy = v2->t - v->t;

	abdet = adx * bdy - bdx * ady;
	bcdet = bdx * cdy - cdx * bdy;
	cadet = cdx * ady - adx * cdy;

	alift = adx * adx + ady * ady;
	blift = bdx * bdx + bdy * bdy;
	clift = cdx * cdx + cdy * cdy;

	return alift * bcdet + blift * cadet + clift * abdet;
}

/*
	Returns 1 is edge is locally delaunay
 */
int tesedgeIsLocallyDelaunay( TESShalfEdge *e )
{
	return inCircle(e->Sym->Lnext->Lnext->Org, e->Lnext->Org, e->Lnext->Lnext->Org, e->Org) < 0;
}