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/*
** 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 );
}
}
/*
Calculate the angle between v1-v2 and v1-v0
*/
TESSreal calcAngle( TESSvertex *v0, TESSvertex *v1, TESSvertex *v2 )
{
TESSreal num;
TESSreal den;
TESSreal a[2];
TESSreal b[2];
a[0] = v2->s - v1->s;
a[1] = v2->t - v1->t;
b[0] = v0->s - v1->s;
b[1] = v0->t - v1->t;
num = a[0] * b[0] + a[1] * b[1];
den = sqrt( a[0] * a[0] + a[1] * a[1] ) * sqrt( b[0] * b[0] + b[1] * b[1] );
if ( den > 0.0 ) num /= den;
if ( num < -1.0 ) num = -1.0;
if ( num > 1.0 ) num = 1.0;
return acos( num );
}
/*
Returns 1 is edge is locally delaunay
*/
int tesedgeIsLocallyDelaunay( TESShalfEdge *e )
{
return (calcAngle(e->Lnext->Org, e->Lnext->Lnext->Org, e->Org) +
calcAngle(e->Sym->Lnext->Org, e->Sym->Lnext->Lnext->Org, e->Sym->Org)) < (M_PI + 0.01);
}