Source/geom.c - third_party/libtess2 - Git at Google

 /*
 ** 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);
 }
	/*
	** 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 (bx+ay)/(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);
	}