src/glu/mesa/polytest.c

/* $Id: polytest.c,v 1.1 1999/08/19 00:55:42 jtg Exp $ */

/*
 * Mesa 3-D graphics library
 * Version:  2.4
 * Copyright (C) 1995-1997  Brian Paul
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Library General Public
 * License as published by the Free Software Foundation; either
 * version 2 of the License, or (at your option) any later version.
 *
 * This library is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * Library General Public License for more details.
 *
 * You should have received a copy of the GNU Library General Public
 * License along with this library; if not, write to the Free
 * Software Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */


/*
 * $Log: polytest.c,v $
 * Revision 1.1  1999/08/19 00:55:42  jtg
 * Initial revision
 *
 * Revision 1.7  1999/06/08 00:44:51  brianp
 * OpenStep updates (pete@ohm.york.ac.uk)
 *
 * Revision 1.6  1998/07/26 02:08:52  brianp
 * updated for Windows compilation per Ted Jump
 *
 * Revision 1.5  1997/10/29 02:02:20  brianp
 * various MS Windows compiler changes (David Bucciarelli, v20 3dfx driver)
 *
 * Revision 1.4  1997/07/24 01:28:44  brianp
 * changed precompiled header symbol from PCH to PC_HEADER
 *
 * Revision 1.3  1997/05/28 02:29:38  brianp
 * added support for precompiled headers (PCH), inserted APIENTRY keyword
 *
 * Revision 1.2  1997/05/08 01:53:21  brianp
 * fixed memory leak in free_current_polygon() reported by Randy Frank
 *
 * Revision 1.1  1996/09/27 01:19:39  brianp
 * Initial revision
 *
 */


/*
 * This file is part of the polygon tesselation code contributed by
 * Bogdan Sikorski
 */


#ifdef PC_HEADER
#include "all.h"
#else
#include <math.h>
#include <stdlib.h>
#include "gluP.h"
#include "tess.h"
#endif



static GLenum store_polygon_as_contour(GLUtriangulatorObj *);
static void free_current_polygon(tess_polygon *);
static void prepare_projection_info(GLUtriangulatorObj *);
static GLdouble twice_the_polygon_area(tess_vertex *,tess_vertex *);
static GLenum verify_edge_vertex_intersections(GLUtriangulatorObj *);
void tess_find_contour_hierarchies(GLUtriangulatorObj *);
static GLenum test_for_overlapping_contours(GLUtriangulatorObj *);
static GLenum contours_overlap(tess_contour *, tess_polygon *);
static GLenum is_contour_contained_in(tess_contour *,tess_contour *);
static void add_new_exterior(GLUtriangulatorObj *,tess_contour *);
static void add_new_interior(GLUtriangulatorObj *,tess_contour *,
	tess_contour *);
static void add_interior_with_hierarchy_check(GLUtriangulatorObj *,
	tess_contour *,tess_contour *);
static void reverse_hierarchy_and_add_exterior(GLUtriangulatorObj *,
	tess_contour *,tess_contour *);
static GLboolean point_in_polygon(tess_contour *,GLdouble,GLdouble);
static void shift_interior_to_exterior(GLUtriangulatorObj *,tess_contour *);
static void add_exterior_with_check(GLUtriangulatorObj *,tess_contour *,
	tess_contour *);
static GLenum cut_out_hole(GLUtriangulatorObj *,tess_contour *,
	tess_contour *);
static GLenum merge_hole_with_contour(GLUtriangulatorObj *,
	tess_contour *,tess_contour *,tess_vertex *,
	tess_vertex *);

static GLenum
find_normal(GLUtriangulatorObj *tobj)
{
	tess_polygon *polygon=tobj->current_polygon;
	tess_vertex *va,*vb,*vc;
	GLdouble A,B,C;
	GLdouble A0,A1,A2,B0,B1,B2;

	va=polygon->vertices;
	vb=va->next;
	A0=vb->location[0]-va->location[0];
	A1=vb->location[1]-va->location[1];
	A2=vb->location[2]-va->location[2];
	for(vc=vb->next;vc!=va;vc=vc->next)
	{
		B0=vc->location[0]-va->location[0];
		B1=vc->location[1]-va->location[1];
		B2=vc->location[2]-va->location[2];
		A=A1*B2-A2*B1;
		B=A2*B0-A0*B2;
		C=A0*B1-A1*B0;
		if(fabs(A)>EPSILON || fabs(B)>EPSILON || fabs(C)>EPSILON)
		{
			polygon->A=A;
			polygon->B=B;
			polygon->C=C;
			polygon->D= -A*va->location[0]-B*va->location[1]-C*va->location[2];
			return GLU_NO_ERROR;
		}
	}
	tess_call_user_error(tobj,GLU_TESS_ERROR7);
	return GLU_ERROR;
}

void
tess_test_polygon( GLUtriangulatorObj *tobj )
{
	tess_polygon *polygon=tobj->current_polygon;

	/* any vertices defined? */
	if(polygon->vertex_cnt<3)
	{
		free_current_polygon(polygon);
		return;
	}
	/* wrap pointers */
	polygon->last_vertex->next=polygon->vertices;
	polygon->vertices->previous=polygon->last_vertex;
	/* determine the normal */
	if(find_normal(tobj)==GLU_ERROR)
		return;
	/* compare the normals of previously defined contours and this one */
	/* first contour define ? */
	if(tobj->contours==NULL)
	{
		tobj->A=polygon->A;
		tobj->B=polygon->B;
		tobj->C=polygon->C;
		tobj->D=polygon->D;
		/* determine the best projection to use */
		if(fabs(polygon->A) > fabs(polygon->B))
			if(fabs(polygon->A) > fabs(polygon->C))
				tobj->projection=OYZ;
			else
				tobj->projection=OXY;
		else
			if(fabs(polygon->B) > fabs(polygon->C))
				tobj->projection=OXZ;
			else
				tobj->projection=OXY;
	}
	else
	{
		GLdouble a[3],b[3];
		tess_vertex *vertex=polygon->vertices;

		a[0]=tobj->A;
		a[1]=tobj->B;
		a[2]=tobj->C;
		b[0]=polygon->A;
		b[1]=polygon->B;
		b[2]=polygon->C;

		/* compare the normals */
		if( fabs(a[1]*b[2]-a[2]*b[1]) > EPSILON ||
			fabs(a[2]*b[0]-a[0]*b[2]) > EPSILON ||
			fabs(a[0]*b[1]-a[1]*b[0]) > EPSILON)
		{
			/* not coplanar */
			tess_call_user_error(tobj,GLU_TESS_ERROR9);
			return;
		}
		/* the normals are parallel - test for plane equation */
		if(fabs(a[0]*vertex->location[0]+a[1]*vertex->location[1]+
			a[2]*vertex->location[2]+tobj->D) > EPSILON)
		{
			/* not the same plane */
			tess_call_user_error(tobj,GLU_TESS_ERROR9);
			return;
		}
	}
	prepare_projection_info(tobj);
	if(verify_edge_vertex_intersections(tobj)==GLU_ERROR)
		return;
	if(test_for_overlapping_contours(tobj)==GLU_ERROR)
		return;
	if(store_polygon_as_contour(tobj)==GLU_ERROR)
		return;
}

static GLenum test_for_overlapping_contours(GLUtriangulatorObj *tobj)
{
	tess_contour *contour;
	tess_polygon *polygon;

	polygon=tobj->current_polygon;
	for(contour=tobj->contours;contour!=NULL;contour=contour->next)
		if(contours_overlap(contour,polygon)!=GLU_NO_ERROR)
		{
			tess_call_user_error(tobj,GLU_TESS_ERROR5);
			return GLU_ERROR;
		}
	return GLU_NO_ERROR;
}

static GLenum store_polygon_as_contour(GLUtriangulatorObj *tobj)
{
	tess_polygon *polygon=tobj->current_polygon;
	tess_contour *contour=tobj->contours;

	/* the first contour defined */
	if(contour==NULL)
	{
		if((contour=(tess_contour *)malloc(
			sizeof(tess_contour)))==NULL)
		{
			tess_call_user_error(tobj,GLU_OUT_OF_MEMORY);
			free_current_polygon(polygon);
			return GLU_ERROR;
		}
		tobj->contours=tobj->last_contour=contour;
		contour->next=contour->previous=NULL;
	}
	else
	{
		if((contour=(tess_contour *)malloc(
			sizeof(tess_contour)))==NULL)
		{
			tess_call_user_error(tobj,GLU_OUT_OF_MEMORY);
			free_current_polygon(polygon);
			return GLU_ERROR;
		}
		contour->previous=tobj->last_contour;
		tobj->last_contour->next=contour;
		tobj->last_contour=contour;
		contour->next=NULL;
	}
	/* mark all vertices in new contour as not special */
	/* and all are boundary edges */
	{
		tess_vertex *vertex;
		GLuint vertex_cnt,i;

		for(vertex=polygon->vertices , i=0 , vertex_cnt=polygon->vertex_cnt;
			i<vertex_cnt;
			vertex=vertex->next , i++)
		{
			vertex->shadow_vertex=NULL;
			vertex->edge_flag=GL_TRUE;
		}
	}
	contour->vertex_cnt=polygon->vertex_cnt;
	contour->area=polygon->area;
	contour->orientation=polygon->orientation;
	contour->type=GLU_UNKNOWN;
	contour->vertices=polygon->vertices;
	contour->last_vertex=polygon->last_vertex;
	polygon->vertices=polygon->last_vertex=NULL;
	polygon->vertex_cnt=0;
	++(tobj->contour_cnt);
	return GLU_NO_ERROR;
}

static void free_current_polygon(tess_polygon *polygon)
{
	tess_vertex *vertex,*vertex_tmp;
	GLuint	i;

	/* free current_polygon structures */
	for(vertex=polygon->vertices,i=0;i<polygon->vertex_cnt;i++)
	{
		vertex_tmp=vertex->next;
		free(vertex);
		vertex=vertex_tmp;
	}
	polygon->vertices=polygon->last_vertex=NULL;
	polygon->vertex_cnt=0;
}

static void prepare_projection_info(GLUtriangulatorObj *tobj)
{
	tess_polygon *polygon=tobj->current_polygon;
	tess_vertex *vertex,*last_vertex_ptr;
	GLdouble area;

	last_vertex_ptr=polygon->last_vertex;
	switch(tobj->projection)
	{
		case OXY:
			for(vertex=polygon->vertices;vertex!=last_vertex_ptr;
				vertex=vertex->next)
			{
				vertex->x=vertex->location[0];
				vertex->y=vertex->location[1];
			}
			last_vertex_ptr->x=last_vertex_ptr->location[0];
			last_vertex_ptr->y=last_vertex_ptr->location[1];
			break;
		case OXZ:
			for(vertex=polygon->vertices;vertex!=last_vertex_ptr;
				vertex=vertex->next)
			{
				vertex->x=vertex->location[0];
				vertex->y=vertex->location[2];
			}
			last_vertex_ptr->x=last_vertex_ptr->location[0];
			last_vertex_ptr->y=last_vertex_ptr->location[2];
			break;
		case OYZ:
			for(vertex=polygon->vertices;vertex!=last_vertex_ptr;
				vertex=vertex->next)
			{
				vertex->x=vertex->location[1];
				vertex->y=vertex->location[2];
			}
			last_vertex_ptr->x=last_vertex_ptr->location[1];
			last_vertex_ptr->y=last_vertex_ptr->location[2];
			break;
	}
	area=twice_the_polygon_area(polygon->vertices,polygon->last_vertex);
	if(area >= 0.0)
	{
		polygon->orientation=GLU_CCW;
		polygon->area=area;
	}
	else
	{
		polygon->orientation=GLU_CW;
		polygon->area= -area;
	}
}

static GLdouble twice_the_polygon_area(tess_vertex *vertex,
	tess_vertex *last_vertex)
{
	tess_vertex *next;
	GLdouble area,x,y;

	area=0.0;
	x=vertex->x;
	y=vertex->y;
	vertex=vertex->next;
	for(; vertex!=last_vertex; vertex=vertex->next)
	{
		next=vertex->next;
		area+=(vertex->x - x)*(next->y - y) - (vertex->y - y)*(next->x - x);
	}
	return area;
}

/* test if edges ab and cd intersect */
/* if not return GLU_NO_ERROR, else if cross return GLU_TESS_ERROR8, */
/* else if adjacent return GLU_TESS_ERROR4 */
static GLenum edge_edge_intersect(
	tess_vertex *a,
	tess_vertex *b,
	tess_vertex *c,
	tess_vertex *d)
{
	GLdouble denom,r,s;
	GLdouble xba,ydc,yba,xdc,yac,xac;

	xba=b->x - a->x;
	yba=b->y - a->y;
	xdc=d->x - c->x;
	ydc=d->y - c->y;
	xac=a->x - c->x;
	yac=a->y - c->y;
	denom= xba*ydc - yba*xdc;
	r = yac*xdc - xac*ydc;
	/* parallel? */
	if(fabs(denom) < EPSILON)
	{
		if(fabs(r) < EPSILON)
		{
			/* colinear */
			if(fabs(xba) < EPSILON)
			{
				/* compare the Y coordinate */
				if(yba > 0.0)
				{
					if((fabs(a->y - c->y)<EPSILON && fabs(c->y - b->y)<EPSILON)
						||
						(fabs(a->y - d->y)<EPSILON && fabs(d->y - b->y)<EPSILON))
					return GLU_TESS_ERROR4;

				}
				else
				{
					if((fabs(b->y - c->y)<EPSILON && fabs(c->y - a->y)<EPSILON)
						||
						(fabs(b->y - d->y)<EPSILON && fabs(d->y - a->y)<EPSILON))
					return GLU_TESS_ERROR4;
				}
			}
			else
			{
				/* compare the X coordinate */
				if(xba > 0.0)
				{
					if((fabs(a->x - c->x)<EPSILON && fabs(c->x - b->x)<EPSILON)
						||
						(fabs(a->x - d->x)<EPSILON && fabs(d->x - b->x)<EPSILON))
					return GLU_TESS_ERROR4;
				}
				else
				{
					if((fabs(b->x - c->x)<EPSILON && fabs(c->x - a->x)<EPSILON)
						||
						(fabs(b->x - d->x)<EPSILON && fabs(d->x - a->x)<EPSILON))
					return GLU_TESS_ERROR4;
				}
			}
		}
		return GLU_NO_ERROR;
	}
	r /= denom;
	s = (yac*xba - xac*yba) / denom;
	/* test if one vertex lies on other edge */
	if(((fabs(r) < EPSILON || (r < 1.0+EPSILON && r > 1.0-EPSILON)) &&
		s > -EPSILON && s < 1.0+EPSILON) ||
		((fabs(s) < EPSILON || (s < 1.0+EPSILON && s > 1.0-EPSILON)) &&
		r > -EPSILON && r < 1.0+EPSILON))
	{
		return GLU_TESS_ERROR4;
	}
	/* test for crossing */
	if(r > -EPSILON && r < 1.0+EPSILON &&
		s > -EPSILON && s < 1.0+EPSILON)
	{
		return GLU_TESS_ERROR8;
	}
	return GLU_NO_ERROR;
}

static GLenum verify_edge_vertex_intersections(GLUtriangulatorObj *tobj)
{
	tess_polygon *polygon=tobj->current_polygon;
	tess_vertex *vertex1,*last_vertex,*vertex2;
	GLenum test;

	last_vertex=polygon->last_vertex;
	vertex1=last_vertex;
	for(vertex2=vertex1->next->next;
		vertex2->next!=last_vertex;
		vertex2=vertex2->next)
	{
		test=edge_edge_intersect(vertex1,vertex1->next,vertex2,
			vertex2->next);
		if(test!=GLU_NO_ERROR)
		{
			tess_call_user_error(tobj,test);
			return GLU_ERROR;
		}
	}
	for(vertex1=polygon->vertices;
		vertex1->next->next!=last_vertex;
		vertex1=vertex1->next)
	{
		for(vertex2=vertex1->next->next;
			vertex2!=last_vertex;
			vertex2=vertex2->next)
		{
			test=edge_edge_intersect(vertex1,vertex1->next,vertex2,
				vertex2->next);
			if(test!=GLU_NO_ERROR)
			{
				tess_call_user_error(tobj,test);
				return GLU_ERROR;
			}
		}
	}
	return GLU_NO_ERROR;
}

static int
#if defined(WIN32) && !defined(OPENSTEP)
__cdecl
#endif
area_compare(const void *a,const void *b)
{
	GLdouble area1,area2;

	area1=(*((tess_contour **)a))->area;
	area2=(*((tess_contour **)b))->area;
	if(area1 < area2)
		return 1;
	if(area1 > area2)
		return -1;
	return 0;
}

void tess_find_contour_hierarchies(GLUtriangulatorObj *tobj)
{
	tess_contour **contours; /* dinamic array of pointers */
	tess_contour *tmp_contour_ptr=tobj->contours;
	GLuint cnt,i;
	GLenum result;
	GLboolean hierarchy_changed;

	/* any contours? */
	if(tobj->contour_cnt < 2)
	{
		tobj->contours->type=GLU_EXTERIOR;
		return;
	}
	if((contours=(tess_contour **)
		malloc(sizeof(tess_contour *)*(tobj->contour_cnt)))==NULL)
	{
		tess_call_user_error(tobj,GLU_OUT_OF_MEMORY);
		return;
	}
	for(tmp_contour_ptr=tobj->contours , cnt=0;
		tmp_contour_ptr!=NULL;
		tmp_contour_ptr=tmp_contour_ptr->next)
		contours[cnt++]=tmp_contour_ptr;
	/* now sort the contours in decreasing area size order */
	qsort((void *)contours,(size_t)cnt,(size_t)sizeof(tess_contour *),area_compare);
	/* we leave just the first contour - remove others from list */
	tobj->contours=contours[0];
	tobj->contours->next=tobj->contours->previous=NULL;
	tobj->last_contour=tobj->contours;
	tobj->contour_cnt=1;
	/* first contour is the one with greatest area */
	/* must be EXTERIOR */
	tobj->contours->type=GLU_EXTERIOR;
	tmp_contour_ptr=tobj->contours;
	/* now we play! */
	for(i=1;i<cnt;i++)
	{
		hierarchy_changed=GL_FALSE;
		for(tmp_contour_ptr=tobj->contours;
			tmp_contour_ptr!=NULL;
			tmp_contour_ptr=tmp_contour_ptr->next)
		{
			if(tmp_contour_ptr->type==GLU_EXTERIOR)
			{
				/* check if contour completely contained in EXTERIOR */
				result=is_contour_contained_in(tmp_contour_ptr,contours[i]);
				switch(result)
				{
					case GLU_INTERIOR:
						/* now we have to check if contour is inside interiors */
						/* or not */
						/* any interiors? */
						if(tmp_contour_ptr->next!=NULL &&
							tmp_contour_ptr->next->type==GLU_INTERIOR)
						{
							/* for all interior, check if inside any of them */
							/* if not inside any of interiors, its another */
							/* interior */
							/* or it may contain some interiors, then change */
							/* the contained interiors to exterior ones */
							add_interior_with_hierarchy_check(tobj,
								tmp_contour_ptr,contours[i]);
						}
						else
						{
							/* not in interior, add as new interior contour */
							add_new_interior(tobj,tmp_contour_ptr,contours[i]);
						}
						hierarchy_changed=GL_TRUE;
						break;
					case GLU_EXTERIOR:
						/* ooops, the marked as EXTERIOR (contours[i]) is */
						/* actually an interior of tmp_contour_ptr */
						/*  reverse the local hierarchy */
						reverse_hierarchy_and_add_exterior(tobj,tmp_contour_ptr,
							contours[i]);
						hierarchy_changed=GL_TRUE;
						break;
					case GLU_NO_ERROR:
						break;
					default:
						abort();
				}
			}
			if(hierarchy_changed)
				break; /* break from for loop */
		}
		if(hierarchy_changed==GL_FALSE)
		{
			/* disjoint with all contours, add to contour list */
			add_new_exterior(tobj,contours[i]);
		}
	}
	free(contours);
}

/* returns GLU_INTERIOR if inner is completey enclosed within outer */
/* returns GLU_EXTERIOR if outer is completely enclosed within inner */
/* returns GLU_NO_ERROR if contours are disjoint */
static GLenum is_contour_contained_in(
	tess_contour *outer,
	tess_contour *inner)
{
	GLenum relation_flag;

	/* set relation_flag to relation of containment of first inner vertex */
	/* regarding outer contour */
	if(point_in_polygon(outer,inner->vertices->x,inner->vertices->y))
		relation_flag=GLU_INTERIOR;
	else
		relation_flag=GLU_EXTERIOR;
	if(relation_flag==GLU_INTERIOR)
		return GLU_INTERIOR;
	if(point_in_polygon(inner,outer->vertices->x,outer->vertices->y))
		return GLU_EXTERIOR;
	return GLU_NO_ERROR;
}

static GLboolean point_in_polygon(
	tess_contour *contour,
	GLdouble x,
	GLdouble y)
{
	tess_vertex *v1,*v2;
	GLuint i,vertex_cnt;
	GLdouble xp1,yp1,xp2,yp2;
	GLboolean tst;

	tst=GL_FALSE;
	v1=contour->vertices;
	v2=contour->vertices->previous;
	for(i=0 , vertex_cnt=contour->vertex_cnt;
		i < vertex_cnt;
		i++)
	{
		xp1=v1->x;
		yp1=v1->y;
		xp2=v2->x;
		yp2=v2->y;
		if ((((yp1<=y) && (y<yp2)) || ((yp2<=y)  && (y<yp1))) &&
			(x < (xp2 - xp1) * (y - yp1) /  (yp2 - yp1) + xp1))
				tst = (tst==GL_FALSE ? GL_TRUE : GL_FALSE);
		v2=v1;
		v1=v1->next;
	}
	return tst;
}

static GLenum contours_overlap(
	tess_contour *contour,
	tess_polygon *polygon)
{
	tess_vertex *vertex1,*vertex2;
	GLuint vertex1_cnt,vertex2_cnt,i,j;
	GLenum test;

	vertex1=contour->vertices;
	vertex2=polygon->vertices;
	vertex1_cnt=contour->vertex_cnt;
	vertex2_cnt=polygon->vertex_cnt;
	for(i=0; i<vertex1_cnt; vertex1=vertex1->next , i++)
	{
		for(j=0; j<vertex2_cnt; vertex2=vertex2->next , j++)
			if((test=edge_edge_intersect(vertex1,vertex1->next,vertex2,
				vertex2->next))!=GLU_NO_ERROR)
				return test;
	}
	return GLU_NO_ERROR;
}

static void add_new_exterior(
	GLUtriangulatorObj *tobj,
	tess_contour *contour)
{
	contour->type=GLU_EXTERIOR;
	contour->next=NULL;
	contour->previous=tobj->last_contour;
	tobj->last_contour->next=contour;
	tobj->last_contour=contour;
}

static void add_new_interior(
	GLUtriangulatorObj *tobj,
	tess_contour *outer,
	tess_contour *contour)
{
	contour->type=GLU_INTERIOR;
	contour->next=outer->next;
	contour->previous=outer;
	if(outer->next!=NULL)
		outer->next->previous=contour;
	outer->next=contour;
	if(tobj->last_contour==outer)
		tobj->last_contour=contour;
}

static void add_interior_with_hierarchy_check(
	GLUtriangulatorObj *tobj,
	tess_contour *outer,
	tess_contour *contour)
{
	tess_contour *ptr;

	/* for all interiors of outer check if they are interior of contour */
	/* if so, change that interior to exterior and move it of of the */
	/* interior sequence */
	if(outer->next!=NULL && outer->next->type==GLU_INTERIOR)
	{
		GLenum test;

		for(ptr=outer->next;ptr!=NULL && ptr->type==GLU_INTERIOR;ptr=ptr->next)
		{
			test=is_contour_contained_in(ptr,contour);
			switch(test)
			{
				case GLU_INTERIOR:
					/* contour is contained in one of the interiors */
					/* check if possibly contained in other exteriors */
					/* move ptr to first EXTERIOR */
					for(;ptr!=NULL && ptr->type==GLU_INTERIOR;ptr=ptr->next);
					if(ptr==NULL)
						/* another exterior */
						add_new_exterior(tobj,contour);
					else
						add_exterior_with_check(tobj,ptr,contour);
					return;
				case GLU_EXTERIOR:
					/* one of the interiors is contained in the contour */
					/* change it to EXTERIOR, and shift it away from the */
					/* interior sequence */
					shift_interior_to_exterior(tobj,ptr);
					break;
				case GLU_NO_ERROR:
					/* disjoint */
					break;
				default:
					abort();
			}
		}
	}
	/* add contour to the interior sequence */
	add_new_interior(tobj,outer,contour);
}

static void reverse_hierarchy_and_add_exterior(
	GLUtriangulatorObj *tobj,
	tess_contour *outer,
	tess_contour *contour)
{
	tess_contour *ptr;

	/* reverse INTERIORS to EXTERIORS */
	/* any INTERIORS? */
	if(outer->next!=NULL && outer->next->type==GLU_INTERIOR)
		for(ptr=outer->next;ptr!=NULL && ptr->type==GLU_INTERIOR;ptr=ptr->next)
			ptr->type=GLU_EXTERIOR;
	/* the outer now becomes inner */
	outer->type=GLU_INTERIOR;
	/* contour is the EXTERIOR */
	contour->next=outer;
	if(tobj->contours==outer)
	{
		/* first contour beeing reversed */
		contour->previous=NULL;
		tobj->contours=contour;
	}
	else
	{
		outer->previous->next=contour;
		contour->previous=outer->previous;
	}
	outer->previous=contour;
}

static void shift_interior_to_exterior(
	GLUtriangulatorObj *tobj,
	tess_contour *contour)
{
	contour->previous->next=contour->next;
	if(contour->next!=NULL)
		contour->next->previous=contour->previous;
	else
		tobj->last_contour=contour->previous;
}

static void add_exterior_with_check(
	GLUtriangulatorObj *tobj,
	tess_contour *outer,
	tess_contour *contour)
{
	GLenum test;

	/* this contour might be interior to further exteriors - check */
	/* if not, just add as a new exterior */
	for(;outer!=NULL && outer->type==GLU_EXTERIOR;outer=outer->next)
	{
		test=is_contour_contained_in(outer,contour);
		switch(test)
		{
			case GLU_INTERIOR:
				/* now we have to check if contour is inside interiors */
				/* or not */
				/* any interiors? */
				if(outer->next!=NULL && outer->next->type==GLU_INTERIOR)
				{
					/* for all interior, check if inside any of them */
					/* if not inside any of interiors, its another */
					/* interior */
					/* or it may contain some interiors, then change */
					/* the contained interiors to exterior ones */
					add_interior_with_hierarchy_check(tobj,
						outer,contour);
				}
				else
				{
					/* not in interior, add as new interior contour */
					add_new_interior(tobj,outer,contour);
				}
				return;
			case GLU_NO_ERROR:
				/* disjoint */
				break;
			default:
				abort();
		}
	}
	/* add contour to the exterior sequence */
	add_new_exterior(tobj,contour);
}

void tess_handle_holes(GLUtriangulatorObj *tobj)
{
	tess_contour *contour,*hole;
	GLenum exterior_orientation;

	/* verify hole orientation */
	for(contour=tobj->contours;contour!=NULL;)
	{
		exterior_orientation=contour->orientation;
		for(contour=contour->next;
			contour!=NULL && contour->type==GLU_INTERIOR;
			contour=contour->next)
		{
			if(contour->orientation==exterior_orientation)
			{
				tess_call_user_error(tobj,GLU_TESS_ERROR5);
				return;
			}
		}
	}
	/* now cut-out holes */
	for(contour=tobj->contours;contour!=NULL;)
	{
		hole=contour->next;
		while(hole!=NULL && hole->type==GLU_INTERIOR)
		{
			if(cut_out_hole(tobj,contour,hole)==GLU_ERROR)
				return;
			hole=contour->next;
		}
		contour=contour->next;
	}
}

static GLenum cut_out_hole(
	GLUtriangulatorObj *tobj,
	tess_contour *contour,
	tess_contour *hole)
{
	tess_contour *tmp_hole;
	tess_vertex *v1,*v2,*tmp_vertex;
	GLuint vertex1_cnt,vertex2_cnt,tmp_vertex_cnt;
	GLuint i,j,k;
	GLenum test;

	/* find an edge connecting contour and hole not intersecting any other */
	/* edge belonging to either the contour or any of the other holes */
	for(v1=contour->vertices , vertex1_cnt=contour->vertex_cnt , i=0;
		i<vertex1_cnt;
		i++ , v1=v1->next)
	{
		for(v2=hole->vertices , vertex2_cnt=hole->vertex_cnt , j=0;
			j<vertex2_cnt;
			j++ , v2=v2->next)
		{
			/* does edge (v1,v2) intersect any edge of contour */
			for(tmp_vertex=contour->vertices , tmp_vertex_cnt=contour->vertex_cnt ,
					k=0;
				k<tmp_vertex_cnt;
				tmp_vertex=tmp_vertex->next , k++)
			{
				/* skip edge tests for edges directly connected */
				if(v1==tmp_vertex || v1==tmp_vertex->next)
					continue;
				test=edge_edge_intersect(v1,v2,tmp_vertex,tmp_vertex->next);
				if(test!=GLU_NO_ERROR)
					break;
			}
			if(test==GLU_NO_ERROR)
			{
				/* does edge (v1,v2) intersect any edge of hole */
				for(tmp_vertex=hole->vertices ,
						tmp_vertex_cnt=hole->vertex_cnt , k=0;
					k<tmp_vertex_cnt;
					tmp_vertex=tmp_vertex->next , k++)
				{
					/* skip edge tests for edges directly connected */
					if(v2==tmp_vertex || v2==tmp_vertex->next)
						continue;
					test=edge_edge_intersect(v1,v2,tmp_vertex,tmp_vertex->next);
					if(test!=GLU_NO_ERROR)
						break;
				}
				if(test==GLU_NO_ERROR)
				{
					/* does edge (v1,v2) intersect any other hole? */
					for(tmp_hole=hole->next;
						tmp_hole!=NULL && tmp_hole->type==GLU_INTERIOR;
						tmp_hole=tmp_hole->next)
					{
						/* does edge (v1,v2) intersect any edge of hole */
						for(tmp_vertex=tmp_hole->vertices ,
								tmp_vertex_cnt=tmp_hole->vertex_cnt , k=0;
							k<tmp_vertex_cnt;
							tmp_vertex=tmp_vertex->next , k++)
						{
							test=edge_edge_intersect(v1,v2,tmp_vertex,
								tmp_vertex->next);
							if(test!=GLU_NO_ERROR)
								break;
						}
						if(test!=GLU_NO_ERROR)
							break;
					}
				}
			}
			if(test==GLU_NO_ERROR)
			{
				/* edge (v1,v2) is good for eliminating the hole */
				if(merge_hole_with_contour(tobj,contour,hole,v1,v2)
					==GLU_NO_ERROR)
					return GLU_NO_ERROR;
				else
					return GLU_ERROR;
			}
		}
	}
	/* other holes are blocking all possible connections of hole */
	/* with contour, we shift this hole as the last hole and retry */
	for(tmp_hole=hole;
		tmp_hole!=NULL && tmp_hole->type==GLU_INTERIOR;
		tmp_hole=tmp_hole->next);
	contour->next=hole->next;
	hole->next->previous=contour;
	if(tmp_hole==NULL)
	{
		/* last EXTERIOR contour, shift hole as last contour */
		hole->next=NULL;
		hole->previous=tobj->last_contour;
		tobj->last_contour->next=hole;
		tobj->last_contour=hole;
	}
	else
	{
		tmp_hole->previous->next=hole;
		hole->previous=tmp_hole->previous;
		tmp_hole->previous=hole;
		hole->next=tmp_hole;
	}
	hole=contour->next;
	/* try once again - recurse */
	return cut_out_hole(tobj,contour,hole);
}

static GLenum merge_hole_with_contour(
	GLUtriangulatorObj *tobj,
	tess_contour *contour,
	tess_contour *hole,
	tess_vertex *v1,
	tess_vertex *v2)
{
	tess_vertex *v1_new,*v2_new;

	/* make copies of v1 and v2, place them respectively after their originals */
	if((v1_new=(tess_vertex *)malloc(sizeof(tess_vertex)))==NULL)
	{
		tess_call_user_error(tobj,GLU_OUT_OF_MEMORY);
		return GLU_ERROR;
	}
	if((v2_new=(tess_vertex *)malloc(sizeof(tess_vertex)))==NULL)
	{
		tess_call_user_error(tobj,GLU_OUT_OF_MEMORY);
		return GLU_ERROR;
	}
	v1_new->edge_flag=GL_TRUE;
	v1_new->data=v1->data;
	v1_new->location[0]=v1->location[0];
	v1_new->location[1]=v1->location[1];
	v1_new->location[2]=v1->location[2];
	v1_new->x=v1->x;
	v1_new->y=v1->y;
	v1_new->shadow_vertex=v1;
	v1->shadow_vertex=v1_new;
	v1_new->next=v1->next;
	v1_new->previous=v1;
	v1->next->previous=v1_new;
	v1->next=v1_new;
	v2_new->edge_flag=GL_TRUE;
	v2_new->data=v2->data;
	v2_new->location[0]=v2->location[0];
	v2_new->location[1]=v2->location[1];
	v2_new->location[2]=v2->location[2];
	v2_new->x=v2->x;
	v2_new->y=v2->y;
	v2_new->shadow_vertex=v2;
	v2->shadow_vertex=v2_new;
	v2_new->next=v2->next;
	v2_new->previous=v2;
	v2->next->previous=v2_new;
	v2->next=v2_new;
	/* link together the two lists */
	v1->next=v2_new;
	v2_new->previous=v1;
	v2->next=v1_new;
	v1_new->previous=v2;
	/* update the vertex count of the contour */
	contour->vertex_cnt += hole->vertex_cnt+2;
	/* remove the INTERIOR contour */
	contour->next=hole->next;
	if(hole->next!=NULL)
		hole->next->previous=contour;
	free(hole);
	/* update tobj structure */
	--(tobj->contour_cnt);
	if(contour->last_vertex==v1)
		contour->last_vertex=v1_new;
	/* mark two vertices with edge_flag */
	v2->edge_flag=GL_FALSE;
	v1->edge_flag=GL_FALSE;
	return GLU_NO_ERROR;
}