SGI SI GLU library

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diff --git a/src/glu/sgi/libnurbs/nurbtess/partitionY.cc b/src/glu/sgi/libnurbs/nurbtess/partitionY.cc
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+/*
+** License Applicability. Except to the extent portions of this file are
+** made subject to an alternative license as permitted in the SGI Free
+** Software License B, Version 1.1 (the "License"), the contents of this
+** file are subject only to the provisions of the License. You may not use
+** this file except in compliance with the License. You may obtain a copy
+** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
+** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
+** 
+** http://oss.sgi.com/projects/FreeB
+** 
+** Note that, as provided in the License, the Software is distributed on an
+** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
+** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
+** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
+** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
+** 
+** Original Code. The Original Code is: OpenGL Sample Implementation,
+** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
+** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
+** Copyright in any portions created by third parties is as indicated
+** elsewhere herein. All Rights Reserved.
+** 
+** Additional Notice Provisions: The application programming interfaces
+** established by SGI in conjunction with the Original Code are The
+** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
+** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
+** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
+** Window System(R) (Version 1.3), released October 19, 1998. This software
+** was created using the OpenGL(R) version 1.2.1 Sample Implementation
+** published by SGI, but has not been independently verified as being
+** compliant with the OpenGL(R) version 1.2.1 Specification.
+**
+** $Date: 2001/03/17 00:25:41 $ $Revision: 1.1 $
+*/
+/*
+** $Header: /home/krh/git/sync/mesa-cvs-repo/Mesa/src/glu/sgi/libnurbs/nurbtess/partitionY.cc,v 1.1 2001/03/17 00:25:41 brianp Exp $
+*/
+
+#include <stdlib.h>
+#include <stdio.h>
+#include <time.h>
+
+#include "zlassert.h"
+#include "partitionY.h"
+#include "searchTree.h"
+#include "quicksort.h"
+#include "polyUtil.h"
+
+
+#define max(a,b) ((a>b)? a:b)
+#define min(a,b) ((a>b)? b:a)
+
+
+/*retrurn 
+ *-1: if A < B (Ya<Yb) || (Ya==Yb)
+ * 0: if A == B
+ * 1: if A>B
+ */
+static Int compVertInY(Real A[2], Real B[2])
+{
+  if( (A[1] < B[1]) || (A[1]==B[1] && A[0]<B[0])) 
+    return -1;
+  else if
+    ( A[1] == B[1] && A[0] == B[0]) return 0;
+  else
+    return 1;
+}
+
+/*v is a vertex: the head of en edge,
+ *e is an edge,
+ *return 1 if e is below v: assume v1 and v2 are the two endpoints of e:
+ * v1<= v, v2<=v.
+ */
+Int isBelow(directedLine *v, directedLine *e)
+{
+  Real* vert = v->head();
+  if(   compVertInY(e->head(), vert) != 1 
+     && compVertInY(e->tail(), vert) != 1
+     )
+    return 1;
+  else
+    return 0;
+}
+
+/*v is a vertex: the head of en edge,
+ *e is an edge,
+ *return 1 if e is below v: assume v1 and v2 are the two endpoints of e:
+ * v1>= v, v2>=v.
+ */
+Int isAbove(directedLine *v, directedLine *e)
+{
+  Real* vert = v->head();
+  if(   compVertInY(e->head(), vert) != -1 
+     && compVertInY(e->tail(), vert) != -1
+     )
+    return 1;
+  else
+    return 0;
+}
+
+Int isCusp(directedLine *v)
+{
+  Real *A=v->getPrev()->head();
+  Real *B=v->head();
+  Real *C=v->tail();
+  if(A[1] < B[1] && B[1] < C[1])
+    return 0;
+  else if(A[1] > B[1] && B[1] > C[1])
+    return 0;
+  else if(A[1] < B[1] && C[1] < B[1])
+    return 1;
+  else if(A[1] > B[1] && C[1] > B[1])
+    return 1;
+
+  if(isAbove(v, v) && isAbove(v, v->getPrev()) ||
+     isBelow(v, v) && isBelow(v, v->getPrev()))
+    return 1;
+  else
+    return 0;
+}
+
+/*crossproduct is strictly less than 0*/
+Int isReflex(directedLine *v)
+{
+  Real* A = v->getPrev()->head();
+  Real* B = v->head();
+  Real* C = v->tail();
+  Real Bx,By, Cx, Cy;
+  Bx = B[0] - A[0];
+  By = B[1] - A[1];
+  Cx = C[0] - A[0];
+  Cy = C[1] - A[1];
+
+  if(Bx*Cy - Cx*By < 0) return 1;
+  else return 0;
+}
+
+ /*return 
+ *0: not-cusp
+ *1: interior cusp
+ *2: exterior cusp
+ */
+Int cuspType(directedLine *v)
+{
+  if(! isCusp(v)) return 0;
+  else if(isReflex(v)) return 1;
+  else
+    return 2;
+}
+
+sweepRange* sweepRangeMake(directedLine* left, Int leftType,
+			   directedLine* right, Int rightType)
+{
+  sweepRange* ret = (sweepRange*)malloc(sizeof(sweepRange));
+  assert(ret);
+  ret->left = left;
+  ret->leftType = leftType;
+  ret->right = right;
+  ret->rightType = rightType;
+  return ret;
+}
+
+void sweepRangeDelete(sweepRange* range)
+{
+  free(range);
+}
+
+Int sweepRangeEqual(sweepRange* src1, sweepRange* src2)
+{
+  Int leftEqual;
+  Int rightEqual;
+  
+  
+  /*The case when both are vertices should not happen*/
+  assert(! (src1->leftType == 0 && src2->leftType == 0));    
+  if(src1->leftType == 0 && src2->leftType == 1){
+    if(src1->left == src2->left ||
+       src1->left->getPrev() == src2->left
+       )
+      leftEqual = 1;
+    else
+      leftEqual = 0;
+  }
+  else if(src1->leftType == 1 && src2->leftType == 1){
+    if(src1->left == src2->left)
+      leftEqual = 1;
+    else
+      leftEqual = 0;
+  }
+  else /*src1->leftType == 1 && src2->leftType == 0*/{
+    if(src1->left == src2->left ||
+       src1->left == src2->left->getPrev()
+       )
+      leftEqual = 1;
+    else 
+      leftEqual = 0;
+  }
+
+  /*the same thing for right*/
+  /*The case when both are vertices should not happen*/
+  assert(! (src1->rightType == 0 && src2->rightType == 0));    
+  if(src1->rightType == 0 && src2->rightType == 1){
+    if(src1->right == src2->right ||
+       src1->right->getPrev() == src2->right
+       )
+      rightEqual = 1;
+    else
+      rightEqual = 0;
+  }
+  else if(src1->rightType == 1 && src2->rightType == 1){
+    if(src1->right == src2->right)
+      rightEqual = 1;
+    else
+      rightEqual = 0;
+  }
+  else /*src1->rightType == 1 && src2->rightType == 0*/{
+    if(src1->right == src2->right ||
+       src1->right == src2->right->getPrev()
+       )
+      rightEqual = 1;
+    else 
+      rightEqual = 0;
+  }
+  
+  return (leftEqual == 1 || rightEqual == 1);
+}
+
+/*given (x_1, y_1) and (x_2, y_2), and y
+ *return x such that (x,y) is on the line
+ */
+inline/*static*/ Real intersectHoriz(Real x1, Real y1, Real x2, Real y2, Real y)
+{
+  return ((y2==y1)? (x1+x2)*0.5 : x1 + ((y-y1)/(y2-y1)) * (x2-x1));
+/*
+  if(y2 == y1) return (x1+x2)*0.5;
+  else return x1 + ((y-y1)/(y2-y1)) * (x2-x1);
+*/
+}
+
+/*compare two edges of a polygon.
+ *edge A < edge B if there is a horizontal line so that the intersection
+ *with A is to the left of the intersection with B.
+ *This function is used in sweepY for the dynamic search tree insertion to
+ *order the edges.
+ * Implementation: (x_1,y_1) and (x_2, y_2)
+ */
+static Int compEdges(directedLine *e1, directedLine *e2)
+{
+  Real* head1 = e1->head();
+  Real* tail1 = e1->tail();
+  Real* head2 = e2->head();
+  Real* tail2 = e2->tail();
+/*
+  Real h10 = head1[0];
+  Real h11 = head1[1];
+  Real t10 = tail1[0];
+  Real t11 = tail1[1];
+  Real h20 = head2[0];
+  Real h21 = head2[1];
+  Real t20 = tail2[0];
+  Real t21 = tail2[1];
+*/
+  Real e1_Ymax, e1_Ymin, e2_Ymax, e2_Ymin;
+/*
+  if(h11>t11) {
+    e1_Ymax= h11;
+    e1_Ymin= t11;
+  }
+  else{
+    e1_Ymax = t11;
+    e1_Ymin = h11;
+  }
+
+  if(h21>t21) {
+    e2_Ymax= h21;
+    e2_Ymin= t21;
+  }
+  else{
+    e2_Ymax = t21;
+    e2_Ymin = h21;
+  }
+*/
+ 
+  if(head1[1]>tail1[1]) {
+    e1_Ymax= head1[1];
+    e1_Ymin= tail1[1];
+  }
+  else{
+    e1_Ymax = tail1[1];
+    e1_Ymin = head1[1];
+  }
+
+  if(head2[1]>tail2[1]) {
+    e2_Ymax= head2[1];
+    e2_Ymin= tail2[1];
+  }
+  else{
+    e2_Ymax = tail2[1];
+    e2_Ymin = head2[1];
+  }
+
+  
+  /*Real e1_Ymax = max(head1[1], tail1[1]);*/ /*max(e1->head()[1], e1->tail()[1]);*/
+  /*Real e1_Ymin = min(head1[1], tail1[1]);*/ /*min(e1->head()[1], e1->tail()[1]);*/
+  /*Real e2_Ymax = max(head2[1], tail2[1]);*/ /*max(e2->head()[1], e2->tail()[1]);*/
+  /*Real e2_Ymin = min(head2[1], tail2[1]);*/ /*min(e2->head()[1], e2->tail()[1]);*/
+
+  Real Ymax = min(e1_Ymax, e2_Ymax);
+  Real Ymin = max(e1_Ymin, e2_Ymin);
+    
+  Real y = 0.5*(Ymax + Ymin);
+
+/*  Real x1 = intersectHoriz(e1->head()[0], e1->head()[1], e1->tail()[0], e1->tail()[1], y);
+  Real x2 = intersectHoriz(e2->head()[0], e2->head()[1], e2->tail()[0], e2->tail()[1], y);
+*/
+/*
+  Real x1 = intersectHoriz(h10, h11, t10, t11, y);
+  Real x2 = intersectHoriz(h20, h21, t20, t21, y);
+*/
+  Real x1 = intersectHoriz(head1[0], head1[1], tail1[0], tail1[1], y);
+  Real x2 = intersectHoriz(head2[0], head2[1], tail2[0], tail2[1], y);
+
+  if(x1<= x2) return -1;
+  else return 1;
+}
+  
+/*used by sort precedures
+ */
+static Int compInY(directedLine* v1, directedLine* v2)
+{
+  return v1->compInY(v2);
+}
+
+void findDiagonals(Int total_num_edges, directedLine** sortedVertices, sweepRange** ranges, Int& num_diagonals, directedLine** diagonal_vertices)
+{
+  Int i,j,k;
+
+  k=0;
+
+  for(i=0; i<total_num_edges; i++)
+    {
+      directedLine* vert =sortedVertices[i];
+      directedLine* thisEdge = vert;
+      directedLine* prevEdge = vert->getPrev();
+/*
+printf("find i=%i\n", i);            
+printf("the vertex is\n");
+vert->printSingle();
+*/
+      if(isBelow(vert, thisEdge) && isBelow(vert, prevEdge) && compEdges(prevEdge, thisEdge)<0)
+	{
+	  /*this is an upward interior cusp*/
+	  diagonal_vertices[k++] = vert;
+
+	  for(j=i+1; j<total_num_edges; j++)
+	    if(sweepRangeEqual(ranges[i], ranges[j]))
+	      {
+		diagonal_vertices[k++] = sortedVertices[j];
+		break;
+	      }
+	  assert(j<total_num_edges);
+
+
+	}
+      else if(isAbove(vert, thisEdge) && isAbove(vert, prevEdge) && compEdges(prevEdge, thisEdge)>0)
+	{
+	  /*this is an downward interior cusp*/
+	  diagonal_vertices[k++] = vert;
+	  for(j=i-1; j>=0; j--)
+	    if(sweepRangeEqual(ranges[i], ranges[j]))
+	      {
+		diagonal_vertices[k++] = sortedVertices[j];
+		break;
+	      }
+/*	  printf("j=%i\n", j);*/
+	  assert(j>=0);
+
+
+
+	}
+    }
+  num_diagonals = k/2;
+}
+
+/*get rid of repeated diagonlas so that each diagonal appears only once in the array
+ */
+Int deleteRepeatDiagonals(Int num_diagonals, directedLine** diagonal_vertices, directedLine** new_vertices)
+{
+  Int i,k;
+  Int j,l;
+  Int index;
+  index=0;
+  for(i=0,k=0; i<num_diagonals; i++, k+=2)
+    {
+      Int isRepeated=0;
+      /*check the diagonla (diagonal_vertice[k], diagonal_vertices[k+1])
+       *is repeated or not
+       */
+      for(j=0,l=0; j<index; j++, l+=2)
+	{
+	  if(
+	     (diagonal_vertices[k] == new_vertices[l] && 
+	      diagonal_vertices[k+1] == new_vertices[l+1]
+	      )
+	     ||
+	     (
+	      diagonal_vertices[k] == new_vertices[l+1] && 
+	      diagonal_vertices[k+1] == new_vertices[l]
+	      )
+	     )
+	    {
+	      isRepeated=1;
+	      break;
+	    }
+	}
+      if(! isRepeated)
+	{
+	  new_vertices[index+index] = diagonal_vertices[k];
+	  new_vertices[index+index+1] = diagonal_vertices[k+1];	  
+	  index++;
+	}
+    }
+  return index;
+}
+
+/*for debug only*/	  
+directedLine** DBGfindDiagonals(directedLine *polygons, Int& num_diagonals)
+{
+  Int total_num_edges = 0;
+  directedLine** array = polygons->toArrayAllPolygons(total_num_edges);
+  quicksort( (void**)array, 0, total_num_edges-1, (Int (*)(void*, void*)) compInY);
+  sweepRange** ranges = (sweepRange**) malloc(sizeof(sweepRange*) * total_num_edges);
+  assert(ranges);
+
+  sweepY(total_num_edges, array, ranges);
+
+ directedLine** diagonal_vertices = (directedLine**) malloc(sizeof(directedLine*) * total_num_edges);
+  assert(diagonal_vertices);
+  findDiagonals(total_num_edges, array, ranges, num_diagonals, diagonal_vertices);
+
+  num_diagonals=deleteRepeatDiagonals(num_diagonals, diagonal_vertices, diagonal_vertices);
+  return diagonal_vertices;
+
+}
+
+
+/*partition into Y-monotone polygons*/
+directedLine* partitionY(directedLine *polygons, sampledLine **retSampledLines)
+{
+  Int total_num_edges = 0;
+  directedLine** array = polygons->toArrayAllPolygons(total_num_edges);
+
+  quicksort( (void**)array, 0, total_num_edges-1, (Int (*)(void*, void*)) compInY);
+
+  sweepRange** ranges = (sweepRange**) malloc(sizeof(sweepRange*) * (total_num_edges));
+  assert(ranges);
+
+
+
+  sweepY(total_num_edges, array, ranges);
+
+
+
+  /*the diagonal vertices are stored as:
+   *v0-v1: 1st diagonal
+   *v2-v3: 2nd diagonal
+   *v5-v5: 3rd diagonal
+   *...
+   */
+
+
+  Int num_diagonals;
+  /*number diagonals is < total_num_edges*total_num_edges*/
+  directedLine** diagonal_vertices = (directedLine**) malloc(sizeof(directedLine*) * total_num_edges*2/*total_num_edges*/);
+  assert(diagonal_vertices);
+
+
+
+  findDiagonals(total_num_edges, array, ranges, num_diagonals, diagonal_vertices);
+
+
+
+  directedLine* ret_polygons = polygons;
+  sampledLine* newSampledLines = NULL;
+  Int i,k;
+
+num_diagonals=deleteRepeatDiagonals(num_diagonals, diagonal_vertices, diagonal_vertices);
+
+
+
+  Int *removedDiagonals=(Int*)malloc(sizeof(Int) * num_diagonals);
+  for(i=0; i<num_diagonals; i++)
+    removedDiagonals[i] = 0;
+
+
+
+
+
+  for(i=0,k=0; i<num_diagonals; i++,k+=2)
+    {
+
+
+      directedLine* v1=diagonal_vertices[k];
+      directedLine* v2=diagonal_vertices[k+1];
+      directedLine* ret_p1;
+      directedLine* ret_p2;
+      
+      /*we ahve to determine whether v1 and v2 belong to the same polygon before
+       *their structure are modified by connectDiagonal().
+       */
+/*
+      directedLine *root1 = v1->findRoot();
+      directedLine *root2 = v2->findRoot();
+      assert(root1);      
+      assert(root2);
+*/
+
+directedLine*  root1 = v1->rootLinkFindRoot();
+directedLine*  root2 = v2->rootLinkFindRoot();
+
+      if(root1 != root2)
+	{
+
+	  removedDiagonals[i] = 1;
+	  sampledLine* generatedLine;
+
+
+
+	  v1->connectDiagonal(v1,v2, &ret_p1, &ret_p2, &generatedLine, ret_polygons);
+
+
+
+	  newSampledLines = generatedLine->insert(newSampledLines);
+/*
+	  ret_polygons = ret_polygons->cutoffPolygon(root1);
+
+	  ret_polygons = ret_polygons->cutoffPolygon(root2);
+	  ret_polygons = ret_p1->insertPolygon(ret_polygons);
+root1->rootLinkSet(ret_p1);
+root2->rootLinkSet(ret_p1);
+ret_p1->rootLinkSet(NULL);
+ret_p2->rootLinkSet(ret_p1);
+*/
+	  ret_polygons = ret_polygons->cutoffPolygon(root2);
+
+
+
+root2->rootLinkSet(root1);
+ret_p1->rootLinkSet(root1);
+ret_p2->rootLinkSet(root1);
+
+       /*now that we have connected the diagonal v1 and v2, 
+        *we have to check those unprocessed diagonals which 
+        *have v1 or v2 as an end point. Notice that the head of v1
+        *has the same coodinates as the head of v2->prev, and the head of
+        *v2 has the same coordinate as the head of v1->prev. 
+        *Suppose these is a diagonal (v1, x). If (v1,x) is still a valid
+        *diagonal, then x should be on the left hand side of the directed line:        *v1->prev->head -- v1->head -- v1->tail. Otherwise, (v1,x) should be  
+        *replaced by (v2->prev, x), that is, x is on the left of 
+        * v2->prev->prev->head, v2->prev->head, v2->prev->tail.
+        */
+        Int ii, kk;
+        for(ii=0, kk=0; ii<num_diagonals; ii++, kk+=2)
+	  if( removedDiagonals[ii]==0)
+	    {
+	      directedLine* d1=diagonal_vertices[kk];
+	      directedLine* d2=diagonal_vertices[kk+1];
+	      /*check d1, and replace diagonal_vertices[kk] if necessary*/
+	      if(d1 == v1) {
+		/*check if d2 is to left of v1->prev->head:v1->head:v1->tail*/
+		if(! pointLeft2Lines(v1->getPrev()->head(), 
+				     v1->head(), v1->tail(), d2->head()))
+		  {
+/*
+		    assert(pointLeft2Lines(v2->getPrev()->getPrev()->head(),
+					   v2->getPrev()->head(), 
+					   v2->getPrev()->tail(), d2->head()));
+*/
+		    diagonal_vertices[kk] = v2->getPrev();
+		  }
+	      }
+	      if(d1 == v2) {
+		/*check if d2 is to left of v2->prev->head:v2->head:v2->tail*/
+		if(! pointLeft2Lines(v2->getPrev()->head(),
+				     v2->head(), v2->tail(), d2->head()))
+		  {
+/*
+		    assert(pointLeft2Lines(v1->getPrev()->getPrev()->head(),
+					   v1->getPrev()->head(),
+					   v1->getPrev()->tail(), d2->head()));
+*/
+		    diagonal_vertices[kk] = v1->getPrev();
+		  }
+	      }
+	      /*check d2 and replace diagonal_vertices[k+1] if necessary*/
+	      if(d2 == v1) {
+		/*check if d1 is to left of v1->prev->head:v1->head:v1->tail*/
+		if(! pointLeft2Lines(v1->getPrev()->head(), 
+				     v1->head(), v1->tail(), d1->head()))
+		  {
+/*		    assert(pointLeft2Lines(v2->getPrev()->getPrev()->head(),
+					   v2->getPrev()->head(), 
+					   v2->getPrev()->tail(), d1->head()));
+*/
+		    diagonal_vertices[kk+1] = v2->getPrev();
+		  }
+	      }
+	      if(d2 == v2) {
+		/*check if d1 is to left of v2->prev->head:v2->head:v2->tail*/
+		if(! pointLeft2Lines(v2->getPrev()->head(),
+				     v2->head(), v2->tail(), d1->head()))
+		  {
+/*		    assert(pointLeft2Lines(v1->getPrev()->getPrev()->head(),
+					   v1->getPrev()->head(),
+					   v1->getPrev()->tail(), d1->head()));
+*/
+		    diagonal_vertices[kk+1] = v1->getPrev();
+		  }
+	      }
+	    }					    	       
+}/*end if (root1 not equal to root 2)*/
+}
+
+  /*second pass,  now all diagoals should belong to the same polygon*/
+
+
+
+  for(i=0,k=0; i<num_diagonals; i++, k += 2)
+    if(removedDiagonals[i] == 0) 
+      {
+
+
+	directedLine* v1=diagonal_vertices[k];
+	directedLine* v2=diagonal_vertices[k+1];
+
+
+
+	directedLine* ret_p1;
+	directedLine* ret_p2;
+
+	/*we ahve to determine whether v1 and v2 belong to the same polygon before
+	 *their structure are modified by connectDiagonal().
+	 */
+	directedLine *root1 = v1->findRoot();
+/*
+	directedLine *root2 = v2->findRoot();
+
+
+
+	assert(root1);      
+	assert(root2);      
+	assert(root1 == root2);
+  */    
+	sampledLine* generatedLine;
+
+
+
+	v1->connectDiagonal(v1,v2, &ret_p1, &ret_p2, &generatedLine, ret_polygons);
+	newSampledLines = generatedLine->insert(newSampledLines);
+
+	ret_polygons = ret_polygons->cutoffPolygon(root1);
+
+	ret_polygons = ret_p1->insertPolygon(ret_polygons);
+
+	ret_polygons = ret_p2->insertPolygon(ret_polygons);
+
+
+
+	for(Int j=i+1; j<num_diagonals; j++) 
+	  {
+	    if(removedDiagonals[j] ==0)
+	      {
+
+		directedLine* temp1=diagonal_vertices[2*j];
+		directedLine* temp2=diagonal_vertices[2*j+1];
+               if(temp1==v1 || temp1==v2 || temp2==v1 || temp2==v2)
+		if(! temp1->samePolygon(temp1, temp2))
+		  {
+		    /*if temp1 and temp2 are in different polygons, 
+		     *then one of them must be v1 or v2.
+		     */
+
+
+
+		    assert(temp1==v1 || temp1 == v2 || temp2==v1 || temp2 ==v2);
+		    if(temp1==v1) 
+		      {
+			diagonal_vertices[2*j] = v2->getPrev();
+		      }
+		    if(temp2==v1)
+		      {
+			diagonal_vertices[2*j+1] = v2->getPrev();
+		      }
+		    if(temp1==v2)
+		      {
+			diagonal_vertices[2*j] = v1->getPrev();		      
+		      }
+		    if(temp2==v2)
+		      {
+			diagonal_vertices[2*j+1] = v1->getPrev();
+		      }
+		  }
+	      }
+	  }      
+
+      }
+
+  /*clean up spaces*/
+  free(array);
+  free(ranges);
+  free(diagonal_vertices);
+  free(removedDiagonals);
+
+  *retSampledLines = newSampledLines;
+  return ret_polygons;
+}
+	
+/*given a set of simple polygons where the interior 
+ *is decided by left-hand principle,
+ *return a range (sight) for each vertex. This is called
+ *Trapezoidalization.
+ */ 
+void sweepY(Int nVertices, directedLine** sortedVertices, sweepRange** ret_ranges)
+{
+  Int i;
+  /*for each vertex in the sorted list, update the binary search tree.
+   *and store the range information for each vertex.
+   */
+  treeNode* searchTree = NULL;
+  for(i=0; i<nVertices;i++)
+    {
+
+      directedLine* vert = sortedVertices[i];
+
+      directedLine* thisEdge = vert;
+      directedLine* prevEdge = vert->getPrev();
+      
+      if(isBelow(vert, thisEdge) && isAbove(vert, prevEdge))
+	{
+
+	  /*case 1: this < v < prev
+	   *the polygon is going down at v, the interior is to 
+	   *the right hand side.
+	   * find the edge to the right of thisEdge for right range.
+           * delete thisEdge
+           * insert prevEdge
+	   */
+	  treeNode* thisNode = TreeNodeFind(searchTree, thisEdge, ( Int (*) (void *, void *))compEdges);
+	  assert(thisNode);
+
+	  treeNode* succ = TreeNodeSuccessor(thisNode);
+	  assert(succ);
+	  searchTree = TreeNodeDeleteSingleNode(searchTree, thisNode);
+	  searchTree = TreeNodeInsert(searchTree, TreeNodeMake(prevEdge), ( Int (*) (void *, void *))compEdges);
+
+
+	  ret_ranges[i] = sweepRangeMake(vert, 0, (directedLine*) (succ->key), 1);
+
+	}
+      else if(isAbove(vert, thisEdge) && isBelow(vert, prevEdge))
+	{
+
+	  /*case 2: this > v > prev
+	   *the polygon is going up at v, the interior is to 
+	   *the left hand side.
+	   * find the edge to the left of thisEdge for left range.
+           * delete prevEdge
+           * insert thisEdge
+	   */	  
+	  treeNode* prevNode = TreeNodeFind(searchTree, prevEdge, ( Int (*) (void *, void *))compEdges);
+	  assert(prevNode);
+	  treeNode* pred = TreeNodePredecessor(prevNode);
+	  searchTree = TreeNodeDeleteSingleNode(searchTree, prevNode);
+	  searchTree = TreeNodeInsert(searchTree, TreeNodeMake(thisEdge), ( Int (*) (void *, void *))compEdges);
+	  ret_ranges[i] = sweepRangeMake((directedLine*)(pred->key), 1, vert, 0);
+	}
+      else if(isAbove(vert, thisEdge) && isAbove(vert, prevEdge))
+	{
+
+	  /*case 3: insert both edges*/
+	  treeNode* thisNode = TreeNodeMake(thisEdge);
+	  treeNode* prevNode = TreeNodeMake(prevEdge);	  
+	  searchTree = TreeNodeInsert(searchTree, thisNode, ( Int (*) (void *, void *))compEdges);
+	  searchTree = TreeNodeInsert(searchTree, prevNode, ( Int (*) (void *, void *))compEdges);	  
+	  if(compEdges(thisEdge, prevEdge)<0)  /*interior cusp*/
+	    {
+
+	      treeNode* leftEdge = TreeNodePredecessor(thisNode);
+	      treeNode* rightEdge = TreeNodeSuccessor(prevNode);
+	      ret_ranges[i] = sweepRangeMake( (directedLine*) leftEdge->key, 1, 
+					     (directedLine*) rightEdge->key, 1
+					     );
+	    }
+	  else /*exterior cusp*/
+	    {
+
+	      ret_ranges[i] = sweepRangeMake( prevEdge, 1, thisEdge, 1);
+	    }
+	}
+      else if(isBelow(vert, thisEdge) && isBelow(vert, prevEdge))
+	{
+
+	  /*case 4: delete both edges*/
+	  treeNode* thisNode = TreeNodeFind(searchTree, thisEdge, ( Int (*) (void *, void *))compEdges);
+	  treeNode* prevNode = TreeNodeFind(searchTree, prevEdge, ( Int (*) (void *, void *))compEdges);
+	  if(compEdges(thisEdge, prevEdge)>0) /*interior cusp*/
+	    {
+	      treeNode* leftEdge = TreeNodePredecessor(prevNode);
+	      treeNode* rightEdge = TreeNodeSuccessor(thisNode);
+	      ret_ranges[i] = sweepRangeMake( (directedLine*) leftEdge->key, 1, 
+					     (directedLine*) rightEdge->key, 1
+					     );
+	    }
+	  else /*exterior cusp*/
+	    {
+	      ret_ranges[i] = sweepRangeMake( thisEdge, 1, prevEdge, 1);
+	    }
+	  searchTree = TreeNodeDeleteSingleNode(searchTree, thisNode);
+	  searchTree = TreeNodeDeleteSingleNode(searchTree, prevNode);
+	}
+      else
+	{
+	  fprintf(stderr,"error in partitionY.C, invalid case\n");
+	  printf("vert is\n");
+	  vert->printSingle();
+	  printf("thisEdge is\n");
+	  thisEdge->printSingle();
+	  printf("prevEdge is\n");
+	  prevEdge->printSingle();
+	  
+	  exit(1);
+	}
+    }
+
+  /*finaly clean up space: delete the search tree*/
+  TreeNodeDeleteWholeTree(searchTree);
+}