libnurbs/nurbtess/monoChain.cc

/*
** 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.
**
*/
/*
*/

#include "gluos.h"
#include <stdlib.h>
#include <stdio.h>
#include <GL/gl.h>

#include "glimports.h"
#include "zlassert.h"

#include "monoChain.h"
#include "quicksort.h"
#include "searchTree.h"
#include "polyUtil.h"

#ifndef max
#define max(a,b) ((a>b)? a:b)
#endif
#ifndef min
#define min(a,b) ((a>b)? b:a)
#endif

extern Int isCusp(directedLine *v);
extern Int deleteRepeatDiagonals(Int num_diagonals, directedLine** diagonal_vertices, directedLine** new_vertices);

//for debug purpose only
#if 0 // UNUSED
static void drawDiagonals(Int num_diagonals, directedLine** diagonal_vertices)
{
  Int i;
  for(i=0; i<num_diagonals; i++)
    {
      glBegin(GL_LINE);
      glVertex2fv(diagonal_vertices[2*i]->head());
      glVertex2fv(diagonal_vertices[2*i+1]->head());
      glEnd();
    }
}
#endif

/*given (x_1, y_1) and (x_2, y_2), and y
 *return x such that (x,y) is on the line
 */
inline 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));
}

//compare the heads of the two chains
static int compChainHeadInY(monoChain* mc1, monoChain* mc2)
{
  return compV2InY(mc1->getHead()->head(), mc2->getHead()->head());
}

monoChain::monoChain(directedLine* cHead, directedLine* cTail)
{
  chainHead = cHead;
  chainTail = cTail;
  next = this;
  prev = this;

  nextPolygon = NULL;

  //compute bounding box
  directedLine* temp;
  minX = maxX = chainTail->head()[0];
  minY = maxY = chainTail->head()[1];

  for(temp=chainHead; temp!=cTail; temp = temp->getNext())
    {
      if(temp->head()[0] < minX)
	minX = temp->head()[0];
      if(temp->head()[0] > maxX)
	maxX = temp->head()[0];

      if(temp->head()[1] < minY)
	minY = temp->head()[1];
      if(temp->head()[1] > maxY)
	maxY = temp->head()[1];
    }

  //check whether the chain is increasing or decreasing
  if(chainHead->compInY(chainTail) <0)
    isIncrease = 1;
  else
    isIncrease = 0;

  //initilize currrent, this is used for accelerating search
  if(isIncrease)
    current = chainHead;
  else
    current = chainTail;

  isKey = 0;
  keyY = 0;
}

//insert a new line between prev and this
void monoChain::insert(monoChain* nc)
{
  nc->next = this;
  nc->prev = prev;
  prev->next = nc;
  prev = nc;
}

void monoChain::deleteLoop()
{
  monoChain *temp, *tempNext;
  prev->next = NULL;
  for(temp=this; temp != NULL; temp = tempNext)
    {
      tempNext = temp->next;
      delete temp;
    }
}

void monoChain::deleteLoopList()
{
  monoChain *temp, *tempNext;
  for(temp=this; temp != NULL; temp = tempNext)
    {
      tempNext = temp->nextPolygon;
      temp->deleteLoop();
    }
}

Int monoChain::toArraySingleLoop(monoChain** array, Int index)
{
  monoChain *temp;
  array[index++] = this;
  for(temp = next; temp != this; temp = temp->next)
    {
      array[index++] = temp;
    }
  return index;
}

monoChain** monoChain::toArrayAllLoops(Int& num_chains)
{
  num_chains = numChainsAllLoops();
  monoChain **ret =  (monoChain**) malloc(sizeof(monoChain*) * num_chains);
  assert(ret);
  monoChain *temp;
  Int index = 0;
  for(temp = this; temp != NULL; temp=temp->nextPolygon){
    index = temp->toArraySingleLoop(ret, index);
  }
  return ret;
}

Int monoChain::numChainsSingleLoop()
{
  Int ret=0;
  monoChain* temp;
  if(next == this) return 1;
  ret = 1;
  for(temp=next; temp != this; temp = temp->next)
    ret++;
  return ret;
}

Int monoChain::numChainsAllLoops()
{
  Int ret=0;
  monoChain *temp;
  for(temp =this; temp != NULL; temp = temp->nextPolygon)
    ret += temp->numChainsSingleLoop();
  return ret;
}

//update 'current'
Real monoChain::chainIntersectHoriz(Real y)
{
  directedLine* temp;
  if(isIncrease)
    {
      for(temp= current; temp != chainTail; temp = temp->getNext())
	{
	  if(temp->head()[1] > y)
	    break;
	}
      current = temp->getPrev();
    }
  else
    {
      for(temp = current; temp != chainHead; temp = temp->getPrev())
	{
	  if(temp->head()[1] > y)
	    break;
	}
      current = temp->getNext();
    }
  return intersectHoriz(current->head()[0], current->head()[1], current->tail()[0], current->tail()[1], y);
}

monoChain* directedLineLoopToMonoChainLoop(directedLine* loop)
{
  directedLine *temp;
  monoChain *ret=NULL;

  //find the first cusp
  directedLine *prevCusp=NULL;
  directedLine *firstCusp;

  if(isCusp(loop))
    prevCusp = loop;
  else
    {
      for(temp = loop->getNext(); temp != loop; temp = temp->getNext())
	if(isCusp(temp))
	  break;
      prevCusp = temp;
    }
  firstCusp = prevCusp;
//printf("first cusp is (%f,%f), (%f,%f), (%f,%f)\n", prevCusp->getPrev()->head()[0], prevCusp->getPrev()->head()[1], prevCusp->head()[0], prevCusp->head()[1], prevCusp->tail()[0], prevCusp->tail()[1]);

  for(temp = prevCusp->getNext(); temp != loop; temp = temp->getNext())
    {
      if(isCusp(temp))
	{
//printf("the cusp is (%f,%f), (%f,%f), (%f,%f)\n", temp->getPrev()->head()[0], temp->getPrev()->head()[1], temp->head()[0], temp->head()[1], temp->tail()[0], temp->tail()[1]);
	  if(ret == NULL)
	    {
	      ret = new monoChain(prevCusp, temp);
	    }
	  else
	    ret->insert(new monoChain(prevCusp, temp));
	  prevCusp = temp;
	}
    }
  assert(ret);
  ret->insert(new monoChain(prevCusp, firstCusp));

  return ret;
}

monoChain* directedLineLoopListToMonoChainLoopList(directedLine* list)
{
  directedLine* temp;
  monoChain* mc;
  monoChain* mcEnd;
  mc = directedLineLoopToMonoChainLoop(list);
  mcEnd = mc;
  for(temp = list->getNextPolygon(); temp != NULL; temp = temp->getNextPolygon())
    {
      monoChain *newLoop = directedLineLoopToMonoChainLoop(temp);
      mcEnd->setNextPolygon(newLoop);
      mcEnd = newLoop;
    }
  return mc;
}

/*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;
}

Int  compChains(monoChain* mc1, monoChain* mc2)
{
  Real y;
  assert(mc1->isKey || mc2->isKey);
  if(mc1->isKey)
    y = mc1->keyY;
  else
    y = mc2->keyY;
  directedLine *d1 = mc1->find(y);
  directedLine *d2 = mc2->find(y);
  mc2->find(y);
//  Real x1 = mc1->chainIntersectHoriz(y);
//  Real x2 = mc2->chainIntersectHoriz(y);
  return   compEdges(d1, d2);
}

//this function modifies current for efficiency
directedLine* monoChain::find(Real y)
{
  directedLine *ret;
  directedLine *temp;
  assert(current->head()[1] <= y);
  if(isIncrease)
    {
      assert(chainTail->head()[1] >=y);
      for(temp=current; temp!=chainTail; temp = temp->getNext())
	{
	  if(temp->head()[1] > y)
	    break;
	}
      current = temp->getPrev();
      ret = current;
    }
  else
    {
      for(temp=current; temp != chainHead; temp = temp->getPrev())
	{
	  if(temp->head()[1] > y)
	    break;
	}
      current = temp->getNext();
      ret = temp;
    }
  return ret;
}

void monoChain::printOneChain()
{
  directedLine* temp;
  for(temp = chainHead; temp != chainTail; temp = temp->getNext())
    {
      printf("(%f,%f) ", temp->head()[0], temp->head()[1]);
    }
  printf("(%f,%f) \n", chainTail->head()[0], chainTail->head()[1]);
}

void monoChain::printChainLoop()
{
  monoChain* temp;
  this->printOneChain();
  for(temp = next; temp != this; temp = temp->next)
    {
      temp->printOneChain();
    }
  printf("\n");
}

void monoChain::printAllLoops()
{
  monoChain* temp;
  for(temp=this; temp != NULL; temp = temp->nextPolygon)
    temp->printChainLoop();
}

//return 1 if error occures
Int MC_sweepY(Int nVertices, monoChain** sortedVertices, sweepRange** ret_ranges)
{
  Int i;
  Real keyY;
  Int errOccur=0;
//printf("enter MC_sweepY\n");
//printf("nVertices=%i\n", nVertices);
  /*for each vertex in the sorted list, update the binary search tree.
   *and store the range information for each vertex.
   */
  treeNode* searchTree = NULL;
//printf("nVertices=%i\n", nVertices);
  for(i=0; i<nVertices; i++)
    {
      monoChain* vert = sortedVertices[i];
      keyY = vert->getHead()->head()[1]; //the sweep line
      directedLine *dline = vert->getHead();
      directedLine *dlinePrev = dline->getPrev();
      if(isBelow(dline, dline) && isBelow(dline, dlinePrev))
	{
//printf("case 1\n");
	  //this<v and prev < v
	  //delete both edges
	  vert->isKey = 1;
	  vert->keyY = keyY;
	  treeNode* thisNode = TreeNodeFind(searchTree, vert, (Int (*) (void *, void *))compChains);
	  vert->isKey = 0;

	  vert->getPrev()->isKey = 1;
	  vert->getPrev()->keyY = keyY;
	  treeNode* prevNode = TreeNodeFind(searchTree, vert->getPrev(), (Int (*) (void *, void *))compChains);
	  vert->getPrev()->isKey = 0;

	  if(cuspType(dline) == 1)//interior cusp
	    {

	      treeNode* leftEdge = TreeNodePredecessor(prevNode);
	      treeNode* rightEdge = TreeNodeSuccessor(thisNode);
	      if(leftEdge == NULL ||  rightEdge == NULL)
		{
		  errOccur = 1;
		  goto JUMP_HERE;
		}

	      directedLine* leftEdgeDline = ((monoChain* ) leftEdge->key)->find(keyY);


	      directedLine* rightEdgeDline = ((monoChain* ) rightEdge->key)->find(keyY);

	      ret_ranges[i] = sweepRangeMake(leftEdgeDline, 1, rightEdgeDline, 1);
	    }
	  else /*exterior cusp*/
	    {
	      ret_ranges[i] = sweepRangeMake( dline, 1, dlinePrev, 1);
	    }

	  searchTree = TreeNodeDeleteSingleNode(searchTree, thisNode);
	  searchTree = TreeNodeDeleteSingleNode(searchTree, prevNode);

	}
      else if(isAbove(dline, dline) && isAbove(dline, dlinePrev))
	{
//printf("case 2\n");
	  //insert both edges
	  treeNode* thisNode = TreeNodeMake(vert);
	  treeNode* prevNode = TreeNodeMake(vert->getPrev());

	  vert->isKey = 1;
          vert->keyY = keyY;
	  searchTree = TreeNodeInsert(searchTree, thisNode, (Int (*) (void *, void *))compChains);
          vert->isKey = 0;

          vert->getPrev()->isKey = 1;
          vert->getPrev()->keyY = keyY;
	  searchTree = TreeNodeInsert(searchTree, prevNode, (Int (*) (void *, void *))compChains);
          vert->getPrev()->isKey = 0;

	  if(cuspType(dline) == 1) //interior cusp
	    {
//printf("cuspType is 1\n");
	      treeNode* leftEdge = TreeNodePredecessor(thisNode);
	      treeNode* rightEdge = TreeNodeSuccessor(prevNode);
              if(leftEdge == NULL || rightEdge == NULL)
		{
		  errOccur = 1;
		  goto JUMP_HERE;
		}
//printf("leftEdge is %i, rightEdge is %i\n", leftEdge, rightEdge);
	      directedLine* leftEdgeDline = ((monoChain*) leftEdge->key)->find(keyY);
	      directedLine* rightEdgeDline = ((monoChain*) rightEdge->key)->find(keyY);
	      ret_ranges[i] = sweepRangeMake( leftEdgeDline, 1, rightEdgeDline, 1);
	    }
	  else //exterior cusp
	    {
//printf("cuspType is not 1\n");
	      ret_ranges[i] = sweepRangeMake(dlinePrev, 1, dline, 1);
	    }
	}
      else
	{
//printf("%i,%i\n", isAbove(dline, dline), isAbove(dline, dlinePrev));
	  errOccur = 1;
	  goto JUMP_HERE;

	  fprintf(stderr, "error in MC_sweepY\n");
	  exit(1);
	}
    }

 JUMP_HERE:
  //finally clean up space: delete  the search tree
  TreeNodeDeleteWholeTree(searchTree);
  return errOccur;
}

void MC_findDiagonals(Int total_num_edges, monoChain** sortedVertices,
		   sweepRange** ranges, Int& num_diagonals,
		   directedLine** diagonal_vertices)
{
  Int i,j,k;
  k=0;
  //reset 'current' of all the monoChains
  for(i=0; i<total_num_edges; i++)
    sortedVertices[i]->resetCurrent();

  for(i=0; i<total_num_edges; i++)
    {
      directedLine* vert = sortedVertices[i]->getHead();
      directedLine* thisEdge = vert;
      directedLine* prevEdge = vert->getPrev();
      if(isBelow(vert, thisEdge) && isBelow(vert, prevEdge) && compEdges(prevEdge, thisEdge)<0)
	{
	  //this is an upward interior cusp
	  diagonal_vertices[k++] = vert;

	  directedLine* leftEdge = ranges[i]->left;
	  directedLine* rightEdge = ranges[i]->right;

	  directedLine* leftVert = leftEdge;
	  directedLine* rightVert = rightEdge->getNext();
	  assert(leftVert->head()[1] >= vert->head()[1]);
	  assert(rightVert->head()[1] >= vert->head()[1]);
	  directedLine* minVert = (leftVert->head()[1] <= rightVert->head()[1])?leftVert:rightVert;
	  Int found = 0;
	  for(j=i+1; j<total_num_edges; j++)
	    {
	      if(sortedVertices[j]->getHead()->head()[1] > minVert->head()[1])
		break;

	      if(sweepRangeEqual(ranges[i], ranges[j]))
		{
		  found = 1;
		  break;
		}
	    }

	  if(found)
	    diagonal_vertices[k++] = sortedVertices[j]->getHead();
	  else
	    diagonal_vertices[k++] = minVert;
	}
      else if(isAbove(vert, thisEdge) && isAbove(vert, prevEdge) && compEdges(prevEdge, thisEdge)>0)
	{
	  //downward interior cusp
	  diagonal_vertices[k++] = vert;
	  directedLine* leftEdge = ranges[i]->left;
	  directedLine* rightEdge = ranges[i]->right;
	  directedLine* leftVert = leftEdge->getNext();
	  directedLine* rightVert = rightEdge;
	  assert(leftVert->head()[1] <= vert->head()[1]);
	  assert(rightVert->head()[1] <= vert->head()[1]);
	  directedLine* maxVert = (leftVert->head()[1] > rightVert->head()[1])? leftVert:rightVert;
	  Int found=0;
	  for(j=i-1; j>=0; j--)
	    {
	      if(sortedVertices[j]->getHead()->head()[1] < maxVert->head()[1])
		break;
	      if(sweepRangeEqual(ranges[i], ranges[j]))
		{
		  found = 1;
		  break;
		}
	    }
	  if(found)
	    diagonal_vertices[k++] = sortedVertices[j]->getHead();
	  else
	    diagonal_vertices[k++] = maxVert;
	}
    }
  num_diagonals = k/2;
}


directedLine* MC_partitionY(directedLine *polygons, sampledLine **retSampledLines)
{
//printf("enter mc_partitionY\n");
  Int total_num_chains = 0;
  monoChain* loopList = directedLineLoopListToMonoChainLoopList(polygons);
  monoChain** array = loopList->toArrayAllLoops(total_num_chains);

  if(total_num_chains<=2) //there is just one single monotone polygon
    {
      loopList->deleteLoopList();
      free(array);
      *retSampledLines = NULL;
      return polygons;
    }

//loopList->printAllLoops();
//printf("total_num_chains=%i\n", total_num_chains);
  quicksort( (void**)array, 0, total_num_chains-1, (Int (*)(void*, void*))compChainHeadInY);
//printf("after quicksort\n");

  sweepRange** ranges = (sweepRange**)malloc(sizeof(sweepRange*) * (total_num_chains));
  assert(ranges);

  if(MC_sweepY(total_num_chains, array, ranges))
    {
      loopList->deleteLoopList();
      free(array);
      *retSampledLines = NULL;
      return NULL;
    }
//printf("after MC_sweepY\n");


  Int num_diagonals;
  /*number diagonals is < total_num_edges*total_num_edges*/
  directedLine** diagonal_vertices = (directedLine**) malloc(sizeof(directedLine*) * total_num_chains*2/*total_num_edges*/);
  assert(diagonal_vertices);

//printf("before call MC_findDiagonales\n");

  MC_findDiagonals(total_num_chains, array, ranges, num_diagonals, diagonal_vertices);
//printf("after call MC_findDia, num_diagnla=%i\n", num_diagonals);

  directedLine* ret_polygons = polygons;
  sampledLine* newSampledLines = NULL;
  Int i,k;

  num_diagonals=deleteRepeatDiagonals(num_diagonals, diagonal_vertices, diagonal_vertices);


//drawDiagonals(num_diagonals, diagonal_vertices);
//printf("diagoanls are \n");
//for(i=0; i<num_diagonals; i++)
//  {
//    printf("(%f,%f)\n", diagonal_vertices[2*i]->head()[0], diagonal_vertices[2*i]->head()[1]);
//    printf("**(%f,%f)\n", diagonal_vertices[2*i+1]->head()[0], diagonal_vertices[2*i+1]->head()[1]);
//  }

  Int *removedDiagonals=(Int*)malloc(sizeof(Int) * num_diagonals);
  for(i=0; i<num_diagonals; i++)
    removedDiagonals[i] = 0;
//  printf("first pass\n");


 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*/
//printf("second pass: \n");

//  for(i=0; i<num_diagonals; i++)
//    printf("%i ", removedDiagonals[i]);


  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
  loopList->deleteLoopList();
  free(array);
  free(ranges);
  free(diagonal_vertices);
  free(removedDiagonals);

  *retSampledLines = newSampledLines;
  return ret_polygons;
}