Remove libGLU
[mesa.git] / src / glu / sgi / libnurbs / nurbtess / monoChain.cc
diff --git a/src/glu/sgi/libnurbs/nurbtess/monoChain.cc b/src/glu/sgi/libnurbs/nurbtess/monoChain.cc
deleted file mode 100644 (file)
index cb28129..0000000
+++ /dev/null
@@ -1,936 +0,0 @@
-/*
-** 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;
-}
-      
-