Remove libGLU

It's been moved to its own repository, found at
	http://cgit.freedesktop.org/mesa/glu/

Acked-by: Kenneth Graunke <[email protected]>

1 files changed, 0 insertions, 1482 deletions

diff --git a/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.cc b/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.cc
deleted file mode 100644
index 8e8d49dda70..00000000000
--- a/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.cc
+++ /dev/null
@@ -1,1482 +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 <stdlib.h>
-#include <stdio.h>
-#include "gluos.h"
-#include "glimports.h"
-#include "zlassert.h"
-
-#include "monoTriangulation.h"
-#include "polyUtil.h" /*for area*/
-#include "partitionX.h"
-#include "monoPolyPart.h"
-
-
-
-extern  directedLine*  polygonConvert(directedLine* polygon);
-
-/*poly is NOT deleted
- */
-void monoTriangulationOpt(directedLine* poly, primStream* pStream)
-{
-  Int n_cusps;
-  Int n_edges = poly->numEdges();
-  directedLine** cusps = (directedLine**) malloc(sizeof(directedLine*)*n_edges);
-  assert(cusps);
-  findInteriorCuspsX(poly, n_cusps, cusps);
-  if(n_cusps ==0) //u monotine
-    {
-      monoTriangulationFun(poly, compV2InX, pStream);
-    }
-  else if(n_cusps == 1) // one interior cusp
-    {
-      directedLine* new_polygon = polygonConvert(cusps[0]);
-      directedLine* other = findDiagonal_singleCuspX(new_polygon);
-      //<other> should NOT be null unless there are self-intersecting
-      //trim curves. In that case, we don't want to core dump, instead,
-      //we triangulate anyway, and print out error message.
-      if(other == NULL)
-	{
-	  monoTriangulationFun(poly, compV2InX, pStream);
-	}
-      else
-	{
-	  directedLine* ret_p1;
-	  directedLine* ret_p2;
-	  
-	  new_polygon->connectDiagonal_2slines(new_polygon, other, 
-					       &ret_p1,
-					       &ret_p2,
-					       new_polygon);
-	  
-	  monoTriangulationFun(ret_p1, compV2InX, pStream);
-	  monoTriangulationFun(ret_p2, compV2InX, pStream);
-	  
-	  ret_p1->deleteSinglePolygonWithSline();	      
-	  ret_p2->deleteSinglePolygonWithSline();	  
-	}
-    }
-  else
-    {
-      //we need a general partitionX funtion (supposed to be in partitionX.C,
-      //not implemented yet. XXX
-      monoTriangulationFun(poly, compV2InY, pStream);    
-    }
-  
-  free(cusps);
-}
-
-void monoTriangulationRecOpt(Real* topVertex, Real* botVertex, 
-			     vertexArray* left_chain, Int left_current,
-			     vertexArray* right_chain, Int right_current,
-			     primStream* pStream)
-{
-  Int i,j;
-  Int n_left = left_chain->getNumElements();
-  Int n_right = right_chain->getNumElements();
-  if(left_current>= n_left-1 ||
-     right_current>= n_right-1)
-    {
-      monoTriangulationRec(topVertex, botVertex, left_chain, left_current,
-			   right_chain, right_current, pStream);
-      return;
-    }
-  //now both left and right  have at least two vertices each.
-  Real left_v = left_chain->getVertex(left_current)[1];
-  Real right_v = right_chain->getVertex(right_current)[1];
- 
-  if(left_v <= right_v) //first left vertex is below right
-    {
-      //find the last vertex of right which is above or equal to left
-      for(j=right_current; j<=n_right-1; j++)
-	{
-	  if(right_chain->getVertex(j)[1] < left_v)
-	    break;
-	}
-      monoTriangulationRecGen(topVertex, left_chain->getVertex(left_current),
-			      left_chain, left_current, left_current,
-			      right_chain, right_current, j-1,
-			      pStream);
-      monoTriangulationRecOpt(right_chain->getVertex(j-1),
-			      botVertex,
-			      left_chain, left_current,
-			      right_chain, j,
-			      pStream);
-    }
-  else //first right vertex is strictly below left
-    {
-      //find the last vertex of left which is strictly above right
-      for(i=left_current; i<=n_left-1; i++)
-	{
-	  if(left_chain->getVertex(i)[1] <= right_v)
-	    break;
-	}
-      monoTriangulationRecGen(topVertex, right_chain->getVertex(right_current),
-			      left_chain, left_current, i-1,
-			      right_chain, right_current, right_current,
-			      pStream);
-      monoTriangulationRecOpt(left_chain->getVertex(i-1),
-			      botVertex,
-			      left_chain, i,
-			      right_chain, right_current,
-			      pStream);
-    }
-}
-
-
-void monoTriangulationRecGenTBOpt(Real* topVertex, Real* botVertex, 
-			  vertexArray* inc_chain, Int inc_current, Int inc_end,
-			  vertexArray* dec_chain, Int dec_current, Int dec_end,
-			  primStream* pStream)
-{
-  pStream->triangle(topVertex, inc_chain->getVertex(inc_current), dec_chain->getVertex(dec_current));
-  
-/*printf("**(%f,%f)\n", inc_chain->getArray()[0][0],inc_chain->getArray()[0][1]);*/
-  triangulateXYMonoTB(inc_end-inc_current+1, inc_chain->getArray()+inc_current,  dec_end-dec_current+1,  dec_chain->getArray()+dec_current, pStream);
-
-  pStream->triangle(botVertex, dec_chain->getVertex(dec_end), inc_chain->getVertex(inc_end));
-}
-  
-
-/*n_left>=1
- *n_right>=1
- *the strip is going top to bottom. compared to the funtion
- * triangulateXYmono()
- */
-void triangulateXYMonoTB(Int n_left, Real** leftVerts,
-		       Int n_right, Real** rightVerts,
-		       primStream* pStream)
-{
-
-
-  Int i,j,k,l;
-  Real* topMostV;
-
-  assert(n_left>=1 && n_right>=1);
-  if(leftVerts[0][1] >= rightVerts[0][1])
-    {
-      i=1;
-      j=0;
-      topMostV = leftVerts[0];
-    }
-  else
-    {
-      i=0;
-      j=1;
-      topMostV = rightVerts[0];
-    }
-  
-  while(1)
-    {
-      if(i >= n_left) /*case1: no more in left*/
-	{
-
-	  if(j<n_right-1) /*at least two vertices in right*/
-	    {
-	      pStream->begin();
-	      pStream->insert(topMostV);
-	      for(k=n_right-1; k>=j; k--)		
-		pStream->insert(rightVerts[j]);
-
-	      pStream->end(PRIMITIVE_STREAM_FAN);
-	      
-	    }
-
-	  break;	
-	}
-      else if(j>= n_right) /*case2: no more in right*/
-	{
-
-	  if(i<n_left-1) /*at least two vertices in left*/
-	    {
-	      pStream->begin();
-	      pStream->insert(topMostV);
-
-	      for(k=i; k<n_left; k++)
-		pStream->insert(leftVerts[k]);
-
-	      pStream->end(PRIMITIVE_STREAM_FAN);	      
-	    }
-
-	  break;
-	}
-      else /* case3: neither is empty, plus the topMostV, there is at least one triangle to output*/
-	{
-
-	  if(leftVerts[i][1] >=  rightVerts[j][1])
-	    {
-	      pStream->begin();
-	      pStream->insert(rightVerts[j]); /*the origin of this fan*/
-
-	      pStream->insert(topMostV);
-
-	      /*find the last k>=i such that 
-	       *leftverts[k][1] >= rightverts[j][1]
-	       */
-	      k=i;
-	      while(k<n_left)
-		{
-		  if(leftVerts[k][1] < rightVerts[j][1])
-		    break;
-		  k++;
-		}
-	      k--;
-	      for(l=i; l<=k; l++)
-		{
-		  pStream->insert(leftVerts[l]);
-		}
-
-	      pStream->end(PRIMITIVE_STREAM_FAN);
-	      //update i for next loop
-	      i = k+1;
-	      topMostV = leftVerts[k];
-
-	    }
-	  else /*leftVerts[i][1] < rightVerts[j][1]*/
-	    {
-	      pStream->begin();
-	      pStream->insert(leftVerts[i]);/*the origion of this fan*/
-
-	      /*find the last k>=j such that
-	       *rightverts[k][1] > leftverts[i][1]*/
-	      k=j;
-	      while(k< n_right)
-		{
-		  if(rightVerts[k][1] <= leftVerts[i][1])
-		    break;
-		  k++;
-		}
-	      k--;
-
-	      for(l=k; l>= j; l--)
-		pStream->insert(rightVerts[l]);
-
-	      pStream->insert(topMostV);
-	      pStream->end(PRIMITIVE_STREAM_FAN);
-	      j=k+1;
-	      topMostV = rightVerts[j-1];
-	    }	  
-	}
-    }
-}
-
-static int chainConvex(vertexArray* inc_chain, Int inc_current, Int inc_end)
-{
-  Int i;
-  //if there are no more than 2 vertices, return 1
-  if(inc_current >= inc_end-1) return 1;
-  for(i=inc_current; i<= inc_end-2; i++)
-    {
-      if(area(inc_chain->getVertex(i), inc_chain->getVertex(i+1), inc_chain->getVertex(i+2)) <0)
-	return 0;
-    }
-  return 1;
-}
-
-static int chainConcave(vertexArray* dec_chain, Int dec_current, Int dec_end)
-{
-  Int i;
-  //if there are no more than 2 vertices, return 1
-  if(dec_current >= dec_end -1) return 1;
-  for(i=dec_current; i<=dec_end-2; i++)
-    {
-      if(area(dec_chain->getVertex(i), dec_chain->getVertex(i+1), dec_chain->getVertex(i+2)) >0)
-	return 0;
-    }
-  return 1;
-}
- 
-void monoTriangulationRecGenInU(Real* topVertex, Real* botVertex,
-				vertexArray* inc_chain, Int inc_current, Int inc_end,
-				vertexArray* dec_chain, Int dec_current, Int dec_end,
-				primStream* pStream)
-{
-  
-}
-
-void  monoTriangulationRecGenOpt(Real* topVertex, Real* botVertex,
-				 vertexArray* inc_chain, Int inc_current, Int inc_end,
-				 vertexArray* dec_chain, Int dec_current, Int dec_end,
-				 primStream* pStream)
-{
-  Int i;
-  //copy this to a polygon: directedLine Lioop
-  sampledLine* sline;
-  directedLine* dline;
-  directedLine* poly;
-
-  if(inc_current <= inc_end) //at least one vertex in inc_chain
-    {      
-      sline = new sampledLine(topVertex, inc_chain->getVertex(inc_current));
-      poly = new directedLine(INCREASING, sline);
-      for(i=inc_current; i<=inc_end-1; i++)
-	{
-	  sline = new sampledLine(inc_chain->getVertex(i), inc_chain->getVertex(i+1));
-	  dline = new directedLine(INCREASING, sline);
-	  poly->insert(dline);
-	}
-      sline = new sampledLine(inc_chain->getVertex(inc_end), botVertex);
-      dline = new directedLine(INCREASING, sline);
-      poly->insert(dline);
-    }
-  else //inc_chian is empty
-    {
-      sline = new sampledLine(topVertex, botVertex);
-      dline = new directedLine(INCREASING, sline);
-      poly = dline;
-    }
-  
-  assert(poly != NULL);
-
-  if(dec_current <= dec_end) //at least on vertex in dec_Chain
-    {
-      sline = new sampledLine(botVertex, dec_chain->getVertex(dec_end));
-      dline = new directedLine(INCREASING, sline);
-      poly->insert(dline);
-      for(i=dec_end; i>dec_current; i--)
-	{
-	  sline = new sampledLine(dec_chain->getVertex(i), dec_chain->getVertex(i-1));
-	  dline = new directedLine(INCREASING, sline);
-	  poly->insert(dline);
-	}
-      sline = new sampledLine(dec_chain->getVertex(dec_current), topVertex);
-      dline = new directedLine(INCREASING, sline);
-      poly->insert(dline);      
-    }
-  else //dec_chain  is empty
-    {
-      sline = new sampledLine(botVertex, topVertex);
-      dline = new directedLine(INCREASING, sline);
-      poly->insert(dline);
-    }
-
-  {
-    Int n_cusps;
-    Int n_edges = poly->numEdges();
-    directedLine** cusps = (directedLine**) malloc(sizeof(directedLine*)*n_edges);
-    assert(cusps);
-    findInteriorCuspsX(poly, n_cusps, cusps);
-
-    if(n_cusps ==0) //u monotine
-      {
-	monoTriangulationFun(poly, compV2InX, pStream);
-      }
-    else if(n_cusps == 1) // one interior cusp
-      {
-	directedLine* new_polygon = polygonConvert(cusps[0]);
-	directedLine* other = findDiagonal_singleCuspX(new_polygon);
-	  //<other> should NOT be null unless there are self-intersecting
-          //trim curves. In that case, we don't want to core dump, instead,
-          //we triangulate anyway, and print out error message.
-	  if(other == NULL)
-	    {
-	      monoTriangulationFun(poly, compV2InX, pStream);
-	    }
-	  else
-	    {
-	      directedLine* ret_p1;
-	      directedLine* ret_p2;
-	      
-	      new_polygon->connectDiagonal_2slines(new_polygon, other, 
-						   &ret_p1,
-						   &ret_p2,
-						   new_polygon);
-	      
-	      monoTriangulationFun(ret_p1, compV2InX, pStream);
-	      monoTriangulationFun(ret_p2, compV2InX, pStream);
-
-	      ret_p1->deleteSinglePolygonWithSline();	      
-	      ret_p2->deleteSinglePolygonWithSline();	  
-	    }
-      }
-    else
-      {
-	//we need a general partitionX funtion (supposed to be in partitionX.C,
-	//not implemented yet. XXX
-	//monoTriangulationFun(poly, compV2InY, pStream);    
-	
-	directedLine* new_polygon = polygonConvert(poly);
-	directedLine* list = monoPolyPart(new_polygon);
-	for(directedLine* temp = list; temp != NULL; temp = temp->getNextPolygon())
-	  { 
-	    monoTriangulationFun(temp, compV2InX, pStream);
-	  }
-	//clean up
-	list->deletePolygonListWithSline();
-        
-      }
-
-    free(cusps);
-    /*
-      if(numInteriorCuspsX(poly) == 0) //is u monotone
-	monoTriangulationFun(poly, compV2InX, pStream);
-      else //it is not u motone
-	monoTriangulationFun(poly, compV2InY, pStream);    
-	*/
-    //clean up space
-    poly->deleteSinglePolygonWithSline();
-    return;
-  }
-      
-  //apparently the following code is not reachable, 
-  //it is for test purpose
-  if(inc_current > inc_end || dec_current>dec_end)
-    {
-    monoTriangulationRecGen(topVertex, botVertex, inc_chain, inc_current, inc_end,
-			    dec_chain, dec_current, dec_end,
-			    pStream);    
-    return;
-  }
-  
-
-  if(
-     area(dec_chain->getVertex(dec_current),
-	  topVertex,
-	  inc_chain->getVertex(inc_current)) >=0
-     && chainConvex(inc_chain, inc_current, inc_end)
-     && chainConcave(dec_chain, dec_current, dec_end)
-     && area(inc_chain->getVertex(inc_end), botVertex, dec_chain->getVertex(dec_end)) >=0
-     )
-    {
-      monoTriangulationRecFunGen(topVertex, botVertex, 
-				 inc_chain, inc_current, inc_end,
-				 dec_chain, dec_current, dec_end, 
-				 compV2InX, pStream);
-    }
-  else
-    {
-      monoTriangulationRecGen(topVertex, botVertex, inc_chain, inc_current, inc_end,
-			      dec_chain, dec_current, dec_end,
-			      pStream);
-    }
-}
-
-/*if inc_current>inc_end, then inc_chain has no points to be considered
- *same for dec_chain
- */
-void monoTriangulationRecGen(Real* topVertex, Real* botVertex, 
-			  vertexArray* inc_chain, Int inc_current, Int inc_end,
-			  vertexArray* dec_chain, Int dec_current, Int dec_end,
-			  primStream* pStream)
-{
-  Real** inc_array ;
-  Real** dec_array ;
-  Int i;
-
-  if(inc_current > inc_end && dec_current>dec_end)
-    return;
-  else if(inc_current>inc_end) /*no more vertices on inc_chain*/
-    {
-      dec_array = dec_chain->getArray();
-      reflexChain rChain(100,0);
-      /*put the top vertex into the reflex chain*/
-      rChain.processNewVertex(topVertex, pStream);
-      /*process all the vertices on the dec_chain*/
-      for(i=dec_current; i<=dec_end; i++){
-	rChain.processNewVertex(dec_array[i], pStream);
-      }
-      /*process the bottom vertex*/
-      rChain.processNewVertex(botVertex, pStream);
-    }
-  else if(dec_current> dec_end) /*no more vertices on dec_chain*/
-    {
-      inc_array = inc_chain->getArray();
-
-      reflexChain rChain(100,1);
-      /*put the top vertex into the reflex chain*/
-      rChain.processNewVertex(topVertex, pStream);
-      /*process all the vertices on the inc_chain*/
-      for(i=inc_current; i<=inc_end; i++){
-	rChain.processNewVertex(inc_array[i], pStream);
-      }
-      /*process the bottom vertex*/
-      rChain.processNewVertex(botVertex, pStream);
-    }
-  else /*neither chain is empty*/
-    {
-      inc_array = inc_chain -> getArray();
-      dec_array = dec_chain -> getArray();
-
-      /*if top of inc_chain is 'lower' than top of dec_chain, process all the 
-       *vertices on the dec_chain which are higher than top of inc_chain
-       */
-      if(compV2InY(inc_array[inc_current], dec_array[dec_current]) <= 0)
-	{
-
-	  reflexChain rChain(100, 0);
-	  rChain.processNewVertex(topVertex, pStream);
-	  for(i=dec_current; i<=dec_end; i++)
-	    {
-	      if(compV2InY(inc_array[inc_current], dec_array[i]) <= 0)
-		rChain.processNewVertex(dec_array[i], pStream);
-	      else 
-		break;
-	    }
-	  rChain.outputFan(inc_array[inc_current], pStream);
-	  monoTriangulationRecGen(dec_array[i-1], botVertex, 
-			       inc_chain, inc_current, inc_end,
-			       dec_chain, i, dec_end,
-			       pStream);
-	}
-      else /*compV2InY(inc_array[inc_current], dec_array[dec_current]) > 0*/
-	{
-
-	  reflexChain rChain(100, 1);
-	  rChain.processNewVertex(topVertex, pStream);
-	  for(i=inc_current; i<=inc_end; i++)
-	    {
-	      if(compV2InY(inc_array[i], dec_array[dec_current]) >0)		
-		rChain.processNewVertex(inc_array[i], pStream);	      
-	      else
-		break;
-	    }
-	  rChain.outputFan(dec_array[dec_current], pStream);
-	  monoTriangulationRecGen(inc_array[i-1], botVertex, 
-			       inc_chain, i, inc_end,
-			       dec_chain, dec_current,dec_end,
-			       pStream);
-	}
-    }/*end case neither is empty*/
-}
-
-void monoTriangulationFun(directedLine* monoPolygon, Int (*compFun)(Real*, Real*), primStream* pStream)
-{
-  Int i;
-  /*find the top vertex, bottom vertex, inccreasing chain, and decreasing chain,
-   *then call monoTriangulationRec
-   */
-  directedLine* tempV;
-  directedLine* topV;
-  directedLine* botV;
-  topV = botV = monoPolygon;
-  for(tempV = monoPolygon->getNext(); tempV != monoPolygon; tempV = tempV->getNext())
-    {
-      if(compFun(topV->head(), tempV->head())<0) {
-	topV = tempV;
-      }
-      if(compFun(botV->head(), tempV->head())>0) {
-	botV = tempV;
-      }
-    }
-
-  /*creat increase and decrease chains*/
-  vertexArray inc_chain(20); /*this is a dynamic array*/
-  for(i=1; i<=topV->get_npoints()-2; i++) { /*the first vertex is the top vertex which doesn't belong to inc_chain*/
-    inc_chain.appendVertex(topV->getVertex(i));
-  }
-  for(tempV = topV->getNext(); tempV != botV; tempV = tempV->getNext())
-    {
-      for(i=0; i<=tempV->get_npoints()-2; i++){
-	inc_chain.appendVertex(tempV->getVertex(i));
-      }
-    }
-  
-  vertexArray dec_chain(20);
-  for(tempV = topV->getPrev(); tempV != botV; tempV = tempV->getPrev())
-    {
-      for(i=tempV->get_npoints()-2; i>=0; i--){
-	dec_chain.appendVertex(tempV->getVertex(i));
-      }
-    }
-  for(i=botV->get_npoints()-2; i>=1; i--){ 
-    dec_chain.appendVertex(tempV->getVertex(i));
-  }
-  
-  if (!(0 == inc_chain.getNumElements() && 0 == dec_chain.getNumElements())) {
-     monoTriangulationRecFun(topV->head(), botV->head(), &inc_chain, 0,
-                             &dec_chain, 0, compFun, pStream);
-  }
-}  
-
-void monoTriangulation(directedLine* monoPolygon, primStream* pStream)
-{
-  Int i;
-  /*find the top vertex, bottom vertex, inccreasing chain, and decreasing chain,
-   *then call monoTriangulationRec
-   */
-  directedLine* tempV;
-  directedLine* topV;
-  directedLine* botV;
-  topV = botV = monoPolygon;
-  for(tempV = monoPolygon->getNext(); tempV != monoPolygon; tempV = tempV->getNext())
-    {
-      if(compV2InY(topV->head(), tempV->head())<0) {
-	topV = tempV;
-      }
-      if(compV2InY(botV->head(), tempV->head())>0) {
-	botV = tempV;
-      }
-    }
-  /*creat increase and decrease chains*/
-  vertexArray inc_chain(20); /*this is a dynamic array*/
-  for(i=1; i<=topV->get_npoints()-2; i++) { /*the first vertex is the top vertex which doesn't belong to inc_chain*/
-    inc_chain.appendVertex(topV->getVertex(i));
-  }
-  for(tempV = topV->getNext(); tempV != botV; tempV = tempV->getNext())
-    {
-      for(i=0; i<=tempV->get_npoints()-2; i++){
-	inc_chain.appendVertex(tempV->getVertex(i));
-      }
-    }
-  
-  vertexArray dec_chain(20);
-  for(tempV = topV->getPrev(); tempV != botV; tempV = tempV->getPrev())
-    {
-      for(i=tempV->get_npoints()-2; i>=0; i--){
-	dec_chain.appendVertex(tempV->getVertex(i));
-      }
-    }
-  for(i=botV->get_npoints()-2; i>=1; i--){ 
-    dec_chain.appendVertex(tempV->getVertex(i));
-  }
-  
-  monoTriangulationRec(topV->head(), botV->head(), &inc_chain, 0, &dec_chain, 0, pStream);
-
-}
-
-/*the chain could be increasing or decreasing, although we use the
- * name inc_chain.
- *the argument  is_increase_chain indicates whether this chain
- *is increasing (left chain in V-monotone case) or decreaing (right chain
- *in V-monotone case).
- */
-void monoTriangulation2(Real* topVertex, Real* botVertex, 
-			vertexArray* inc_chain, Int inc_smallIndex,
-			Int inc_largeIndex,
-			Int is_increase_chain,
-			primStream* pStream)
-{
-  assert( inc_chain != NULL);
-  Real** inc_array ;
-
-  if(inc_smallIndex > inc_largeIndex)
-    return; //no triangles 
-  if(inc_smallIndex == inc_largeIndex)
-    {
-      if(is_increase_chain)
-	pStream->triangle(inc_chain->getVertex(inc_smallIndex), botVertex, topVertex);
-      else
-	pStream->triangle(inc_chain->getVertex(inc_smallIndex), topVertex, botVertex);	
-      return;
-    }
-  Int i;
-
-  if(is_increase_chain && botVertex[1] == inc_chain->getVertex(inc_largeIndex)[1])
-    {
-      pStream->triangle(botVertex, inc_chain->getVertex(inc_largeIndex-1),
-			inc_chain->getVertex(inc_largeIndex));
-      monoTriangulation2(topVertex, botVertex, inc_chain, inc_smallIndex,
-			 inc_largeIndex-1,
-			 is_increase_chain,
-			 pStream);
-      return;
-    }
-  else if( (!is_increase_chain) && topVertex[1] == inc_chain->getVertex(inc_smallIndex)[1])
-    {
-      pStream->triangle(topVertex, inc_chain->getVertex(inc_smallIndex+1),
-			inc_chain->getVertex(inc_smallIndex));
-      monoTriangulation2(topVertex, botVertex, inc_chain, inc_smallIndex+1,
-			 inc_largeIndex, is_increase_chain, pStream);
-      return ;
-    }		           
-
-  inc_array = inc_chain->getArray();
-
-  reflexChain rChain(20,is_increase_chain); /*1 means the chain is increasing*/
-
-  rChain.processNewVertex(topVertex, pStream);
-
-  for(i=inc_smallIndex; i<=inc_largeIndex; i++){
-    rChain.processNewVertex(inc_array[i], pStream);
-  }
-  rChain.processNewVertex(botVertex, pStream);
-
-}
- 
-/*if compFun == compV2InY, top to bottom: V-monotone
- *if compFun == compV2InX, right to left: U-monotone
- */
-void monoTriangulationRecFunGen(Real* topVertex, Real* botVertex, 
-			  vertexArray* inc_chain, Int inc_current, Int inc_end,
-			  vertexArray* dec_chain, Int dec_current, Int dec_end,
-			  Int  (*compFun)(Real*, Real*),
-			  primStream* pStream)
-{
-  assert( inc_chain != NULL && dec_chain != NULL);
-  assert( ! (inc_current> inc_end &&
-	     dec_current> dec_end));
-  /*
-  Int inc_nVertices;
-  Int dec_nVertices;
-  */
-  Real** inc_array ;
-  Real** dec_array ;
-  Int i;
-  assert( ! ( (inc_chain==NULL) && (dec_chain==NULL)));
-
-  if(inc_current> inc_end) /*no more vertices on inc_chain*/
-    {
-
-      dec_array = dec_chain->getArray();
-      reflexChain rChain(20,0);
-      /*put the top vertex into the reflex chain*/
-      rChain.processNewVertex(topVertex, pStream);
-      /*process all the vertices on the dec_chain*/
-      for(i=dec_current; i<=dec_end; i++){
-	rChain.processNewVertex(dec_array[i], pStream);
-      }
-      /*process the bottom vertex*/
-      rChain.processNewVertex(botVertex, pStream);
-
-    }
-  else if(dec_current> dec_end) /*no more vertices on dec_chain*/
-    {
-      inc_array = inc_chain->getArray();
-      reflexChain rChain(20,1);
-      /*put the top vertex into the reflex chain*/
-      rChain.processNewVertex(topVertex, pStream);
-      /*process all the vertices on the inc_chain*/
-      for(i=inc_current; i<=inc_end; i++){
-	rChain.processNewVertex(inc_array[i], pStream);
-      }
-      /*process the bottom vertex*/
-      rChain.processNewVertex(botVertex, pStream);
-    }
-  else /*neither chain is empty*/
-    {
-      inc_array = inc_chain -> getArray();
-      dec_array = dec_chain -> getArray();
-
-      /*if top of inc_chain is 'lower' than top of dec_chain, process all the 
-       *vertices on the dec_chain which are higher than top of inc_chain
-       */
-      if(compFun(inc_array[inc_current], dec_array[dec_current]) <= 0)
-	{
-
-	  reflexChain rChain(20, 0);
-	  rChain.processNewVertex(topVertex, pStream);
-	  for(i=dec_current; i<=dec_end; i++)
-	    {
-	      if(compFun(inc_array[inc_current], dec_array[i]) <= 0)
-		rChain.processNewVertex(dec_array[i], pStream);
-	      else 
-		break;
-	    }
-	  rChain.outputFan(inc_array[inc_current], pStream);
-	  monoTriangulationRecFunGen(dec_array[i-1], botVertex, 
-			       inc_chain, inc_current, inc_end,
-			       dec_chain, i, dec_end,
-			       compFun,
-			       pStream);
-	}
-      else /*compFun(inc_array[inc_current], dec_array[dec_current]) > 0*/
-	{
-
-	  reflexChain rChain(20, 1);
-	  rChain.processNewVertex(topVertex, pStream);
-	  for(i=inc_current; i<=inc_end; i++)
-	    {
-	      if(compFun(inc_array[i], dec_array[dec_current]) >0)		
-		rChain.processNewVertex(inc_array[i], pStream);	      
-	      else
-		break;
-	    }
-	  rChain.outputFan(dec_array[dec_current], pStream);
-	  monoTriangulationRecFunGen(inc_array[i-1], botVertex, 
-			       inc_chain, i,inc_end,
-			       dec_chain, dec_current,dec_end,
-			       compFun,
-			       pStream);
-	}
-    }/*end case neither is empty*/
-}
-   
-/*if compFun == compV2InY, top to bottom: V-monotone
- *if compFun == compV2InX, right to left: U-monotone
- */
-void monoTriangulationRecFun(Real* topVertex, Real* botVertex, 
-			  vertexArray* inc_chain, Int inc_current,
-			  vertexArray* dec_chain, Int dec_current,
-			  Int  (*compFun)(Real*, Real*),
-			  primStream* pStream)
-{
-  assert( inc_chain != NULL && dec_chain != NULL);
-  assert( ! (inc_current>=inc_chain->getNumElements() &&
-	     dec_current>=dec_chain->getNumElements()));
-  Int inc_nVertices;
-  Int dec_nVertices;
-  Real** inc_array ;
-  Real** dec_array ;
-  Int i;
-  assert( ! ( (inc_chain==NULL) && (dec_chain==NULL)));
-
-  if(inc_current>=inc_chain->getNumElements()) /*no more vertices on inc_chain*/
-    {
-
-      dec_array = dec_chain->getArray();
-      dec_nVertices = dec_chain->getNumElements();      
-      reflexChain rChain(20,0);
-      /*put the top vertex into the reflex chain*/
-      rChain.processNewVertex(topVertex, pStream);
-      /*process all the vertices on the dec_chain*/
-      for(i=dec_current; i<dec_nVertices; i++){
-	rChain.processNewVertex(dec_array[i], pStream);
-      }
-      /*process the bottom vertex*/
-      rChain.processNewVertex(botVertex, pStream);
-
-    }
-  else if(dec_current>= dec_chain->getNumElements()) /*no more vertices on dec_chain*/
-    {
-      inc_array = inc_chain->getArray();
-      inc_nVertices= inc_chain->getNumElements();
-      reflexChain rChain(20,1);
-      /*put the top vertex into the reflex chain*/
-      rChain.processNewVertex(topVertex, pStream);
-      /*process all the vertices on the inc_chain*/
-      for(i=inc_current; i<inc_nVertices; i++){
-	rChain.processNewVertex(inc_array[i], pStream);
-      }
-      /*process the bottom vertex*/
-      rChain.processNewVertex(botVertex, pStream);
-    }
-  else /*neither chain is empty*/
-    {
-      inc_array = inc_chain -> getArray();
-      dec_array = dec_chain -> getArray();
-      inc_nVertices= inc_chain->getNumElements();
-      dec_nVertices= dec_chain->getNumElements();
-      /*if top of inc_chain is 'lower' than top of dec_chain, process all the 
-       *vertices on the dec_chain which are higher than top of inc_chain
-       */
-      if(compFun(inc_array[inc_current], dec_array[dec_current]) <= 0)
-	{
-
-	  reflexChain rChain(20, 0);
-	  rChain.processNewVertex(topVertex, pStream);
-	  for(i=dec_current; i<dec_nVertices; i++)
-	    {
-	      if(compFun(inc_array[inc_current], dec_array[i]) <= 0)
-		rChain.processNewVertex(dec_array[i], pStream);
-	      else 
-		break;
-	    }
-	  rChain.outputFan(inc_array[inc_current], pStream);
-	  monoTriangulationRecFun(dec_array[i-1], botVertex, 
-			       inc_chain, inc_current,
-			       dec_chain, i,
-			       compFun,
-			       pStream);
-	}
-      else /*compFun(inc_array[inc_current], dec_array[dec_current]) > 0*/
-	{
-
-	  reflexChain rChain(20, 1);
-	  rChain.processNewVertex(topVertex, pStream);
-	  for(i=inc_current; i<inc_nVertices; i++)
-	    {
-	      if(compFun(inc_array[i], dec_array[dec_current]) >0)		
-		rChain.processNewVertex(inc_array[i], pStream);	      
-	      else
-		break;
-	    }
-	  rChain.outputFan(dec_array[dec_current], pStream);
-	  monoTriangulationRecFun(inc_array[i-1], botVertex, 
-			       inc_chain, i,
-			       dec_chain, dec_current,
-			       compFun,
-			       pStream);
-	}
-    }/*end case neither is empty*/
-}
-
-
-void monoTriangulationRec(Real* topVertex, Real* botVertex, 
-			  vertexArray* inc_chain, Int inc_current,
-			  vertexArray* dec_chain, Int dec_current,
-			  primStream* pStream)
-{
-  assert( inc_chain != NULL && dec_chain != NULL);
-  assert( ! (inc_current>=inc_chain->getNumElements() &&
-	     dec_current>=dec_chain->getNumElements()));
-  Int inc_nVertices;
-  Int dec_nVertices;
-  Real** inc_array ;
-  Real** dec_array ;
-  Int i;
-  assert( ! ( (inc_chain==NULL) && (dec_chain==NULL)));
-
-  if(inc_current>=inc_chain->getNumElements()) /*no more vertices on inc_chain*/
-    {
-
-      dec_array = dec_chain->getArray();
-      dec_nVertices = dec_chain->getNumElements();      
-      reflexChain rChain(20,0);
-      /*put the top vertex into the reflex chain*/
-      rChain.processNewVertex(topVertex, pStream);
-      /*process all the vertices on the dec_chain*/
-      for(i=dec_current; i<dec_nVertices; i++){
-	rChain.processNewVertex(dec_array[i], pStream);
-      }
-      /*process the bottom vertex*/
-      rChain.processNewVertex(botVertex, pStream);
-
-    }
-  else if(dec_current>= dec_chain->getNumElements()) /*no more vertices on dec_chain*/
-    {
-      inc_array = inc_chain->getArray();
-      inc_nVertices= inc_chain->getNumElements();
-      reflexChain rChain(20,1);
-      /*put the top vertex into the reflex chain*/
-      rChain.processNewVertex(topVertex, pStream);
-      /*process all the vertices on the inc_chain*/
-      for(i=inc_current; i<inc_nVertices; i++){
-	rChain.processNewVertex(inc_array[i], pStream);
-      }
-      /*process the bottom vertex*/
-      rChain.processNewVertex(botVertex, pStream);
-    }
-  else /*neither chain is empty*/
-    {
-      inc_array = inc_chain -> getArray();
-      dec_array = dec_chain -> getArray();
-      inc_nVertices= inc_chain->getNumElements();
-      dec_nVertices= dec_chain->getNumElements();
-      /*if top of inc_chain is 'lower' than top of dec_chain, process all the 
-       *vertices on the dec_chain which are higher than top of inc_chain
-       */
-      if(compV2InY(inc_array[inc_current], dec_array[dec_current]) <= 0)
-	{
-
-	  reflexChain rChain(20, 0);
-	  rChain.processNewVertex(topVertex, pStream);
-	  for(i=dec_current; i<dec_nVertices; i++)
-	    {
-	      if(compV2InY(inc_array[inc_current], dec_array[i]) <= 0)
-		rChain.processNewVertex(dec_array[i], pStream);
-	      else 
-		break;
-	    }
-	  rChain.outputFan(inc_array[inc_current], pStream);
-	  monoTriangulationRec(dec_array[i-1], botVertex, 
-			       inc_chain, inc_current,
-			       dec_chain, i,
-			       pStream);
-	}
-      else /*compV2InY(inc_array[inc_current], dec_array[dec_current]) > 0*/
-	{
-
-	  reflexChain rChain(20, 1);
-	  rChain.processNewVertex(topVertex, pStream);
-	  for(i=inc_current; i<inc_nVertices; i++)
-	    {
-	      if(compV2InY(inc_array[i], dec_array[dec_current]) >0)		
-		rChain.processNewVertex(inc_array[i], pStream);	      
-	      else
-		break;
-	    }
-	  rChain.outputFan(dec_array[dec_current], pStream);
-	  monoTriangulationRec(inc_array[i-1], botVertex, 
-			       inc_chain, i,
-			       dec_chain, dec_current,
-			       pStream);
-	}
-    }/*end case neither is empty*/
-}
-    
-
-
-/* the name here assumes that the polygon is Y-monotone, but 
- *this function also works for X-monotone polygons.
- * a monotne polygon consists of two extrem verteices: topVertex and botVertex, and
- *two monotone chains: inc_chain, and dec_chain. The edges of the increasing chain (inc_chain)
- *is ordered by following pointer: next, while  the edges of the decreasing chain (dec_chain)
- *is ordered by following pointer: prev
- * inc_index index the vertex which is the toppest of the inc_chain which we are handling currently.
- * dec_index index the vertex which is the toppest of the dec_chain which we are handling currently.
- */
-void monoTriangulationRec(directedLine* inc_chain, Int inc_index, 
-			  directedLine* dec_chain, Int dec_index, 
-			  directedLine* topVertex, Int top_index,
-			  directedLine* botVertex,
-			  primStream* pStream)
-{
-  Int i;
-  directedLine *temp, *oldtemp = NULL;
-  Int tempIndex, oldtempIndex = 0;
-  
-  assert(inc_chain != NULL && dec_chain != NULL);
-  
-  if(inc_chain == botVertex) {
-    reflexChain rChain(20, 0);
-    rChain.processNewVertex(topVertex->getVertex(top_index), pStream);
-    for(i=dec_index; i< dec_chain->get_npoints(); i++){
-      rChain.processNewVertex(dec_chain->getVertex(i), pStream);
-    }
-    for(temp = dec_chain->getPrev(); temp != botVertex; temp = temp->getPrev())
-      {
-	for(i=0; i<temp->get_npoints(); i++){
-	  rChain.processNewVertex(temp->getVertex(i), pStream);
-	}
-      }
-  }
-  else if(dec_chain==botVertex) {
-    reflexChain rChain(20, 1);
-    rChain.processNewVertex(topVertex->getVertex(top_index), pStream);
-    for(i=inc_index; i< inc_chain->get_npoints(); i++){
-      rChain.processNewVertex(inc_chain->getVertex(i), pStream);
-    }
-    for(temp = inc_chain->getPrev(); temp != botVertex; temp = temp->getNext())
-      {
-	for(i=0; i<temp->get_npoints(); i++){
-	  rChain.processNewVertex(temp->getVertex(i), pStream);
-	}
-      }
-  }
-  else /*neither reached the bottom*/{
-    if(compV2InY(inc_chain->getVertex(inc_index), dec_chain->getVertex(dec_index)) <=0) {
-      reflexChain rChain(20, 0);
-      rChain.processNewVertex(topVertex -> getVertex(top_index), pStream);
-      temp = dec_chain;
-      tempIndex = dec_index;
-      while( compV2InY(inc_chain->getVertex(inc_index), temp->getVertex(tempIndex))<=0) {
-	oldtemp = temp;
-	oldtempIndex = tempIndex;
-	rChain.processNewVertex(temp->getVertex(tempIndex), pStream);
-	
-	if(tempIndex == temp->get_npoints()-1){
-	  tempIndex = 0;
-	  temp = temp->getPrev();
-	}
-	else{
-	  tempIndex++;
-	}
-      }
-      rChain.outputFan(inc_chain->getVertex(inc_index), pStream);
-      monoTriangulationRec(inc_chain, inc_index, temp, tempIndex, oldtemp, oldtempIndex, botVertex, pStream);
-    }
-    else /* >0*/ {
-      reflexChain rChain(20, 1);
-      rChain.processNewVertex(topVertex -> getVertex(top_index), pStream);
-      temp = inc_chain;
-      tempIndex = inc_index;
-      while( compV2InY(temp->getVertex(tempIndex), dec_chain->getVertex(dec_index))>0){
-	oldtemp = temp;
-	oldtempIndex = tempIndex;
-	rChain.processNewVertex(temp->getVertex(tempIndex), pStream);
-	
-	if(tempIndex == temp->get_npoints()-1){
-	  tempIndex = 0;
-	  temp = temp->getNext();
-	}
-	else{
-	  tempIndex++;
-	}
-      }
-      rChain.outputFan(dec_chain->getVertex(dec_index), pStream);
-      monoTriangulationRec(temp, tempIndex, dec_chain, dec_index, oldtemp, oldtempIndex, botVertex, pStream); 
-    }
-  } /*end case neither reached the bottom*/
-}
-
-/***************************vertexArray begin here**********************************/
-vertexArray::vertexArray(Real2* vertices, Int nVertices)
-{
-  Int i;
-  size = index = nVertices;
-  array = (Real**) malloc(sizeof(Real*) * nVertices);
-  assert(array);
-  for(i=0; i<nVertices; i++)
-    {
-      array[i] = vertices[i];
-      array[i] = vertices[i];
-    }
-}
-
-vertexArray::vertexArray(Int s)
-{
-  size = s;
-  array = (Real**) malloc(sizeof(Real*) * s);
-  assert(array);
-  index = 0;
-}
-
-vertexArray::~vertexArray()
-{
-  free(array);
-}
-
-void vertexArray::appendVertex(Real* ptr)
-{
-  Int i;
-  if(index >= size){
-    Real** temp = (Real**) malloc(sizeof(Real*) * (2*size +1));
-    assert(temp);
-    for(i=0; i<index; i++)
-      temp[i] = array[i];
-    free(array);
-    array = temp;
-    size = 2*size+1;
-  }
-  array[index++] = ptr;
-}
-
-void vertexArray::print()
-{
-  printf("vertex Array:index=%i, size=%i\n", index, size);
-  for(Int i=0; i<index; i++)
-    {
-      printf("(%f,%f) ", array[i][0], array[i][1]);
-    }
-  printf("\n");
-}
-
-/*find the first i such that array[i][1] >= v
- * and array[i+1][1] <v
- * if index == 0 (the array is empty, return -1.
- * if v is above all, return -1.
- * if v is below all, return index-1.
- */
-Int vertexArray::findIndexAbove(Real v)
-{
-  Int i;
-  if(index == 0) 
-    return -1;
-  else if(array[0][1] < v)
-    return -1;
-  else
-    {
-      for(i=1; i<index; i++)
-	{
-	  if(array[i][1] < v)
-	    break;
-	}
-      return i-1;
-    }
-}
-
-/*find the first i<=endIndex such that array[i][1] <= v
- * and array[i-1][1] > v
- *if sartIndex>endIndex, then return endIndex+1.
- *otherwise, startIndex<=endIndex, it is assumed that
- * 0<=startIndex<=endIndex<index.
- * if v is below all, return endIndex+1
- * if v is above all, return startIndex.
- */
-Int vertexArray::findIndexBelowGen(Real v, Int startIndex, Int endIndex)
-{
-  Int i;
-  if(startIndex > endIndex) 
-    return endIndex+1;
-  else if(array[endIndex][1] >  v)
-    return endIndex+1;
-  else //now array[endIndex][1] <= v
-    {
-      for(i=endIndex-1; i>=startIndex; i--)
-	{
-	  if(array[i][1] > v)
-	    break;
-	}
-      return i+1;
-    }
-}
-
-/*find the first i<=endIndex such that array[i-1][1] >= v
- * and array[i][1] < v
- *if sartIndex>endIndex, then return endIndex+1.
- *otherwise, startIndex<=endIndex, it is assumed that
- * 0<=startIndex<=endIndex<index.
- * if v is below or equal to all, return endIndex+1
- * if v is strictly above all, return startIndex.
- */
-Int vertexArray::findIndexStrictBelowGen(Real v, Int startIndex, Int endIndex)
-{
-  Int i;
-  if(startIndex > endIndex) 
-    return endIndex+1;
-  else if(array[endIndex][1] >=  v)
-    return endIndex+1;
-  else //now array[endIndex][1] < v
-    {
-      for(i=endIndex-1; i>=startIndex; i--)
-	{
-	  if(array[i][1] >= v)
-	    break;
-	}
-      return i+1;
-    }
-}
-
-/*find the first i>startIndex such that array[i-1][1] > v
- * and array[i][1] >=v
- *if sartIndex>endIndex, then return startIndex-1.
- *otherwise, startIndex<=endIndex, it is assumed that
- * 0<=startIndex<=endIndex<index.
- * if v is strictly above all, return startIndex-1
- * if v is strictly below all, return endIndex.
- */
-Int vertexArray::findIndexFirstAboveEqualGen(Real v, Int startIndex, Int endIndex)
-{
-
-  Int i;
-  if(startIndex > endIndex) 
-    return startIndex-1;
-  else if(array[startIndex][1] < v)
-    return startIndex-1;
-  else //now array[startIndex][1] >= v
-    {
-
-      for(i=startIndex; i<=endIndex; i++)
-	{
-	  if(array[i][1] <= v)
-	    break;
-	}
-      if(i>endIndex) // v is strictly below all
-	return endIndex;
-      else if(array[i][1] == v)
-	return i;
-      else
-	return i-1;
-    }
-
-}
-
-
-/*find the first i>=startIndex such that array[i][1] >= v
- * and array[i+1][1] <v
- *if sartIndex>endIndex, then return startIndex-1.
- *otherwise, startIndex<=endIndex, it is assumed that
- * 0<=startIndex<=endIndex<index.
- * if v is above all, return startIndex-1
- * if v is below all, return endIndex.
- */
-Int vertexArray::findIndexAboveGen(Real v, Int startIndex, Int endIndex)
-{
-  Int i;
-  if(startIndex > endIndex) 
-    return startIndex-1;
-  else if(array[startIndex][1] < v)
-    return startIndex-1;
-  else //now array[startIndex][1] >= v
-    {
-      for(i=startIndex+1; i<=endIndex; i++)
-	{
-	  if(array[i][1] < v)
-	    break;
-	}
-      return i-1;
-    }
-}
-
-Int vertexArray::findDecreaseChainFromEnd(Int begin, Int end)
-{
-  Int i = end;
-  Real prevU = array[i][0];
-  Real thisU;
-  for(i=end-1; i>=begin; i--){
-    thisU = array[i][0];
-    if(thisU < prevU)
-      prevU = thisU;
-    else
-      break;
-  }
-  return i;
-}
-
-//if(V(start) == v, return start, other wise return the
-//last i so that V(i)==v
-Int vertexArray::skipEqualityFromStart(Real v, Int start, Int end)
-{
-  Int i;
-  if(array[start][1] != v)
-    return start;
-  //now array[start][1] == v
-  for(i=start+1; i<= end; i++)
-    if(array[i][1] != v) 
-      break;
-  return i-1;
-}
-  
-
-/***************************vertexArray end****************************************/
-
-
-
-/***************************relfex chain stuff begin here*****************************/
-
-reflexChain::reflexChain(Int size, Int is_increasing)
-{
-  queue = (Real2*) malloc(sizeof(Real2) * size);
-  assert(queue);
-  index_queue = 0;
-  size_queue = size;
-  isIncreasing = is_increasing;
-}
-
-reflexChain::~reflexChain()
-{
-  free(queue);
-}
-
-/*put (u,v) at the end of the queue
- *pay attention to space
- */
-void reflexChain::insert(Real u, Real v)
-{
-  Int i;
-  if(index_queue >= size_queue) {
-    Real2 *temp = (Real2*) malloc(sizeof(Real2) * (2*size_queue+1));
-    assert(temp);
-
-    /*copy*/
-    for(i=0; i<index_queue; i++){
-      temp[i][0] = queue[i][0];
-      temp[i][1] = queue[i][1];
-    }
-    
-    free(queue);
-    queue = temp;
-    size_queue = 2*size_queue + 1;
-  }
-
-  queue[index_queue][0] = u;
-  queue[index_queue][1] = v;
-  index_queue ++;
-}
-
-void reflexChain::insert(Real v[2])
-{
-  insert(v[0], v[1]);
-}
-
-/*
-static Real area(Real A[2], Real B[2], Real C[2])
-{
-  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];
-  return Bx*Cy - Cx*By;
-}
-*/
-
-/*the chain is reflex, and the vertex v is
- *on the other side of the chain, so that
- *we can outout the fan with v as the
- *the center
- */
-void reflexChain::outputFan(Real v[2], primStream* pStream)
-{
-  Int i;
-  pStream->begin();
-  pStream->insert(v);
-  if(isIncreasing) {
-    for(i=0; i<index_queue; i++)
-      pStream->insert(queue[i]);
-  }
-  else {
-    for(i=index_queue-1; i>=0; i--)
-      pStream->insert(queue[i]);    
-  }
-  pStream->end(PRIMITIVE_STREAM_FAN);
-}
-
-void reflexChain::processNewVertex(Real v[2], primStream* pStream)
-{
-  Int i,j,k;
-  Int isReflex;
-  /*if there are at most one vertex in the queue, then simply insert
-   */
-  if(index_queue <=1){
-    insert(v);
-    return;
-  }
-  
-  /*there are at least two vertices in the queue*/
-  j=index_queue-1;
-  
-  for(i=j; i>=1; i--) {
-    if(isIncreasing) {
-      isReflex = (area(queue[i-1], queue[i], v) <= 0.0);
-    }
-    else /*decreasing*/{
-      isReflex = (area(v, queue[i], queue[i-1]) <= 0.0);	  
-    }
-    if(isReflex) {
-      break;
-    }
-  }
-
-  /*
-   *if i<j then vertices: i+1--j are convex
-   * output triangle fan: 
-   *  v, and queue[i], i+1, ..., j
-   */
-  if(i<j) 
-    {
-      pStream->begin();
-      pStream->insert(v);
-      if(isIncreasing) {
-	for(k=i; k<=j; k++)
-	  pStream->insert(queue[k]);
-      }
-      else {
-	for(k=j; k>=i; k--)
-	  pStream->insert(queue[k]);
-      }
-      
-      pStream->end(PRIMITIVE_STREAM_FAN);
-    }
-
-  /*delete vertices i+1--j from the queue*/
-  index_queue = i+1;
-  /*finally insert v at the end of the queue*/
-  insert(v);
-
-}
-
-void reflexChain::print()
-{
-  Int i;
-  printf("reflex chain: isIncreasing=%i\n", isIncreasing);
-  for(i=0; i<index_queue; i++) {
-    printf("(%f,%f) ", queue[i][0], queue[i][1]);
-  }
-  printf("\n");
-}