svn merge ^/branches/released . --username marha

43 files changed, 14010 insertions, 0 deletions

diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/definitions.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/definitions.h
new file mode 100644
index 000000000..962921da1
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/definitions.h
@@ -0,0 +1,40 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _DEFINITIONS_H
+#define _DEFINITIONS_H
+
+typedef float Real;
+typedef int   Int;
+typedef Real Real2[2];
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/directedLine.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/directedLine.cc
new file mode 100644
index 000000000..74450352d
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/directedLine.cc
@@ -0,0 +1,848 @@
+/*
+** 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 <math.h>
+#include "glimports.h"
+#include "zlassert.h"
+
+#include "quicksort.h"
+#include "directedLine.h"
+#include "polyDBG.h"
+
+#ifdef __WATCOMC__
+#pragma warning 726 10
+#endif
+
+//we must return the newLine
+directedLine* directedLine::deleteChain(directedLine* begin, directedLine* end)
+{
+  if(begin->head()[0] ==  end->tail()[0] &&
+     begin->head()[1] ==  end->tail()[1]
+     )
+    {
+      directedLine *ret = begin->prev;
+      begin->prev->next = end->next;
+      end->next->prev = begin->prev;
+      delete begin->sline;
+      delete end->sline;
+      delete begin;
+      delete end;
+
+      return ret;
+    }
+
+  directedLine* newLine;
+  sampledLine* sline = new sampledLine(begin->head(), end->tail());
+  newLine =  new directedLine(INCREASING, sline);
+  directedLine *p = begin->prev;
+  directedLine *n = end->next;
+  p->next = newLine;
+  n->prev = newLine;
+  newLine->prev = p;
+  newLine->next = n;
+
+  delete begin->sline;
+  delete end->sline;
+  delete begin;
+  delete end;
+  return newLine;
+}
+
+
+void directedLine::deleteSingleLine(directedLine* dline)
+{
+  //make sure that dline->prev->tail is the same as
+  //dline->next->head. This is for numerical erros.
+  //for example, if we delete a line which is almost degeneate
+  //within (epsilon), then we want to make that the polygon after deletion
+  //is still a valid polygon
+
+  dline->next->head()[0] =  dline->prev->tail()[0];
+  dline->next->head()[1] =  dline->prev->tail()[1];
+
+  dline->prev->next = dline->next;
+  dline->next->prev = dline->prev;
+
+  delete dline;
+
+}
+
+static Int myequal(Real a[2], Real b[2])
+{
+  /*
+  if(a[0]==b[0] && a[1] == b[1])
+    return 1;
+  else
+    return 0;
+    */
+
+
+  if(fabs(a[0]-b[0]) < 0.00001 &&
+     fabs(a[1]-b[1]) < 0.00001)
+    return 1;
+  else
+    return 0;
+
+}
+
+directedLine* directedLine::deleteDegenerateLines()
+{
+  //if there is only one edge or two edges, don't do anything
+  if(this->next == this)
+    return this;
+  if(this->next == this->prev)
+    return this;
+
+  //find a nondegenerate line
+  directedLine* temp;
+  directedLine* first = NULL;
+  if(! myequal(head(), tail()))
+    /*
+  if(head()[0] != tail()[0] ||
+  head()[1] != tail()[1])
+  */
+    first = this;
+  else
+    {
+      for(temp = this->next; temp != this; temp = temp->next)
+	{
+	  /*
+	  if(temp->head()[0] != temp->tail()[0] ||
+	     temp->head()[1] != temp->tail()[1])
+	     */
+	  if(! myequal(temp->head(), temp->tail()))
+	    {
+	      first = temp;
+	      break;
+	    }
+        
+	}
+    }
+
+  //if there are no non-degenerate lines, then we simply return NULL.
+  if(first == NULL)
+    {
+      deleteSinglePolygonWithSline();
+      return NULL;
+    }
+
+  directedLine* tempNext = NULL;
+  for(temp =first->next; temp != first; temp = tempNext)
+    {
+      tempNext = temp->getNext();
+/*
+      if(temp->head()[0] == temp->tail()[0] &&
+	 temp->head()[1] == temp->tail()[1])
+*/      
+
+      if(myequal(temp->head(), temp->tail()))
+	deleteSingleLine(temp);
+    }   
+  return first;
+}
+
+directedLine* directedLine::deleteDegenerateLinesAllPolygons()
+{
+  directedLine* temp;
+  directedLine *tempNext = NULL;
+  directedLine* ret= NULL;
+  directedLine* retEnd = NULL;
+  for(temp=this; temp != NULL; temp = tempNext)
+    {
+      tempNext = temp->nextPolygon;
+      temp->nextPolygon = NULL;
+      if(ret == NULL)
+	{
+	  ret = retEnd = temp->deleteDegenerateLines();
+        
+	}
+      else
+	{
+	  directedLine *newPolygon = temp->deleteDegenerateLines();
+	  if(newPolygon != NULL)
+	    {
+	  retEnd->nextPolygon = temp->deleteDegenerateLines();
+	  retEnd = retEnd->nextPolygon;
+	}
+    }
+    }
+  return ret;
+}
+
+directedLine* directedLine::cutIntersectionAllPoly(int &cutOccur)
+{
+  directedLine* temp;
+  directedLine *tempNext = NULL;
+  directedLine* ret= NULL;
+  directedLine* retEnd = NULL;
+  cutOccur = 0;
+  for(temp=this; temp != NULL; temp = tempNext)
+    {
+      int eachCutOccur=0;
+      tempNext = temp->nextPolygon;
+      temp->nextPolygon = NULL;
+      if(ret == NULL)
+	{
+
+	  ret = retEnd = DBG_cutIntersectionPoly(temp, eachCutOccur);
+	  if(eachCutOccur)
+	    cutOccur = 1;
+	}
+      else
+	{
+
+	  retEnd->nextPolygon = DBG_cutIntersectionPoly(temp, eachCutOccur);
+	  retEnd = retEnd->nextPolygon;
+	  if(eachCutOccur)
+	    cutOccur = 1;
+	}
+    }
+  return ret;
+}
+
+
+void directedLine::deleteSinglePolygonWithSline()
+{
+  directedLine *temp, *tempNext;
+  prev->next = NULL;
+  for(temp=this; temp != NULL; temp = tempNext)
+    {
+      tempNext = temp->next;
+      delete temp->sline;
+      delete temp;
+    }
+}
+
+void directedLine::deletePolygonListWithSline()
+{
+  directedLine *temp, *tempNext;
+  for(temp=this; temp != NULL; temp=tempNext)
+    {
+      tempNext = temp->nextPolygon;
+      temp->deleteSinglePolygonWithSline();
+    }
+}
+
+void directedLine::deleteSinglePolygon()
+{
+  directedLine *temp, *tempNext;
+  prev->next = NULL;
+  for(temp=this; temp != NULL; temp = tempNext)
+    {
+      tempNext = temp->next;
+      delete temp;
+    }
+}
+
+void directedLine::deletePolygonList()
+{
+  directedLine *temp, *tempNext;
+  for(temp=this; temp != NULL; temp=tempNext)
+    {
+      tempNext = temp->nextPolygon;
+      temp->deleteSinglePolygon();
+    }
+}
+
+
+/*a loop by itself*/
+directedLine::directedLine(short dir, sampledLine* sl)
+{
+  direction = dir;
+  sline = sl;
+  next = this;
+  prev = this;
+  nextPolygon = NULL;
+//  prevPolygon = NULL;
+  rootBit = 0;/*important to initilzae to 0 meaning not root yet*/
+
+  rootLink = NULL;
+
+}
+
+void directedLine::init(short dir, sampledLine* sl)
+{
+  direction = dir;
+  sline = sl;
+}
+
+directedLine::directedLine()
+{
+  next = this;
+  prev = this;
+  nextPolygon = NULL;
+  rootBit = 0;/*important to initilzae to 0 meaning not root yet*/
+  rootLink = NULL;
+}
+
+directedLine::~directedLine()
+{
+}
+
+Real* directedLine::head()
+{
+
+  return (direction==INCREASING)? (sline->get_points())[0] : (sline->get_points())[sline->get_npoints()-1];
+}
+
+/*inline*/ Real* directedLine::getVertex(Int i)
+{
+  return (direction==INCREASING)? (sline->get_points())[i] : (sline->get_points())[sline->get_npoints() - 1 -i];
+}
+
+Real* directedLine::tail()
+{
+  return (direction==DECREASING)? (sline->get_points())[0] : (sline->get_points())[sline->get_npoints()-1];
+}
+
+ /*insert a new line between prev and this*/
+void directedLine::insert(directedLine* nl)
+{
+  nl->next = this;
+  nl->prev = prev;
+  prev->next = nl;
+  prev = nl;
+  nl->rootLink = this; /*assuming that 'this' is the root!!!*/
+}
+
+Int directedLine::numEdges()
+{
+  Int ret=0;
+  directedLine* temp;
+  if(next == this) return 1;
+
+  ret = 1;
+  for(temp = next; temp != this; temp = temp->next)
+    ret++;
+  return ret;
+}
+
+Int directedLine::numEdgesAllPolygons()
+{
+  Int ret=0;
+  directedLine* temp;
+  for(temp=this; temp!= NULL; temp=temp->nextPolygon)
+    {
+      ret += temp->numEdges();
+    }
+  return ret;
+}
+
+/*return 1 if the double linked list forms a polygon.
+ */
+short directedLine::isPolygon()
+{
+  directedLine* temp;
+
+  /*a polygon contains at least 3 edges*/
+  if(numEdges() <=2) return 0;
+
+  /*check this edge*/
+  if(! isConnected()) return 0;
+
+  /*check all other edges*/
+  for(temp=next; temp != this; temp = temp->next){
+    if(!isConnected()) return 0;
+  }
+  return 1;
+}
+
+/*check if the head of this edge is connected to
+ *the tail of the prev
+ */
+short directedLine::isConnected()
+{
+  if( (head()[0] == prev->tail()[0]) && (head()[1] == prev->tail()[1]))
+    return 1;
+  else
+    return 0;
+}
+
+Int compV2InY(Real A[2], Real B[2])
+{
+  if(A[1] < B[1]) return -1;
+  if(A[1] == B[1] && A[0] < B[0]) return -1;
+  if(A[1] == B[1] && A[0] == B[0]) return 0;
+  return 1;
+}
+
+Int compV2InX(Real A[2], Real B[2])
+{
+  if(A[0] < B[0]) return -1;
+  if(A[0] == B[0] && A[1] < B[1]) return -1;
+  if(A[0] == B[0] && A[1] == B[1]) return 0;
+  return 1;
+}
+
+/*compare two vertices NOT lines!
+ *A vertex is the head of a directed line.
+ *(x_1, y_1) <= (x_2, y_2) if
+ *either y_1 < y_2
+ *or	 y_1 == y_2 && x_1 < x_2.
+ *return -1 if this->head() <= nl->head(),
+ *return  1 otherwise
+ */
+Int directedLine::compInY(directedLine* nl)
+{
+  if(head()[1] < nl->head()[1]) return -1;
+  if(head()[1] == nl->head()[1] && head()[0] < nl->head()[0]) return -1;
+  return 1;
+}
+
+/*compare two vertices NOT lines!
+ *A vertex is the head of a directed line.
+ *(x_1, y_1) <= (x_2, y_2) if
+ *either x_1 < x_2
+ *or	 x_1 == x_2 && y_1 < y_2.
+ *return -1 if this->head() <= nl->head(),
+ *return  1 otherwise
+ */
+Int directedLine::compInX(directedLine* nl)
+{
+  if(head()[0] < nl->head()[0]) return -1;
+  if(head()[0] == nl->head()[0] && head()[1] < nl->head()[1]) return -1;
+  return 1;
+}
+
+/*used by sort precedures
+ */
+static Int compInY2(directedLine* v1, directedLine* v2)
+{
+  return v1->compInY(v2);
+}
+#ifdef NOT_USED
+static Int compInX(directedLine* v1, directedLine* v2)
+{
+  return v1->compInX(v2);
+}
+#endif
+
+/*sort all the vertices NOT the lines!
+ *a vertex is the head of a directed line
+ */
+directedLine** directedLine::sortAllPolygons()
+{
+  Int total_num_edges = 0;
+  directedLine** array = toArrayAllPolygons(total_num_edges);
+  quicksort( (void**)array, 0, total_num_edges-1, (Int (*)(void *, void *)) compInY2);
+
+  return array;
+}
+
+void directedLine::printSingle()
+{
+  if(direction == INCREASING)
+    printf("direction is INCREASING\n");
+  else
+    printf("direction is DECREASING\n");
+  printf("head=%f,%f)\n", head()[0], head()[1]);
+  sline->print();
+}
+
+/*print one polygon*/
+void directedLine::printList()
+{
+  directedLine* temp;
+  printSingle();
+  for(temp = next; temp!=this; temp=temp->next)
+    temp->printSingle();
+}
+
+/*print all the polygons*/
+void directedLine::printAllPolygons()
+{
+  directedLine *temp;
+  for(temp = this; temp!=NULL; temp = temp->nextPolygon)
+    {
+      printf("polygon:\n");
+      temp->printList();
+    }
+}
+
+/*insert this polygon into the head of the old polygon List*/
+directedLine* directedLine::insertPolygon(directedLine* oldList)
+{
+  /*this polygon is a root*/
+  setRootBit();
+  if(oldList == NULL) return this;
+  nextPolygon = oldList;
+/*  oldList->prevPolygon = this;*/
+  return this;
+}
+
+/*cutoff means delete. but we don't deallocate any space,
+ *so we use cutoff instead of delete
+ */
+directedLine* directedLine::cutoffPolygon(directedLine *p)
+{
+  directedLine* temp;
+  directedLine* prev_polygon  = NULL;
+  if(p == NULL) return this;
+
+  for(temp=this; temp != p; temp = temp->nextPolygon)
+    {
+      if(temp == NULL)
+	{
+	  fprintf(stderr, "in cutoffPolygon, not found\n");
+	  exit(1);
+	}
+      prev_polygon = temp;
+    }
+
+/*  prev_polygon = p->prevPolygon;*/
+
+  p->resetRootBit();
+  if(prev_polygon == NULL) /*this is the one to cutoff*/
+    return nextPolygon;
+  else {
+    prev_polygon->nextPolygon = p->nextPolygon;
+    return this;
+  }
+}
+
+Int directedLine::numPolygons()
+{
+  if(nextPolygon == NULL) return 1;
+  else return 1+nextPolygon->numPolygons();
+}
+
+
+/*let  array[index ...] denote
+ *all the edges in this polygon
+ *return the next available index of array.
+ */
+Int directedLine::toArraySinglePolygon(directedLine** array, Int index)
+{
+  directedLine *temp;
+  array[index++] = this;
+  for(temp = next; temp != this; temp = temp->next)
+    {
+      array[index++] = temp;
+    }
+  return index;
+}
+
+/*the space is allocated. The caller is responsible for
+ *deallocate the space.
+ *total_num_edges is set to be the total number of edges of all polygons
+ */
+directedLine** directedLine::toArrayAllPolygons(Int& total_num_edges)
+{
+  total_num_edges=numEdgesAllPolygons();
+  directedLine** ret = (directedLine**) malloc(sizeof(directedLine*) * total_num_edges);
+  assert(ret);
+
+  directedLine *temp;
+  Int index = 0;
+  for(temp=this; temp != NULL; temp=temp->nextPolygon) {
+    index = temp->toArraySinglePolygon(ret, index);
+  }
+  return ret;
+}
+
+/*assume the polygon is a simple polygon, return
+ *the area enclosed by it.
+ *if thee order is counterclock wise, the area is positive.
+ */
+Real directedLine::polyArea()
+{
+  directedLine* temp;
+  Real ret=0.0;
+  Real x1,y1,x2,y2;
+  x1 = this->head()[0];
+  y1 = this->head()[1];
+  x2 = this->next->head()[0];
+  y2 = this->next->head()[1];
+  ret = -(x2*y1-x1*y2);
+  for(temp=this->next; temp!=this; temp = temp->next)
+    {
+      x1 = temp->head()[0];
+      y1 = temp->head()[1];
+      x2 = temp->next->head()[0];
+      y2 = temp->next->head()[1];
+      ret += -( x2*y1-x1*y2);
+    }
+  return Real(0.5)*ret;
+}
+
+/*******************split or combine polygons begin********************/
+/*conect a diagonal of a single simple polygon or  two simple polygons.
+ *If the two vertices v1 (head) and v2 (head) are in the same simple polygon,
+ *then we actually split the simple polygon into two polygons.
+ *If instead two vertices velong to two difference polygons,
+ *then we combine the  two polygons into one polygon.
+ *It is upto the caller to decide whether this is a split or a
+ *combination.
+ *
+ *Case Split:
+ *split a single simple polygon into two simple polygons by
+ *connecting a diagonal (two vertices).
+ *v1, v2: the two vertices are the head() of the two directedLines.
+ *  this routine generates one new sampledLine which is returned in
+ *generatedLine,
+ *and it generates two directedLines returned in ret_p1 and ret_p2.
+ *ret_p1 and ret_p2 are used as the entry to the two new polygons.
+ *Notice the caller should not deallocate the space of v2 and v2 after
+ *calling this function, since all of the edges are connected to
+ *ret_p1 or ret_p2.
+ *
+ *combine:
+ *combine two simpolygons into one by connecting one diagonal.
+ *the returned polygon is returned in ret_p1.
+ */
+/*ARGSUSED*/
+void directedLine::connectDiagonal(directedLine* v1, directedLine* v2,
+			   directedLine** ret_p1,
+			   directedLine** ret_p2,
+			   sampledLine** generatedLine,
+			   directedLine* polygonList								   )
+{
+  sampledLine *nsline  = new sampledLine(2);
+
+
+
+  nsline->setPoint(0, v1->head());
+  nsline->setPoint(1, v2->head());
+
+
+
+  /*the increasing line is from v1 head to v2 head*/
+  directedLine* newLineInc = new directedLine(INCREASING, nsline);
+
+
+
+  directedLine* newLineDec = new directedLine(DECREASING, nsline);
+
+
+  directedLine* v1Prev = v1->prev;
+  directedLine* v2Prev = v2->prev;
+
+  v1	    ->prev = newLineDec;
+  v2Prev    ->next = newLineDec;
+  newLineDec->next = v1;
+  newLineDec->prev = v2Prev;
+
+  v2	    ->prev = newLineInc;
+  v1Prev    ->next = newLineInc;
+  newLineInc->next = v2;
+  newLineInc->prev = v1Prev;
+
+  *ret_p1 = newLineDec;
+  *ret_p2 = newLineInc;
+  *generatedLine = nsline;
+}
+
+//see the function connectDiangle
+/*ARGSUSED*/
+void directedLine::connectDiagonal_2slines(directedLine* v1, directedLine* v2,
+			   directedLine** ret_p1,
+			   directedLine** ret_p2,
+			   directedLine* polygonList								   )
+{
+  sampledLine *nsline  = new sampledLine(2);
+  sampledLine *nsline2	= new sampledLine(2);
+
+  nsline->setPoint(0, v1->head());
+  nsline->setPoint(1, v2->head());
+  nsline2->setPoint(0, v1->head());
+  nsline2->setPoint(1, v2->head());
+
+  /*the increasing line is from v1 head to v2 head*/
+  directedLine* newLineInc = new directedLine(INCREASING, nsline);
+
+  directedLine* newLineDec = new directedLine(DECREASING, nsline2);
+
+  directedLine* v1Prev = v1->prev;
+  directedLine* v2Prev = v2->prev;
+
+  v1	    ->prev = newLineDec;
+  v2Prev    ->next = newLineDec;
+  newLineDec->next = v1;
+  newLineDec->prev = v2Prev;
+
+  v2	    ->prev = newLineInc;
+  v1Prev    ->next = newLineInc;
+  newLineInc->next = v2;
+  newLineInc->prev = v1Prev;
+
+  *ret_p1 = newLineDec;
+  *ret_p2 = newLineInc;
+
+}
+
+Int directedLine::samePolygon(directedLine* v1, directedLine* v2)
+{
+  if(v1 == v2) return 1;
+  directedLine *temp;
+  for(temp = v1->next; temp != v1; temp = temp->next)
+    {
+      if(temp == v2) return 1;
+    }
+  return 0;
+}
+
+directedLine* directedLine::findRoot()
+{
+  if(rootBit) return this;
+  directedLine* temp;
+  for(temp = next; temp != this; temp = temp->next)
+    if(temp -> rootBit ) return temp;
+  return NULL; /*should not happen*/
+}
+
+directedLine* directedLine::rootLinkFindRoot()
+{
+  directedLine* tempRoot;
+  directedLine* tempLink;
+  tempRoot = this;
+  tempLink = rootLink;
+  while(tempLink != NULL){
+    tempRoot = tempLink;
+    tempLink = tempRoot->rootLink;
+  }
+  return tempRoot;
+}
+
+/*******************split or combine polygons end********************/
+
+/*****************IO stuff begin*******************/
+
+/*format:
+ *#polygons
+ * #vertices
+ *  vertices
+ * #vertices
+ *  vertices
+ *...
+ */
+void directedLine::writeAllPolygons(char* filename)
+{
+  FILE* fp = fopen(filename, "w");
+  assert(fp);
+  Int nPolygons = numPolygons();
+  directedLine *root;
+  fprintf(fp, "%i\n", nPolygons);
+  for(root = this; root != NULL; root = root->nextPolygon)
+    {
+      directedLine *temp;
+      Int npoints=0;
+      npoints = root->get_npoints()-1;
+      for(temp = root->next; temp != root; temp=temp->next)
+	npoints += temp->get_npoints()-1;
+      fprintf(fp, "%i\n", npoints/*root->numEdges()*/);
+
+
+      for(Int i=0; i<root->get_npoints()-1; i++){
+	fprintf(fp, "%f ", root->getVertex(i)[0]);
+	fprintf(fp, "%f ", root->getVertex(i)[1]);
+      }
+
+      for(temp=root->next; temp != root; temp = temp->next)
+	{
+	  for(Int i=0; i<temp->get_npoints()-1; i++){
+
+	    fprintf(fp, "%f ", temp->getVertex(i)[0]);
+	    fprintf(fp, "%f ", temp->getVertex(i)[1]);
+	  }
+	  fprintf(fp,"\n");
+	}
+      fprintf(fp, "\n");
+    }
+  fclose(fp);
+}
+
+directedLine* readAllPolygons(char* filename)
+{
+  Int i,j;
+  FILE* fp = fopen(filename, "r");
+  assert(fp);
+  Int nPolygons;
+  fscanf(fp, "%i", &nPolygons);
+  directedLine *ret = NULL;
+
+  for(i=0; i<nPolygons; i++)
+    {
+      Int nEdges;
+      fscanf(fp, "%i", &nEdges);
+      Real vert[2][2];
+      Real VV[2][2];
+      /*the first two vertices*/
+      fscanf(fp, "%f", &(vert[0][0]));
+      fscanf(fp, "%f", &(vert[0][1]));
+      fscanf(fp, "%f", &(vert[1][0]));
+      fscanf(fp, "%f", &(vert[1][1]));
+      VV[1][0] = vert[0][0];
+      VV[1][1] = vert[0][1];
+      sampledLine *sLine = new sampledLine(2, vert);
+      directedLine *thisPoly = new directedLine(INCREASING, sLine);
+thisPoly->rootLinkSet(NULL);
+
+      directedLine *dLine;
+      for(j=2; j<nEdges; j++)
+	{
+	  vert[0][0]=vert[1][0];
+	  vert[0][1]=vert[1][1];
+	  fscanf(fp, "%f", &(vert[1][0]));
+	  fscanf(fp, "%f", &(vert[1][1]));
+	  sLine = new sampledLine(2,vert);
+	  dLine = new directedLine(INCREASING, sLine);
+dLine->rootLinkSet(thisPoly);
+	  thisPoly->insert(dLine);
+	}
+
+      VV[0][0]=vert[1][0];
+      VV[0][1]=vert[1][1];
+      sLine = new sampledLine(2,VV);
+      dLine = new directedLine(INCREASING, sLine);
+dLine->rootLinkSet(thisPoly);
+      thisPoly->insert(dLine);
+
+      ret = thisPoly->insertPolygon(ret);
+    }
+  fclose(fp);
+  return ret;
+}
+
+
+
+
+
+
+
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/directedLine.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/directedLine.h
new file mode 100644
index 000000000..4ed0128ca
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/directedLine.h
@@ -0,0 +1,171 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _DIRECTEDLINE_H
+#define _DIRECTEDLINE_H
+
+#include "definitions.h"
+#include "sampledLine.h"
+
+enum {INCREASING, DECREASING};
+
+class directedLine {
+  short direction; /*INCREASING or DECREASING*/
+  sampledLine* sline;
+  directedLine* next; /*double linked list*/
+  directedLine* prev; /*double linked list*/
+
+  /*in case we need a list of polygons each 
+   *consisting of a double linked list
+   */
+  directedLine* nextPolygon; 
+
+  /*optimization make cutoff polygon faster*/
+/*  directedLine* prevPolygon;*/
+
+  Int rootBit; /*1 if this is a root of the polygon, set by setRootBit*/
+               /*and reset by resetRootBit()*/
+
+  directedLine* rootLink; /*fast root-finding*/
+
+
+
+public:
+  directedLine(short dir, sampledLine* sl);
+  directedLine();
+  ~directedLine();
+
+  void init(short dir, sampledLine* sl);
+  
+  Real* head(); /*points[0] if INCREASING, points[n-1] otherwise*/
+  Real* tail(); /*points[n-1] if INCREASING, points[0] otherwise*/
+  Real* getVertex(Int i); /*points[i] if INCREASING, points[n-1-i] otherwise*/
+  Int get_npoints() {return sline->get_npoints();}
+  directedLine* getPrev() {return prev;}
+  directedLine* getNext() {return next;}
+  directedLine* getNextPolygon()  {return nextPolygon;}
+  sampledLine*  getSampledLine()  {return sline;}
+
+  short getDirection(){return direction;}
+  void putDirection(short dir) {direction = dir;}
+  void putPrev(directedLine *p) {prev = p;}
+  void putNext(directedLine *p) {next = p;}
+
+  /*insert a new line between prev and this*/
+  void insert(directedLine* nl);
+
+  /*delete all the polygons following the link: nextPolygon.
+   *notice that sampledLine is not deleted. The caller is
+   *responsible for that
+   */
+  void  deletePolygonList();
+  void  deleteSinglePolygon();
+
+  void  deleteSinglePolygonWithSline(); //also delete sanmpled line
+  void  deletePolygonListWithSline(); //also delete sanmpled line
+
+  void deleteSingleLine(directedLine* dline);
+  directedLine* deleteDegenerateLines();
+  directedLine* deleteDegenerateLinesAllPolygons();
+  directedLine* cutIntersectionAllPoly(int& cutOccur);
+
+  /*check to see if the list forms a closed polygon
+   *return 1 if yes
+   */
+  short isPolygon(); 
+  
+  Int compInY(directedLine* nl);
+  Int compInX(directedLine* nl);
+
+  /*return an array of pointers.
+   *the 
+   */
+  directedLine** sortAllPolygons();
+
+  Int numEdges();
+  Int numEdgesAllPolygons();
+  Int numPolygons();
+
+  /*check if the head of this edge is connected to 
+   *the tail of the prev
+   */
+  short isConnected();
+
+  Real polyArea();
+
+  void printSingle();
+  void printList();
+  void printAllPolygons();
+  void writeAllPolygons(char* filename);
+  
+
+  /*insert a polygon: using nextPolygon*/
+  directedLine* insertPolygon(directedLine* newpolygon);
+  directedLine* cutoffPolygon(directedLine *p);
+
+  Int toArraySinglePolygon(directedLine** array, Int index);
+  directedLine** toArrayAllPolygons(Int& total_num_edges);
+
+  void connectDiagonal(directedLine* v1, directedLine* v2, 
+			   directedLine** ret_p1, 
+			   directedLine** ret_p2,
+			   sampledLine** generatedLine, directedLine* list);
+
+  /*generate two slines
+   */
+  void connectDiagonal_2slines(directedLine* v1, directedLine* v2, 
+			   directedLine** ret_p1, 
+			   directedLine** ret_p2,
+			   directedLine* list);
+
+  Int samePolygon(directedLine* v1, directedLine* v2);
+  void setRootBit() {rootBit = 1;}
+  void resetRootBit() {rootBit = 0;}
+  directedLine* findRoot();
+
+  void rootLinkSet(directedLine* r) {rootLink = r;}
+  directedLine* rootLinkFindRoot();
+
+  //the chain from begin to end is deleted (the space is deallocated)
+  //and a new edge(which connectes the head of begin and the tail of end)
+  // is inserted. The new polygon is returned.
+  //notice that "this" is arbitrary
+  directedLine* deleteChain(directedLine* begin, directedLine* end);
+};
+
+directedLine*  readAllPolygons(char* filename);
+
+extern Int compV2InY(Real A[2], Real B[2]);
+extern Int compV2InX(Real A[2], Real B[2]);
+
+#endif
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/glimports.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/glimports.h
new file mode 100644
index 000000000..6e69feb40
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/glimports.h
@@ -0,0 +1,42 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+
+/*
+ * glimports.h
+ *
+ */
+
+#ifndef __gluimports_h_
+#define __gluimports_h_
+
+#include "mystdlib.h"
+#include "mystdio.h"
+
+#endif /* __gluimports_h_ */
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/gridWrap.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/gridWrap.cc
new file mode 100644
index 000000000..3c92039ba
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/gridWrap.cc
@@ -0,0 +1,293 @@
+/*
+** 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 "zlassert.h"
+#include "gridWrap.h"
+
+
+/*******************grid structure****************************/
+void gridWrap::print()
+{
+  printf("n_ulines = %i\n", n_ulines);
+  printf("n_vlines = %i\n", n_vlines);
+  printf("u_min=%f, umax=%f, vmin=%f, vmax=%f\n", u_min, u_max, v_min, v_max);
+}
+
+gridWrap::gridWrap(Int nUlines, Real* uvals,
+		   Int nVlines, Real* vvals)
+{
+  assert(nUlines>=2);
+  assert(nVlines>=2);
+
+  is_uniform = 0;
+  n_ulines = nUlines;
+  n_vlines = nVlines;
+  u_min = uvals[0];
+  u_max = uvals[nUlines-1];
+  v_min = vvals[0];
+  v_max = vvals[nVlines-1];
+  u_values = (Real*) malloc(sizeof(Real) * n_ulines);
+  assert(u_values);
+  v_values = (Real*) malloc(sizeof(Real) * n_vlines);
+  assert(v_values);  
+  
+  Int i;
+  for(i=0; i<n_ulines; i++)
+    u_values[i] = uvals[i];
+  for(i=0; i<n_vlines; i++)
+    v_values[i] = vvals[i];
+}
+  
+gridWrap::gridWrap(Int nUlines, Int nVlines,
+		   Real uMin, Real uMax,
+		   Real vMin, Real vMax
+		   )
+{
+  is_uniform = 1;
+  n_ulines = nUlines;
+  n_vlines = nVlines;
+  u_min = uMin;
+  u_max = uMax;
+  v_min = vMin;
+  v_max = vMax;
+  u_values = (Real*) malloc(sizeof(Real) * n_ulines);
+  assert(u_values);
+  v_values = (Real*) malloc(sizeof(Real) * n_vlines);
+  assert(v_values);
+  
+  Int i;
+  assert(nUlines>=2);
+  assert(nVlines>=2);
+  Real du = (uMax-uMin)/(nUlines-1);
+  Real dv = (vMax-vMin)/(nVlines-1);
+
+  float tempu=uMin;
+  u_values[0] = tempu;
+  for(i=1; i<nUlines; i++)
+    {
+      tempu += du;
+      u_values[i] = tempu;
+    }
+  u_values[nUlines-1] = uMax;
+
+  float tempv=vMin;
+  v_values[0] = tempv;
+  for(i=1; i<nVlines; i++)
+    {
+      tempv += dv;
+      v_values[i] = tempv;
+    }
+  v_values[nVlines-1] = vMax;
+}
+
+gridWrap::~gridWrap()
+{
+  free(u_values);
+  free(v_values);
+}
+
+void gridWrap::draw()
+{
+  int i,j;
+  glBegin(GL_POINTS);
+  for(i=0; i<n_ulines; i++)
+    for(j=0; j<n_vlines; j++)
+      glVertex2f(get_u_value(i), get_v_value(j));
+  glEnd();
+}
+
+void gridWrap::outputFanWithPoint(Int v, Int uleft, Int uright, Real vert[2], primStream* pStream)
+{
+  Int i;
+  if(uleft >= uright) 
+    return; //no triangles to output.
+    
+  pStream->begin();
+  pStream->insert(vert);
+
+  assert(vert[1] != v_values[v]); //don't output degenerate triangles
+
+  if(vert[1] > v_values[v]) //vertex is above this grid line: notice the orientation
+    {
+      for(i=uleft; i<=uright; i++)
+	pStream->insert(u_values[i], v_values[v]);
+    }
+  else //vertex is below the grid line
+    {
+      for(i=uright; i>= uleft; i--)
+	pStream->insert(u_values[i], v_values[v]);
+    }	
+  
+  pStream->end(PRIMITIVE_STREAM_FAN);
+}
+
+
+
+/*each chain stores a number of consecutive 
+ *V-lines within a grid. 
+ *There is one grid vertex on each V-line.
+ * The total number of V-lines is:
+ *   nVlines.
+ * with respect to the grid, the index of the first V-line is 
+ *   firstVlineIndex.
+ * So with respect to the grid, the index of the ith V-line is 
+ *   firstVlineIndex-i.
+ * the grid-index of the uline at the ith vline (recall that each vline has one grid point)
+ * is ulineIndices[i]. The u_value is cached in ulineValues[i], that is,
+ *   ulineValues[i] = grid->get_u_value(ulineIndices[i]) 
+ */
+gridBoundaryChain::gridBoundaryChain(
+				     gridWrap* gr, 
+				     Int first_vline_index, 
+				     Int n_vlines, 
+				     Int* uline_indices,
+				     Int* inner_indices
+				     )
+: grid(gr), firstVlineIndex(first_vline_index), nVlines(n_vlines)
+{
+  ulineIndices = (Int*) malloc(sizeof(Int) * n_vlines);
+  assert(ulineIndices);
+
+  innerIndices = (Int*) malloc(sizeof(Int) * n_vlines);
+  assert(innerIndices);
+
+  vertices = (Real2*) malloc(sizeof(Real2) * n_vlines);
+  assert(vertices);
+  
+
+
+  Int i;
+  for(i=0; i<n_vlines; i++){
+    ulineIndices[i] = uline_indices[i];
+    innerIndices[i] = inner_indices[i];
+  }
+  
+  for(i=0; i<n_vlines; i++){
+    vertices[i][0] = gr->get_u_value(ulineIndices[i]);
+    vertices[i][1] = gr->get_v_value(first_vline_index-i);
+  }
+}
+  
+void gridBoundaryChain::draw()
+{
+  Int i;
+  glBegin(GL_LINE_STRIP);
+  for(i=0; i<nVlines; i++)
+    {
+      glVertex2fv(vertices[i]);
+    }
+  glEnd();
+}
+
+void gridBoundaryChain::drawInner()
+{
+  Int i;
+  for(i=1; i<nVlines; i++)
+    {
+      glBegin(GL_LINE_STRIP);
+      glVertex2f(grid->get_u_value(innerIndices[i]), get_v_value(i-1) );
+      glVertex2f(grid->get_u_value(innerIndices[i]), get_v_value(i) );
+      glEnd();
+    }
+}
+  
+Int gridBoundaryChain::lookfor(Real v, Int i1, Int i2)
+{
+  Int mid;
+  while(i1 < i2-1)
+    {
+      mid = (i1+i2)/2;
+      if(v > vertices[mid][1])
+	{
+	  i2 = mid;
+	}
+      else
+	i1 = mid;
+    }
+  return i1;
+}
+
+/*output the fan of the right end between grid line i-1 and grid line i*/
+void gridBoundaryChain::rightEndFan(Int i, primStream* pStream)
+{
+  Int j;
+  if(getUlineIndex(i) > getUlineIndex(i-1))
+    {
+      pStream->begin();
+      pStream->insert(get_vertex(i-1));
+      for(j=getUlineIndex(i-1); j<= getUlineIndex(i); j++)
+	pStream->insert(grid->get_u_value(j), get_v_value(i));
+      pStream->end(PRIMITIVE_STREAM_FAN);
+    }
+  else if(getUlineIndex(i) < getUlineIndex(i-1))
+    {
+      pStream->begin();
+      pStream->insert(get_vertex(i));
+      for(j=getUlineIndex(i-1); j>= getUlineIndex(i); j--)
+	pStream->insert(grid->get_u_value(j), get_v_value(i-1));
+      pStream->end(PRIMITIVE_STREAM_FAN);
+    }
+  //otherside, the two are equal, so there is no fan to output
+}
+		      
+
+/*output the fan of the left end between grid line i-1 and grid line i*/
+void gridBoundaryChain::leftEndFan(Int i, primStream* pStream)
+{
+  Int j;
+  if(getUlineIndex(i) < getUlineIndex(i-1))
+    {
+      pStream->begin();
+      pStream->insert(get_vertex(i-1));
+      for(j=getUlineIndex(i); j<= getUlineIndex(i-1); j++)
+	pStream->insert(grid->get_u_value(j), get_v_value(i));
+      pStream->end(PRIMITIVE_STREAM_FAN);
+    }
+  else if(getUlineIndex(i) > getUlineIndex(i-1))
+    {
+      pStream->begin();
+      pStream->insert(get_vertex(i));
+      for(j=getUlineIndex(i); j>= getUlineIndex(i-1); j--)
+	pStream->insert(grid->get_u_value(j), get_v_value(i-1));
+      pStream->end(PRIMITIVE_STREAM_FAN);
+    }
+  /*otherwisem, the two are equal, so there is no fan to outout*/	  
+}
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/gridWrap.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/gridWrap.h
new file mode 100644
index 000000000..b6428484f
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/gridWrap.h
@@ -0,0 +1,137 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _GRIDWRAP_H
+#define _GRIDWRAP_H
+
+#include <stdio.h>
+#include "definitions.h"
+
+#include "primitiveStream.h"
+#include "zlassert.h"
+
+class gridWrap{
+  Int n_ulines;
+  Int n_vlines;
+  Real u_min, u_max;
+  Real v_min, v_max;
+
+  /*cache the coordinate values for efficiency. 
+   *these are redundant information when 
+   *the grid is uniform.
+   */
+  Real* u_values; /*size is n_ulines*/
+  Real* v_values; /*size is n_vlines*/
+
+  Int is_uniform; 
+
+public:
+  //uniform grid constructor
+  gridWrap(Int nUlines, Int nVlines,
+	   Real uMin, Real uMax,
+	   Real vMin, Real vMax
+	   );
+
+  //nonuniform grid constructor.
+  gridWrap(Int nUlines, Real *uvals,
+	   Int nVlines, Real *vvlas
+	   );
+  ~gridWrap();
+  
+  void print();
+  Int get_n_ulines() {return n_ulines;}
+  Int get_n_vlines() {return n_vlines;}
+  Real get_u_min() {return u_min;}
+  Real get_u_max() {return u_max;}
+  Real get_v_min() {return v_min;}
+  Real get_v_max() {return v_max;}
+
+  Real get_u_value(Int i) 
+    {
+      assert(i<n_ulines);
+      /*if(i>=n_ulines){printf("ERROR, n_ulines=%i,i=%i\n",n_ulines,i);exit(0);}*/      
+      return u_values[i];}
+  Real get_v_value(Int j) {return v_values[j];}
+
+  Real* get_u_values() {return u_values;}
+  Real* get_v_values() {return v_values;}
+
+  void outputFanWithPoint(Int v, Int uleft, Int uright, 
+			  Real vert[2], primStream* pStream);
+
+  void draw();
+
+  Int isUniform() {return is_uniform;}
+};
+
+class gridBoundaryChain{
+  gridWrap* grid;
+  Int firstVlineIndex;
+  Int nVlines;
+  Int* ulineIndices; /*each v line has a boundary*/
+  Int* innerIndices; /*the segment of the vertical gridline from */
+                     /*(innerIndices[i], i) to (innerIndices[i+1], i-1) */
+                     /*is inside the polygon: i=1,...,nVlines-1*/
+
+  Real2* vertices; /*one grid point at each grid V-line, cached for efficiency*/
+
+public:
+  gridBoundaryChain(gridWrap* gr, Int first_vline_index, Int n_vlines, Int* uline_indices, Int* inner_indices);
+
+  ~gridBoundaryChain()
+    {
+      free(innerIndices);
+      free(ulineIndices);
+      free(vertices);
+    }
+
+  /*i indexes the vlines in this chain.
+   */
+  Int getVlineIndex(Int i) {return firstVlineIndex-i;}
+  Int getUlineIndex(Int i) {return ulineIndices[i];}
+  Real get_u_value(Int i) {return vertices[i][0];}
+  Real get_v_value(Int i) {return vertices[i][1];}
+  Int get_nVlines() {return nVlines;}
+  Int getInnerIndex(Int i) {return innerIndices[i];}
+  Real getInner_u_value(Int i) {return grid->get_u_value(innerIndices[i]);}
+
+  Real* get_vertex(Int i) {return vertices[i];}
+  gridWrap* getGrid() {return grid;}
+  void leftEndFan(Int i, primStream* pStream);
+  void rightEndFan(Int i, primStream* pStream);
+
+  Int lookfor(Real v, Int i1, Int i2); //find i in [i1,i2] so that  vertices[i][1]>= v > vertices[i+1][1]
+  void draw();
+  void drawInner();
+};
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/monoChain.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoChain.cc
new file mode 100644
index 000000000..814bf32fa
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoChain.cc
@@ -0,0 +1,934 @@
+/*
+** 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;
+}
+
+//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;	  
+	}
+    }
+  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;
+}
+      
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/monoChain.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoChain.h
new file mode 100644
index 000000000..999f16319
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoChain.h
@@ -0,0 +1,103 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _MONO_CHAIN_H
+#define _MONO_CHAIN_H
+
+#include "directedLine.h"
+#include "partitionY.h"
+
+class monoChain;
+
+class monoChain{
+  directedLine* chainHead;
+  directedLine* chainTail;
+  monoChain* next;
+  monoChain* prev;
+  monoChain* nextPolygon; //a list of polygons
+  
+  //cached informatin
+  //bounding box
+  Real minX, maxX, minY, maxY;
+  Int isIncrease;
+  
+  //for efficiently comparing two chains
+
+  directedLine* current;
+  
+public:
+  monoChain(directedLine* cHead, directedLine* cTail);
+  ~monoChain() {}
+  
+  inline  void setNext(monoChain* n) {next = n;}
+  inline void setPrev(monoChain* p) {prev = p;}
+  inline void setNextPolygon(monoChain* np) {nextPolygon = np;}
+  inline monoChain* getNext() {return next;}
+  inline monoChain* getPrev() {return prev;}
+  inline directedLine* getHead() {return chainHead;}
+  inline directedLine* getTail() {return chainTail;}
+  
+  inline void resetCurrent() { current = ((isIncrease==1)? chainHead:chainTail);}
+
+  void deleteLoop();
+  void deleteLoopList();
+
+  //insert a new chain between prev and this
+  void insert(monoChain* nc);
+
+  Int numChainsSingleLoop();
+  Int numChainsAllLoops();
+  monoChain** toArrayAllLoops(Int& num_chains);
+  Int toArraySingleLoop(monoChain** array, Int index);
+
+  Int isKey;
+  Real keyY; //the current horizotal line  
+  Real chainIntersectHoriz(Real y); //updates current incrementally for efficiency
+  directedLine* find(Real y);//find dline so that y intersects dline.
+
+  void printOneChain();
+  void printChainLoop();
+  void printAllLoops();
+    
+};
+
+monoChain* directedLineLoopToMonoChainLoop(directedLine* loop);
+monoChain* directedLineLoopListToMonoChainLoopList(directedLine* list);
+Int MC_sweepY(Int nVertices, monoChain** sortedVertices, sweepRange** ret_ranges);
+
+void MC_findDiagonals(Int total_num_edges, monoChain** sortedVertices,
+		   sweepRange** ranges, Int& num_diagonals, 
+		   directedLine** diagonal_vertices);
+
+directedLine* MC_partitionY(directedLine *polygons, sampledLine **retSampledLines);
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/monoPolyPart.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoPolyPart.cc
new file mode 100644
index 000000000..8391205bf
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoPolyPart.cc
@@ -0,0 +1,299 @@
+/*
+** 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.
+**
+*/
+/*
+ *monoPolyPart.C
+ *
+ *To partition a v-monotone polygon into some uv-monotone polygons.
+ *The algorithm is different from the general monotone partition algorithm.
+ *while the general monotone partition algorithm works for this special case,
+ *but it is more expensive (O(nlogn)). The algorithm implemented here takes
+ *advantage of the fact that the input is a v-monotone polygon and it is
+ *conceptually simpler and  computationally cheaper (a linear time algorithm).
+ *The algorithm is described in Zicheng Liu's  paper
+ * "Quality-Oriented Linear Time Tessellation".
+ */
+
+#include <stdlib.h>
+#include <stdio.h>
+#include "directedLine.h"
+#include "monoPolyPart.h"
+
+/*a vertex is u_maximal if both of its two neightbors are to the left of this 
+ *vertex
+ */
+static Int is_u_maximal(directedLine* v)
+{
+  if (compV2InX(v->getPrev()->head(), v->head()) == -1 &&
+      compV2InX(v->getNext()->head(), v->head()) == -1)
+    return 1;
+  else
+    return 0;
+}
+
+/*a vertex is u_minimal if both of its two neightbors are to the right of this 
+ *vertex
+ */
+static Int is_u_minimal(directedLine* v)
+{
+  if (compV2InX(v->getPrev()->head(), v->head()) == 1 &&
+      compV2InX(v->getNext()->head(), v->head()) == 1)
+    return 1;
+  else
+    return 0;
+}
+
+/*poly: a v-monotone polygon
+ *return: a linked list of uv-monotone polygons.
+ */
+directedLine* monoPolyPart(directedLine* polygon)
+{
+  //handle special cases:
+  if(polygon == NULL)
+    return NULL;
+  if(polygon->getPrev() == polygon)
+    return polygon;
+  if(polygon->getPrev() == polygon->getNext())
+    return polygon;
+  if(polygon->getPrev()->getPrev() == polygon->getNext())
+    return polygon;
+
+  //find the top and bottom vertexes
+  directedLine *tempV, *topV, *botV;
+  topV = botV = polygon;
+  for(tempV = polygon->getNext(); tempV != polygon; tempV = tempV->getNext())
+    {
+      if(compV2InY(topV->head(), tempV->head())<0) {
+	topV = tempV;
+      }
+      if(compV2InY(botV->head(), tempV->head())>0) {
+	botV = tempV;
+      }
+    }
+
+  //initilization
+  directedLine *A, *B, *C, *D, *G, *H;
+  //find A:the first u_maximal vertex on the left chain
+  //and C: the left most vertex between top and A
+  A = NULL;
+  C = topV;
+  for(tempV=topV->getNext(); tempV != botV; tempV = tempV->getNext())
+    {
+      if(tempV->head()[0] < C->head()[0])
+	C = tempV;
+
+      if(is_u_maximal(tempV))
+	{
+	  A = tempV;
+	  break;
+	}
+    }
+  if(A == NULL)
+    {
+      A = botV;
+      if(A->head()[0] < C->head()[0])
+	C = A;
+    }
+      
+  //find B: the first u_minimal vertex on the right chain
+  //and  D: the right most vertex between top and B
+  B = NULL;
+  D = topV;
+  for(tempV=topV->getPrev(); tempV != botV; tempV = tempV->getPrev())
+    {
+      if(tempV->head()[0] > D->head()[0])
+	D = tempV;
+      if(is_u_minimal(tempV))
+	{
+	  B = tempV;
+	  break;
+	}
+    }
+  if(B == NULL)
+    {
+      B = botV;
+      if(B->head()[0] > D->head()[0])
+	D = B;
+    }
+
+  //error checking XXX
+  if(C->head()[0] >= D->head()[0])
+    return polygon;
+
+  //find G on the left chain that is right above B
+  for(tempV=topV; compV2InY(tempV->head(), B->head()) == 1;  tempV=tempV->getNext());
+  G = tempV->getPrev();
+  //find H on the right chain that is right above A
+  for(tempV=topV; compV2InY(tempV->head(), A->head()) == 1; tempV = tempV->getPrev());
+  H = tempV->getNext();
+  
+  //Main Loop
+  directedLine* ret = NULL;
+  directedLine* currentPolygon = polygon;
+  while(1)
+    {
+      //if both B and D are equal to botV, then this polygon is already 
+      //u-monotone
+      if(A == botV && B == botV)
+	{
+	  ret = currentPolygon->insertPolygon(ret);
+	  return ret;
+	}
+      else //not u-monotone
+	{
+	  directedLine *ret_p1, *ret_p2;
+	  if(compV2InY(A->head(),B->head()) == 1) //A is above B
+	    {
+	      directedLine* E = NULL;
+	      for(tempV = C; tempV != D; tempV = tempV->getPrev())
+		{
+		  if(tempV->head()[0] >= A->head()[0])
+		    {
+		      E = tempV;
+		      break;
+		    }
+		}
+
+	      if(E == NULL)
+		E = D;
+	      if(E->head()[0]> H->head()[0])
+		E = H;
+	      //connect AE and output polygon ECA
+	      polygon->connectDiagonal_2slines(A, E,
+					       &ret_p1,
+					       &ret_p2,
+					       NULL);
+	      ret = ret_p2->insertPolygon(ret);
+	      currentPolygon = ret_p1;
+
+	      if(E == D)
+		D = ret_p1;
+	      if(E == H)
+		H = ret_p1;
+              if(G->head()[1] >= A->head()[1])
+		G = A;
+	      //update A to be the next u-maxiaml vertex on left chain
+	      //and C the leftmost vertex between the old A and the new A
+	      C = A;
+	      for(tempV = A->getNext(); tempV != botV; tempV = tempV->getNext())
+		{
+
+		  if(tempV->head()[0] < C->head()[0])
+		    C = tempV;
+		  if(is_u_maximal(tempV))
+		    {
+		      A = tempV;
+		      break;
+		    }
+		}
+
+	      if(tempV == botV)
+		{
+		  A = botV;
+		  if(botV->head()[0] < C->head()[0])
+		    C = botV;
+		}
+	      //update H
+
+              if(A == botV)
+		H = botV;
+              else
+		{
+		  for(tempV = H; compV2InY(tempV->head(), A->head()) == 1; tempV = tempV->getPrev());
+		  H = tempV->getNext();
+		}
+
+	    }
+	  else //A is below B
+	    {
+
+	      directedLine* F = NULL;
+	      for(tempV = D; tempV != C; tempV = tempV->getNext())
+		{
+		  if(tempV->head()[0] <= B->head()[0])
+		    {
+		      F = tempV;
+		      break;
+		    }
+		}
+	      if(F == NULL)
+		F = C;
+	      if(F->head()[0] < G->head()[0])
+		F = G;
+
+	      //connect FB
+	      polygon->connectDiagonal_2slines(F, B, 
+					       &ret_p1,
+					       &ret_p2,
+					       NULL);
+	      ret = ret_p2->insertPolygon(ret);
+	      currentPolygon = ret_p1;
+	      B = ret_p1;
+	      if(H ->head()[1] >= B->head()[1])
+		H = ret_p1;
+
+	      //update B to be the next u-minimal vertex on right chain
+	      //and D the rightmost vertex between the old B and the new B
+	      D = B;
+	      for(tempV = B->getPrev(); tempV != botV; tempV = tempV->getPrev())
+		{
+		  if(tempV->head()[0] > D->head()[0])
+		    D = tempV;
+		  if(is_u_minimal(tempV))
+		    {
+		      B = tempV;
+		      break;
+		    }
+		}
+	      if(tempV == botV)
+		{
+		  B = botV;
+		  if(botV->head()[0] > D->head()[0])
+		    D = botV;
+		}
+	      //update G
+              if(B == botV)
+		G = botV; 
+              else
+		{
+		  for(tempV = G; compV2InY(tempV->head(), B->head()) == 1;  tempV = tempV->getNext());
+		  G = tempV->getPrev();
+		}
+	    } //end of A is below B
+	} //end not u-monotone	
+    } //end of main loop
+}
+
+
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/monoPolyPart.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoPolyPart.h
new file mode 100644
index 000000000..6877a59c2
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoPolyPart.h
@@ -0,0 +1,41 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+ *monoPolyPart.h
+ */
+
+#ifndef _MONO_POLY_PART_H
+#define _MONO_POLY_PART_H
+ 
+class directedLine;
+
+directedLine* monoPolyPart(directedLine* polygon);
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.cc
new file mode 100644
index 000000000..8e8d49dda
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.cc
@@ -0,0 +1,1482 @@
+/*
+** 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");
+}
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.h
new file mode 100644
index 000000000..f78b8f402
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/monoTriangulation.h
@@ -0,0 +1,184 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _MONO_TRIANGULATION_H
+#define _MONO_TRIANGULATION_H
+
+#include "definitions.h"
+#include "primitiveStream.h"
+#include "directedLine.h"
+#include "arc.h"
+
+class Backend;
+
+class reflexChain{
+  Real2 *queue; 
+  /*the order of the polygon vertices: either q[0],q[1].., or 
+   * q[n-1], q[n-2], ..., q[0]
+   *this order determines the interior of the polygon, so it
+   *also used to determines whether a chain is reflex or convex
+   */
+  Int isIncreasing; 
+  Int index_queue;
+  Int size_queue; /*allocated size*/
+  
+public:
+  reflexChain(Int size, Int isIncreasing);
+  ~reflexChain();
+  
+  void insert(Real u, Real v);
+  void insert(Real v[2]);
+  
+  void processNewVertex(Real v[2], primStream* pStream);
+  void outputFan(Real v[2], primStream* pStream);
+
+  void processNewVertex(Real v[2], Backend* backend);
+  void outputFan(Real v[2], Backend* backend);
+
+  void print();
+};
+
+/*dynamic array of pointers to reals.
+ *Intended to store an array of (u,v).
+ *Notice that it doesn't allocate or dealocate the space
+ *for the (u,v) themselfs. So it assums that someone else 
+ *is taking care of them, while this class only plays with
+ *the pointers.
+ */
+class vertexArray{
+  Real** array;
+  Int index;
+  Int size;
+public:
+  vertexArray(Int s);
+  vertexArray(Real vertices[][2], Int nVertices);
+  ~vertexArray();
+  void appendVertex(Real* ptr); /*the content (pointed by ptr is NOT copied*/
+  Real* getVertex(Int i) {return array[i];}
+  Real** getArray() {return array;}
+  Int getNumElements() {return index;}
+  Int findIndexAbove(Real v);
+  Int findIndexAboveGen(Real v, Int startIndex, Int EndIndex);
+  Int findIndexBelowGen(Real v, Int startIndex, Int EndIndex);
+  Int findIndexStrictBelowGen(Real v, Int startIndex, Int EndIndex);
+  Int findIndexFirstAboveEqualGen(Real v, Int startIndex, Int endIndex);
+  Int skipEqualityFromStart(Real v, Int start, Int end);
+  //return i such that fron [i+1, end] is strictly U-monotone (left to right
+  Int findDecreaseChainFromEnd(Int begin, Int end);
+  void print();
+};
+
+void monoTriangulation(directedLine* monoPolygon, primStream* pStream);
+
+void monoTriangulationRec(Real* topVertex, Real* botVertex, 
+			  vertexArray* inc_chain, Int inc_current,
+			  vertexArray* dec_chain, Int dec_current,
+			  primStream* pStream);
+
+void monoTriangulationRec(directedLine* inc_chain, Int inc_index, 
+			  directedLine* dec_chain, Int dec_index, 
+			  directedLine* topVertex, Int top_index,
+			  directedLine* botVertex,
+			  primStream* 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);
+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); 
+
+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); 
+
+void triangulateXYMonoTB(Int n_left, Real** leftVerts,
+		       Int n_right, Real** rightVerts,
+		       primStream* 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);
+
+void monoTriangulationRecOpt(Real* topVertex, Real* botVertex, 
+			     vertexArray* left_chain, Int left_current,
+			     vertexArray* right_chain, Int right_current,
+			     primStream* pStream);
+
+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);
+
+void monoTriangulationRecFun(Real* topVertex, Real* botVertex, 
+			  vertexArray* inc_chain, Int inc_current,
+			  vertexArray* dec_chain, Int dec_current,
+			   Int (*compFun)(Real*, Real*),
+			  primStream* pStream);
+void monoTriangulationFun(directedLine* monoPolygon, 
+			  Int (*compFun)(Real*, Real*), primStream* pStream);
+
+
+
+
+void monoTriangulationRec(Real* topVertex, Real* botVertex, 
+			  vertexArray* inc_chain, Int inc_current,
+			  vertexArray* dec_chain, Int dec_current,
+			  Backend* backend);
+
+void monoTriangulationFunBackend(Arc_ptr loop, Int (*compFun)(Real*, Real*), Backend* backend);
+
+void monoTriangulationRecFunBackend(Real* topVertex, Real* botVertex, 
+			  vertexArray* inc_chain, Int inc_current,
+			  vertexArray* dec_chain, Int dec_current,
+			  Int  (*compFun)(Real*, Real*),
+			  Backend* backend);
+
+void monoTriangulationOpt(directedLine* poly, primStream* pStream);
+
+#endif
+
+
+
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/mystdio.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/mystdio.h
new file mode 100644
index 000000000..a394e0ff9
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/mystdio.h
@@ -0,0 +1,60 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+
+/*
+ * mystdio.h
+ *
+ */
+
+#ifndef __glumystdio_h_
+#define __glumystdio_h_
+
+#ifdef STANDALONE
+inline void _glu_dprintf( char *, ... ) { }
+#endif
+
+#ifdef LIBRARYBUILD
+#ifndef NDEBUG
+#include <stdio.h>
+#define _glu_dprintf printf
+#else
+inline void _glu_dprintf( char *, ... ) { }
+#endif
+#endif
+
+#ifdef GLBUILD
+inline void _glu_dprintf( char *, ... ) { }
+#endif
+
+#ifndef NULL
+#define NULL		0
+#endif
+
+#endif /* __glumystdio_h_ */
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/mystdlib.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/mystdlib.h
new file mode 100644
index 000000000..ab7a3b273
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/mystdlib.h
@@ -0,0 +1,57 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+
+/*
+ * mystdlib.h
+ *
+ */
+
+#ifndef __glumystdlib_h_
+#define __glumystdlib_h_
+
+#ifdef STANDALONE
+typedef unsigned int size_t;
+extern "C" void 	abort( void );
+extern "C" void *	malloc( size_t );
+extern "C" void 	free( void * );
+#endif
+
+#ifdef LIBRARYBUILD
+#include <stdlib.h>
+#endif
+
+#ifdef GLBUILD
+typedef unsigned int size_t;
+extern "C" void 	abort( void );
+extern "C" void *	malloc( size_t );
+extern "C" void 	free( void * );
+#endif
+
+#endif /* __glumystdlib_h_ */
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionX.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionX.cc
new file mode 100644
index 000000000..e25e30b0f
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionX.cc
@@ -0,0 +1,162 @@
+/*
+** 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 "partitionX.h"
+
+#define CONCAVITY_ZERO 1.0e-6 //this number is used to test whether a vertex is concave (refelx) 
+                              //or not. The test needs to compute the area of the three adjacent 
+                              //vertices to see if the are is positive or negative. 
+
+Int isCuspX(directedLine *v)
+{
+  //if v->prev <= v && v->next <= v
+  //|| v->prev >= v && v->next >= v
+  Real* T = v->head();
+  Real* P = v->getPrev()->head();
+  Real* N = v->getNext()->head();
+  if(
+     (compV2InX(T,P) != -1 && 
+      compV2InX(T,N) != -1
+      ) ||
+     (compV2InX(T,P) != 1 && 
+      compV2InX(T,N) != 1
+      )
+     )
+    return 1;
+  else
+    return 0;
+}
+
+Int isReflexX(directedLine* v)
+{
+  Real* A = v->getPrev()->head();
+  Real* B = v->head();
+  Real* C = v->tail();
+  Real Bx,By, Cx, Cy;
+  //scale them in case they are too small
+  Bx = 10*(B[0] - A[0]);
+  By = 10*(B[1] - A[1]);
+  Cx = 10*(C[0] - A[0]);
+  Cy = 10*(C[1] - A[1]);
+
+  if(Bx*Cy - Cx*By < -CONCAVITY_ZERO) return 1;
+  else return 0;
+}
+
+
+/*return 
+ *0: not-cusp
+ *1: interior cusp
+ *2: exterior cusp
+ */
+Int cuspTypeX(directedLine *v)
+{
+  if(! isCuspX(v)) return 0;
+  else 
+    {
+//printf("isCusp,%f,%f\n", v->head()[0], v->head()[1]);
+      if(isReflexX(v)) 
+	{
+//	  printf("isReflex\n");
+	  return 1;
+	}
+      else
+	{
+//	  printf("not isReflex\n");
+	  return 2;
+	}
+    }
+}
+
+Int numInteriorCuspsX(directedLine *polygon)
+{
+  directedLine *temp;
+  int ret = 0;
+  if(cuspTypeX(polygon) == 1)
+    ret++;
+  for(temp = polygon->getNext(); temp != polygon; temp = temp->getNext())
+    if(cuspTypeX(temp) == 1)
+      ret++;
+  return ret;
+}
+  
+
+void findInteriorCuspsX(directedLine *polygon, Int& ret_n_interior_cusps,
+			directedLine** ret_interior_cusps)
+{
+  directedLine *temp;
+  ret_n_interior_cusps = 0;
+  if(cuspTypeX(polygon) == 1)
+    {
+      ret_interior_cusps[ret_n_interior_cusps++] = polygon;
+    }
+  for(temp = polygon->getNext(); temp != polygon; temp = temp->getNext())    
+    if(cuspTypeX(temp) == 1)
+      {
+	ret_interior_cusps[ret_n_interior_cusps++] = temp;    
+      }
+}
+
+directedLine* findDiagonal_singleCuspX(directedLine* cusp)
+{
+  directedLine* temp;
+  Int is_minimal = ((compV2InX(cusp->head(), cusp->tail()) == -1)? 1:0);
+
+  if(is_minimal)
+    for(temp = cusp->getNext(); temp != cusp; temp = temp->getNext())
+      {
+	if(compV2InX(cusp->head(), temp->head()) == 1)
+	  {	   
+	    return temp;
+	  }
+      }
+  else //is maxmal 
+    for(temp = cusp->getNext(); temp != cusp; temp = temp->getNext())
+      {
+	if(compV2InX(cusp->head(), temp->head()) == -1)
+	  {	   
+	    return temp;
+	  }
+      }
+  return NULL;
+}
+      
+
+     
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionX.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionX.h
new file mode 100644
index 000000000..69f2b2df2
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionX.h
@@ -0,0 +1,54 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _PARTITIONX_H
+#define _PARTITIONX_H
+
+#include "directedLine.h"
+
+Int isCuspX(directedLine *v);
+Int isReflexX(directedLine *v);
+Int cuspTypeX(directedLine *v);
+
+//assuming the array of ret_interior_cusps has been allocated
+void findInteriorCuspsX(directedLine* polygon, Int& ret_n_interior_cusps,
+		       directedLine** ret_interior_cusps);
+
+Int numInteriorCuspsX(directedLine* polygon);
+
+/*a single polygon with a single cusp
+ *return the diagonal vertex corresponding to this cusp
+ */
+directedLine* findDiagonal_singleCuspX(directedLine* cusp);
+
+#endif
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionY.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionY.cc
new file mode 100644
index 000000000..297c62997
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionY.cc
@@ -0,0 +1,836 @@
+/*
+** 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 <time.h>
+
+#include "zlassert.h"
+#include "partitionY.h"
+#include "searchTree.h"
+#include "quicksort.h"
+#include "polyUtil.h"
+
+
+#define max(a,b) ((a>b)? a:b)
+#define min(a,b) ((a>b)? b:a)
+
+
+/*retrurn 
+ *-1: if A < B (Ya<Yb) || (Ya==Yb)
+ * 0: if A == B
+ * 1: if A>B
+ */
+static Int compVertInY(Real A[2], Real B[2])
+{
+  if( (A[1] < B[1]) || (A[1]==B[1] && A[0]<B[0])) 
+    return -1;
+  else if
+    ( A[1] == B[1] && A[0] == B[0]) return 0;
+  else
+    return 1;
+}
+
+/*v is a vertex: the head of en edge,
+ *e is an edge,
+ *return 1 if e is below v: assume v1 and v2 are the two endpoints of e:
+ * v1<= v, v2<=v.
+ */
+Int isBelow(directedLine *v, directedLine *e)
+{
+  Real* vert = v->head();
+  if(   compVertInY(e->head(), vert) != 1 
+     && compVertInY(e->tail(), vert) != 1
+     )
+    return 1;
+  else
+    return 0;
+}
+
+/*v is a vertex: the head of en edge,
+ *e is an edge,
+ *return 1 if e is below v: assume v1 and v2 are the two endpoints of e:
+ * v1>= v, v2>=v.
+ */
+Int isAbove(directedLine *v, directedLine *e)
+{
+  Real* vert = v->head();
+  if(   compVertInY(e->head(), vert) != -1 
+     && compVertInY(e->tail(), vert) != -1
+     )
+    return 1;
+  else
+    return 0;
+}
+
+Int isCusp(directedLine *v)
+{
+  Real *A=v->getPrev()->head();
+  Real *B=v->head();
+  Real *C=v->tail();
+  if(A[1] < B[1] && B[1] < C[1])
+    return 0;
+  else if(A[1] > B[1] && B[1] > C[1])
+    return 0;
+  else if(A[1] < B[1] && C[1] < B[1])
+    return 1;
+  else if(A[1] > B[1] && C[1] > B[1])
+    return 1;
+
+  if(isAbove(v, v) && isAbove(v, v->getPrev()) ||
+     isBelow(v, v) && isBelow(v, v->getPrev()))
+    return 1;
+  else
+    return 0;
+}
+
+/*crossproduct is strictly less than 0*/
+Int isReflex(directedLine *v)
+{
+  Real* A = v->getPrev()->head();
+  Real* B = v->head();
+  Real* C = v->tail();
+  Real Bx,By, Cx, Cy;
+  Bx = B[0] - A[0];
+  By = B[1] - A[1];
+  Cx = C[0] - A[0];
+  Cy = C[1] - A[1];
+
+  if(Bx*Cy - Cx*By < 0) return 1;
+  else return 0;
+}
+
+ /*return 
+ *0: not-cusp
+ *1: interior cusp
+ *2: exterior cusp
+ */
+Int cuspType(directedLine *v)
+{
+  if(! isCusp(v)) return 0;
+  else if(isReflex(v)) return 1;
+  else
+    return 2;
+}
+
+sweepRange* sweepRangeMake(directedLine* left, Int leftType,
+			   directedLine* right, Int rightType)
+{
+  sweepRange* ret = (sweepRange*)malloc(sizeof(sweepRange));
+  assert(ret);
+  ret->left = left;
+  ret->leftType = leftType;
+  ret->right = right;
+  ret->rightType = rightType;
+  return ret;
+}
+
+void sweepRangeDelete(sweepRange* range)
+{
+  free(range);
+}
+
+Int sweepRangeEqual(sweepRange* src1, sweepRange* src2)
+{
+  Int leftEqual;
+  Int rightEqual;
+  
+  
+  /*The case when both are vertices should not happen*/
+  assert(! (src1->leftType == 0 && src2->leftType == 0));    
+  if(src1->leftType == 0 && src2->leftType == 1){
+    if(src1->left == src2->left ||
+       src1->left->getPrev() == src2->left
+       )
+      leftEqual = 1;
+    else
+      leftEqual = 0;
+  }
+  else if(src1->leftType == 1 && src2->leftType == 1){
+    if(src1->left == src2->left)
+      leftEqual = 1;
+    else
+      leftEqual = 0;
+  }
+  else /*src1->leftType == 1 && src2->leftType == 0*/{
+    if(src1->left == src2->left ||
+       src1->left == src2->left->getPrev()
+       )
+      leftEqual = 1;
+    else 
+      leftEqual = 0;
+  }
+
+  /*the same thing for right*/
+  /*The case when both are vertices should not happen*/
+  assert(! (src1->rightType == 0 && src2->rightType == 0));    
+  if(src1->rightType == 0 && src2->rightType == 1){
+    if(src1->right == src2->right ||
+       src1->right->getPrev() == src2->right
+       )
+      rightEqual = 1;
+    else
+      rightEqual = 0;
+  }
+  else if(src1->rightType == 1 && src2->rightType == 1){
+    if(src1->right == src2->right)
+      rightEqual = 1;
+    else
+      rightEqual = 0;
+  }
+  else /*src1->rightType == 1 && src2->rightType == 0*/{
+    if(src1->right == src2->right ||
+       src1->right == src2->right->getPrev()
+       )
+      rightEqual = 1;
+    else 
+      rightEqual = 0;
+  }
+  
+  return (leftEqual == 1 || rightEqual == 1);
+}
+
+/*given (x_1, y_1) and (x_2, y_2), and y
+ *return x such that (x,y) is on the line
+ */
+inline/*static*/ Real intersectHoriz(Real x1, Real y1, Real x2, Real y2, Real y)
+{
+  return ((y2==y1)? (x1+x2)*Real(0.5) : x1 + ((y-y1)/(y2-y1)) * (x2-x1));
+/*
+  if(y2 == y1) return (x1+x2)*0.5;
+  else return x1 + ((y-y1)/(y2-y1)) * (x2-x1);
+*/
+}
+
+/*compare two edges of a polygon.
+ *edge A < edge B if there is a horizontal line so that the intersection
+ *with A is to the left of the intersection with B.
+ *This function is used in sweepY for the dynamic search tree insertion to
+ *order the edges.
+ * Implementation: (x_1,y_1) and (x_2, y_2)
+ */
+static Int compEdges(directedLine *e1, directedLine *e2)
+{
+  Real* head1 = e1->head();
+  Real* tail1 = e1->tail();
+  Real* head2 = e2->head();
+  Real* tail2 = e2->tail();
+/*
+  Real h10 = head1[0];
+  Real h11 = head1[1];
+  Real t10 = tail1[0];
+  Real t11 = tail1[1];
+  Real h20 = head2[0];
+  Real h21 = head2[1];
+  Real t20 = tail2[0];
+  Real t21 = tail2[1];
+*/
+  Real e1_Ymax, e1_Ymin, e2_Ymax, e2_Ymin;
+/*
+  if(h11>t11) {
+    e1_Ymax= h11;
+    e1_Ymin= t11;
+  }
+  else{
+    e1_Ymax = t11;
+    e1_Ymin = h11;
+  }
+
+  if(h21>t21) {
+    e2_Ymax= h21;
+    e2_Ymin= t21;
+  }
+  else{
+    e2_Ymax = t21;
+    e2_Ymin = h21;
+  }
+*/
+ 
+  if(head1[1]>tail1[1]) {
+    e1_Ymax= head1[1];
+    e1_Ymin= tail1[1];
+  }
+  else{
+    e1_Ymax = tail1[1];
+    e1_Ymin = head1[1];
+  }
+
+  if(head2[1]>tail2[1]) {
+    e2_Ymax= head2[1];
+    e2_Ymin= tail2[1];
+  }
+  else{
+    e2_Ymax = tail2[1];
+    e2_Ymin = head2[1];
+  }
+
+  
+  /*Real e1_Ymax = max(head1[1], tail1[1]);*/ /*max(e1->head()[1], e1->tail()[1]);*/
+  /*Real e1_Ymin = min(head1[1], tail1[1]);*/ /*min(e1->head()[1], e1->tail()[1]);*/
+  /*Real e2_Ymax = max(head2[1], tail2[1]);*/ /*max(e2->head()[1], e2->tail()[1]);*/
+  /*Real e2_Ymin = min(head2[1], tail2[1]);*/ /*min(e2->head()[1], e2->tail()[1]);*/
+
+  Real Ymax = min(e1_Ymax, e2_Ymax);
+  Real Ymin = max(e1_Ymin, e2_Ymin);
+    
+  Real y = Real(0.5)*(Ymax + Ymin);
+
+/*  Real x1 = intersectHoriz(e1->head()[0], e1->head()[1], e1->tail()[0], e1->tail()[1], y);
+  Real x2 = intersectHoriz(e2->head()[0], e2->head()[1], e2->tail()[0], e2->tail()[1], y);
+*/
+/*
+  Real x1 = intersectHoriz(h10, h11, t10, t11, y);
+  Real x2 = intersectHoriz(h20, h21, t20, t21, y);
+*/
+  Real x1 = intersectHoriz(head1[0], head1[1], tail1[0], tail1[1], y);
+  Real x2 = intersectHoriz(head2[0], head2[1], tail2[0], tail2[1], y);
+
+  if(x1<= x2) return -1;
+  else return 1;
+}
+  
+/*used by sort precedures
+ */
+static Int compInY(directedLine* v1, directedLine* v2)
+{
+  return v1->compInY(v2);
+}
+
+void findDiagonals(Int total_num_edges, directedLine** sortedVertices, sweepRange** ranges, Int& num_diagonals, directedLine** diagonal_vertices)
+{
+  Int i,j,k;
+
+  k=0;
+
+  for(i=0; i<total_num_edges; i++)
+    {
+      directedLine* vert =sortedVertices[i];
+      directedLine* thisEdge = vert;
+      directedLine* prevEdge = vert->getPrev();
+/*
+printf("find i=%i\n", i);            
+printf("the vertex is\n");
+vert->printSingle();
+*/
+      if(isBelow(vert, thisEdge) && isBelow(vert, prevEdge) && compEdges(prevEdge, thisEdge)<0)
+	{
+	  /*this is an upward interior cusp*/
+	  diagonal_vertices[k++] = vert;
+
+	  for(j=i+1; j<total_num_edges; j++)
+	    if(sweepRangeEqual(ranges[i], ranges[j]))
+	      {
+		diagonal_vertices[k++] = sortedVertices[j];
+		break;
+	      }
+	  assert(j<total_num_edges);
+
+
+	}
+      else if(isAbove(vert, thisEdge) && isAbove(vert, prevEdge) && compEdges(prevEdge, thisEdge)>0)
+	{
+	  /*this is an downward interior cusp*/
+	  diagonal_vertices[k++] = vert;
+	  for(j=i-1; j>=0; j--)
+	    if(sweepRangeEqual(ranges[i], ranges[j]))
+	      {
+		diagonal_vertices[k++] = sortedVertices[j];
+		break;
+	      }
+/*	  printf("j=%i\n", j);*/
+	  assert(j>=0);
+
+
+
+	}
+    }
+  num_diagonals = k/2;
+}
+
+/*get rid of repeated diagonlas so that each diagonal appears only once in the array
+ */
+Int deleteRepeatDiagonals(Int num_diagonals, directedLine** diagonal_vertices, directedLine** new_vertices)
+{
+  Int i,k;
+  Int j,l;
+  Int index;
+  index=0;
+  for(i=0,k=0; i<num_diagonals; i++, k+=2)
+    {
+      Int isRepeated=0;
+      /*check the diagonla (diagonal_vertice[k], diagonal_vertices[k+1])
+       *is repeated or not
+       */
+      for(j=0,l=0; j<index; j++, l+=2)
+	{
+	  if(
+	     (diagonal_vertices[k] == new_vertices[l] && 
+	      diagonal_vertices[k+1] == new_vertices[l+1]
+	      )
+	     ||
+	     (
+	      diagonal_vertices[k] == new_vertices[l+1] && 
+	      diagonal_vertices[k+1] == new_vertices[l]
+	      )
+	     )
+	    {
+	      isRepeated=1;
+	      break;
+	    }
+	}
+      if(! isRepeated)
+	{
+	  new_vertices[index+index] = diagonal_vertices[k];
+	  new_vertices[index+index+1] = diagonal_vertices[k+1];	  
+	  index++;
+	}
+    }
+  return index;
+}
+
+/*for debug only*/	  
+directedLine** DBGfindDiagonals(directedLine *polygons, Int& num_diagonals)
+{
+  Int total_num_edges = 0;
+  directedLine** array = polygons->toArrayAllPolygons(total_num_edges);
+  quicksort( (void**)array, 0, total_num_edges-1, (Int (*)(void*, void*)) compInY);
+  sweepRange** ranges = (sweepRange**) malloc(sizeof(sweepRange*) * total_num_edges);
+  assert(ranges);
+
+  sweepY(total_num_edges, array, ranges);
+
+ directedLine** diagonal_vertices = (directedLine**) malloc(sizeof(directedLine*) * total_num_edges);
+  assert(diagonal_vertices);
+  findDiagonals(total_num_edges, array, ranges, num_diagonals, diagonal_vertices);
+
+  num_diagonals=deleteRepeatDiagonals(num_diagonals, diagonal_vertices, diagonal_vertices);
+  return diagonal_vertices;
+
+}
+
+
+/*partition into Y-monotone polygons*/
+directedLine* partitionY(directedLine *polygons, sampledLine **retSampledLines)
+{
+  Int total_num_edges = 0;
+  directedLine** array = polygons->toArrayAllPolygons(total_num_edges);
+
+  quicksort( (void**)array, 0, total_num_edges-1, (Int (*)(void*, void*)) compInY);
+
+  sweepRange** ranges = (sweepRange**) malloc(sizeof(sweepRange*) * (total_num_edges));
+  assert(ranges);
+
+
+
+  sweepY(total_num_edges, array, ranges);
+
+
+
+  /*the diagonal vertices are stored as:
+   *v0-v1: 1st diagonal
+   *v2-v3: 2nd diagonal
+   *v5-v5: 3rd diagonal
+   *...
+   */
+
+
+  Int num_diagonals;
+  /*number diagonals is < total_num_edges*total_num_edges*/
+  directedLine** diagonal_vertices = (directedLine**) malloc(sizeof(directedLine*) * total_num_edges*2/*total_num_edges*/);
+  assert(diagonal_vertices);
+
+
+
+  findDiagonals(total_num_edges, array, ranges, num_diagonals, diagonal_vertices);
+
+
+
+  directedLine* ret_polygons = polygons;
+  sampledLine* newSampledLines = NULL;
+  Int i,k;
+
+num_diagonals=deleteRepeatDiagonals(num_diagonals, diagonal_vertices, diagonal_vertices);
+
+
+
+  Int *removedDiagonals=(Int*)malloc(sizeof(Int) * num_diagonals);
+  for(i=0; i<num_diagonals; i++)
+    removedDiagonals[i] = 0;
+
+
+
+
+
+  for(i=0,k=0; i<num_diagonals; i++,k+=2)
+    {
+
+
+      directedLine* v1=diagonal_vertices[k];
+      directedLine* v2=diagonal_vertices[k+1];
+      directedLine* ret_p1;
+      directedLine* ret_p2;
+      
+      /*we ahve to determine whether v1 and v2 belong to the same polygon before
+       *their structure are modified by connectDiagonal().
+       */
+/*
+      directedLine *root1 = v1->findRoot();
+      directedLine *root2 = v2->findRoot();
+      assert(root1);      
+      assert(root2);
+*/
+
+directedLine*  root1 = v1->rootLinkFindRoot();
+directedLine*  root2 = v2->rootLinkFindRoot();
+
+      if(root1 != root2)
+	{
+
+	  removedDiagonals[i] = 1;
+	  sampledLine* generatedLine;
+
+
+
+	  v1->connectDiagonal(v1,v2, &ret_p1, &ret_p2, &generatedLine, ret_polygons);
+
+
+
+	  newSampledLines = generatedLine->insert(newSampledLines);
+/*
+	  ret_polygons = ret_polygons->cutoffPolygon(root1);
+
+	  ret_polygons = ret_polygons->cutoffPolygon(root2);
+	  ret_polygons = ret_p1->insertPolygon(ret_polygons);
+root1->rootLinkSet(ret_p1);
+root2->rootLinkSet(ret_p1);
+ret_p1->rootLinkSet(NULL);
+ret_p2->rootLinkSet(ret_p1);
+*/
+	  ret_polygons = ret_polygons->cutoffPolygon(root2);
+
+
+
+root2->rootLinkSet(root1);
+ret_p1->rootLinkSet(root1);
+ret_p2->rootLinkSet(root1);
+
+       /*now that we have connected the diagonal v1 and v2, 
+        *we have to check those unprocessed diagonals which 
+        *have v1 or v2 as an end point. Notice that the head of v1
+        *has the same coodinates as the head of v2->prev, and the head of
+        *v2 has the same coordinate as the head of v1->prev. 
+        *Suppose these is a diagonal (v1, x). If (v1,x) is still a valid
+        *diagonal, then x should be on the left hand side of the directed line:        *v1->prev->head -- v1->head -- v1->tail. Otherwise, (v1,x) should be  
+        *replaced by (v2->prev, x), that is, x is on the left of 
+        * v2->prev->prev->head, v2->prev->head, v2->prev->tail.
+        */
+        Int ii, kk;
+        for(ii=0, kk=0; ii<num_diagonals; ii++, kk+=2)
+	  if( removedDiagonals[ii]==0)
+	    {
+	      directedLine* d1=diagonal_vertices[kk];
+	      directedLine* d2=diagonal_vertices[kk+1];
+	      /*check d1, and replace diagonal_vertices[kk] if necessary*/
+	      if(d1 == v1) {
+		/*check if d2 is to left of v1->prev->head:v1->head:v1->tail*/
+		if(! pointLeft2Lines(v1->getPrev()->head(), 
+				     v1->head(), v1->tail(), d2->head()))
+		  {
+/*
+		    assert(pointLeft2Lines(v2->getPrev()->getPrev()->head(),
+					   v2->getPrev()->head(), 
+					   v2->getPrev()->tail(), d2->head()));
+*/
+		    diagonal_vertices[kk] = v2->getPrev();
+		  }
+	      }
+	      if(d1 == v2) {
+		/*check if d2 is to left of v2->prev->head:v2->head:v2->tail*/
+		if(! pointLeft2Lines(v2->getPrev()->head(),
+				     v2->head(), v2->tail(), d2->head()))
+		  {
+/*
+		    assert(pointLeft2Lines(v1->getPrev()->getPrev()->head(),
+					   v1->getPrev()->head(),
+					   v1->getPrev()->tail(), d2->head()));
+*/
+		    diagonal_vertices[kk] = v1->getPrev();
+		  }
+	      }
+	      /*check d2 and replace diagonal_vertices[k+1] if necessary*/
+	      if(d2 == v1) {
+		/*check if d1 is to left of v1->prev->head:v1->head:v1->tail*/
+		if(! pointLeft2Lines(v1->getPrev()->head(), 
+				     v1->head(), v1->tail(), d1->head()))
+		  {
+/*		    assert(pointLeft2Lines(v2->getPrev()->getPrev()->head(),
+					   v2->getPrev()->head(), 
+					   v2->getPrev()->tail(), d1->head()));
+*/
+		    diagonal_vertices[kk+1] = v2->getPrev();
+		  }
+	      }
+	      if(d2 == v2) {
+		/*check if d1 is to left of v2->prev->head:v2->head:v2->tail*/
+		if(! pointLeft2Lines(v2->getPrev()->head(),
+				     v2->head(), v2->tail(), d1->head()))
+		  {
+/*		    assert(pointLeft2Lines(v1->getPrev()->getPrev()->head(),
+					   v1->getPrev()->head(),
+					   v1->getPrev()->tail(), d1->head()));
+*/
+		    diagonal_vertices[kk+1] = v1->getPrev();
+		  }
+	      }
+	    }					    	       
+}/*end if (root1 not equal to root 2)*/
+}
+
+  /*second pass,  now all diagoals should belong to the same polygon*/
+
+
+
+  for(i=0,k=0; i<num_diagonals; i++, k += 2)
+    if(removedDiagonals[i] == 0) 
+      {
+
+
+	directedLine* v1=diagonal_vertices[k];
+	directedLine* v2=diagonal_vertices[k+1];
+
+
+
+	directedLine* ret_p1;
+	directedLine* ret_p2;
+
+	/*we ahve to determine whether v1 and v2 belong to the same polygon before
+	 *their structure are modified by connectDiagonal().
+	 */
+	directedLine *root1 = v1->findRoot();
+/*
+	directedLine *root2 = v2->findRoot();
+
+
+
+	assert(root1);      
+	assert(root2);      
+	assert(root1 == root2);
+  */    
+	sampledLine* generatedLine;
+
+
+
+	v1->connectDiagonal(v1,v2, &ret_p1, &ret_p2, &generatedLine, ret_polygons);
+	newSampledLines = generatedLine->insert(newSampledLines);
+
+	ret_polygons = ret_polygons->cutoffPolygon(root1);
+
+	ret_polygons = ret_p1->insertPolygon(ret_polygons);
+
+	ret_polygons = ret_p2->insertPolygon(ret_polygons);
+
+
+
+	for(Int j=i+1; j<num_diagonals; j++) 
+	  {
+	    if(removedDiagonals[j] ==0)
+	      {
+
+		directedLine* temp1=diagonal_vertices[2*j];
+		directedLine* temp2=diagonal_vertices[2*j+1];
+               if(temp1==v1 || temp1==v2 || temp2==v1 || temp2==v2)
+		if(! temp1->samePolygon(temp1, temp2))
+		  {
+		    /*if temp1 and temp2 are in different polygons, 
+		     *then one of them must be v1 or v2.
+		     */
+
+
+
+		    assert(temp1==v1 || temp1 == v2 || temp2==v1 || temp2 ==v2);
+		    if(temp1==v1) 
+		      {
+			diagonal_vertices[2*j] = v2->getPrev();
+		      }
+		    if(temp2==v1)
+		      {
+			diagonal_vertices[2*j+1] = v2->getPrev();
+		      }
+		    if(temp1==v2)
+		      {
+			diagonal_vertices[2*j] = v1->getPrev();		      
+		      }
+		    if(temp2==v2)
+		      {
+			diagonal_vertices[2*j+1] = v1->getPrev();
+		      }
+		  }
+	      }
+	  }      
+
+      }
+
+  /*clean up spaces*/
+  free(array);
+  free(ranges);
+  free(diagonal_vertices);
+  free(removedDiagonals);
+
+  *retSampledLines = newSampledLines;
+  return ret_polygons;
+}
+	
+/*given a set of simple polygons where the interior 
+ *is decided by left-hand principle,
+ *return a range (sight) for each vertex. This is called
+ *Trapezoidalization.
+ */ 
+void sweepY(Int nVertices, directedLine** sortedVertices, sweepRange** ret_ranges)
+{
+  Int i;
+  /*for each vertex in the sorted list, update the binary search tree.
+   *and store the range information for each vertex.
+   */
+  treeNode* searchTree = NULL;
+  for(i=0; i<nVertices;i++)
+    {
+
+      directedLine* vert = sortedVertices[i];
+
+      directedLine* thisEdge = vert;
+      directedLine* prevEdge = vert->getPrev();
+      
+      if(isBelow(vert, thisEdge) && isAbove(vert, prevEdge))
+	{
+
+	  /*case 1: this < v < prev
+	   *the polygon is going down at v, the interior is to 
+	   *the right hand side.
+	   * find the edge to the right of thisEdge for right range.
+           * delete thisEdge
+           * insert prevEdge
+	   */
+	  treeNode* thisNode = TreeNodeFind(searchTree, thisEdge, ( Int (*) (void *, void *))compEdges);
+	  assert(thisNode);
+
+	  treeNode* succ = TreeNodeSuccessor(thisNode);
+	  assert(succ);
+	  searchTree = TreeNodeDeleteSingleNode(searchTree, thisNode);
+	  searchTree = TreeNodeInsert(searchTree, TreeNodeMake(prevEdge), ( Int (*) (void *, void *))compEdges);
+
+
+	  ret_ranges[i] = sweepRangeMake(vert, 0, (directedLine*) (succ->key), 1);
+
+	}
+      else if(isAbove(vert, thisEdge) && isBelow(vert, prevEdge))
+	{
+
+	  /*case 2: this > v > prev
+	   *the polygon is going up at v, the interior is to 
+	   *the left hand side.
+	   * find the edge to the left of thisEdge for left range.
+           * delete prevEdge
+           * insert thisEdge
+	   */	  
+	  treeNode* prevNode = TreeNodeFind(searchTree, prevEdge, ( Int (*) (void *, void *))compEdges);
+	  assert(prevNode);
+	  treeNode* pred = TreeNodePredecessor(prevNode);
+	  searchTree = TreeNodeDeleteSingleNode(searchTree, prevNode);
+	  searchTree = TreeNodeInsert(searchTree, TreeNodeMake(thisEdge), ( Int (*) (void *, void *))compEdges);
+	  ret_ranges[i] = sweepRangeMake((directedLine*)(pred->key), 1, vert, 0);
+	}
+      else if(isAbove(vert, thisEdge) && isAbove(vert, prevEdge))
+	{
+
+	  /*case 3: insert both edges*/
+	  treeNode* thisNode = TreeNodeMake(thisEdge);
+	  treeNode* prevNode = TreeNodeMake(prevEdge);	  
+	  searchTree = TreeNodeInsert(searchTree, thisNode, ( Int (*) (void *, void *))compEdges);
+	  searchTree = TreeNodeInsert(searchTree, prevNode, ( Int (*) (void *, void *))compEdges);	  
+	  if(compEdges(thisEdge, prevEdge)<0)  /*interior cusp*/
+	    {
+
+	      treeNode* leftEdge = TreeNodePredecessor(thisNode);
+	      treeNode* rightEdge = TreeNodeSuccessor(prevNode);
+	      ret_ranges[i] = sweepRangeMake( (directedLine*) leftEdge->key, 1, 
+					     (directedLine*) rightEdge->key, 1
+					     );
+	    }
+	  else /*exterior cusp*/
+	    {
+
+	      ret_ranges[i] = sweepRangeMake( prevEdge, 1, thisEdge, 1);
+	    }
+	}
+      else if(isBelow(vert, thisEdge) && isBelow(vert, prevEdge))
+	{
+
+	  /*case 4: delete both edges*/
+	  treeNode* thisNode = TreeNodeFind(searchTree, thisEdge, ( Int (*) (void *, void *))compEdges);
+	  treeNode* prevNode = TreeNodeFind(searchTree, prevEdge, ( Int (*) (void *, void *))compEdges);
+	  if(compEdges(thisEdge, prevEdge)>0) /*interior cusp*/
+	    {
+	      treeNode* leftEdge = TreeNodePredecessor(prevNode);
+	      treeNode* rightEdge = TreeNodeSuccessor(thisNode);
+	      ret_ranges[i] = sweepRangeMake( (directedLine*) leftEdge->key, 1, 
+					     (directedLine*) rightEdge->key, 1
+					     );
+	    }
+	  else /*exterior cusp*/
+	    {
+	      ret_ranges[i] = sweepRangeMake( thisEdge, 1, prevEdge, 1);
+	    }
+	  searchTree = TreeNodeDeleteSingleNode(searchTree, thisNode);
+	  searchTree = TreeNodeDeleteSingleNode(searchTree, prevNode);
+	}
+      else
+	{
+	  fprintf(stderr,"error in partitionY.C, invalid case\n");
+	  printf("vert is\n");
+	  vert->printSingle();
+	  printf("thisEdge is\n");
+	  thisEdge->printSingle();
+	  printf("prevEdge is\n");
+	  prevEdge->printSingle();
+	  
+	  exit(1);
+	}
+    }
+
+  /*finaly clean up space: delete the search tree*/
+  TreeNodeDeleteWholeTree(searchTree);
+}
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionY.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionY.h
new file mode 100644
index 000000000..8dda409de
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/partitionY.h
@@ -0,0 +1,97 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+ *partitionY.h:
+ *partition a polygon into a Y-monotone polygon:
+ * A polygon is Y-monotone if the boundary can be split into two polygon chains
+ *A and B such that each chain is Y-monotonic that is the intersection of any
+ *horizontal line intersects each chain has at most one connected componenets
+ * (empty, single point or a single line).
+ * 
+ * A vertex is a cusp if both its ajacent vertices are either at or above v, 
+ *or both at or below v. In addition, at least one of the ajacent verteces is
+ *strictly below or above v. 
+ * A vertex is a relex vertex if the internals angle is strictly greater than 
+ *180. In other words, if the the signed area is negative:
+ *(x1, y1), (x2, y2), (x3, y3) are the three vertices along a polygon, the 
+ *order is such that left hand side is inside the polygon. Then (x2,y2) is
+ *reflex if: 
+ *  (x2-x1, y2-y1) cross (x3-x1, y3-y1) <0.
+ *A vertex is an interior cusp if it is a cusp and a reflex.
+ *A vertex is an exterior cusp if it is a cusp but not a reflex.
+ *
+ */
+
+#ifndef _PARTITIONY_H
+#define _PARTITIONY_H
+
+#include "directedLine.h"
+
+/*whether an edge is below a vertex*/
+Int isBelow(directedLine *v, directedLine *e);
+
+/*whether an edge is above a vertex*/
+Int isAbove(directedLine *v, directedLine *e);
+
+/*not-cusp,
+ *inerior cusp
+ *exterior cusp
+ */
+Int cuspType(directedLine *v);
+
+/*used in trapezoidalization*/
+typedef struct sweepRange{
+  directedLine *left;
+  Int leftType; /*either a vertex (leftType=0) or an edge (leftType =1) */
+  directedLine *right;
+  Int rightType; /*either a vertex (rightType=0) or an edge (rightType =1) */  
+} sweepRange;
+
+sweepRange* sweepRangeMake(directedLine* left, Int leftType,
+			   directedLine* right, Int rightType);
+
+void sweepRangeDelete(sweepRange* range);
+Int sweepRangeEqual(sweepRange* sr1, sweepRange* sr2);
+
+/*given a set of simple polygons where the interior 
+ *is decided by left-hand principle,
+ *return a range (sight) for each vertex. This is called
+ *Trapezoidalization.
+ */
+void sweepY(Int nVertices, directedLine **sortedVerteces, sweepRange** ret_ranges);
+
+
+directedLine* partitionY(directedLine *polygons, sampledLine **retSampledLines);
+
+void findDiagonals(Int total_num_edges, directedLine** sortedVertices, sweepRange** ranges, Int& num_diagonals, directedLine** diagonal_vertices);
+
+directedLine** DBGfindDiagonals(directedLine *polygons, Int& num_diagonals);
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/polyDBG.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/polyDBG.cc
new file mode 100644
index 000000000..4d04df73f
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/polyDBG.cc
@@ -0,0 +1,734 @@
+/*
+** 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 <math.h>
+#include "zlassert.h"
+#include "polyDBG.h"
+
+#ifdef __WATCOMC__
+#pragma warning 14  10
+#pragma warning 391 10
+#pragma warning 726 10
+#endif
+
+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;
+}
+
+Int DBG_isConvex(directedLine *poly)
+{
+  directedLine* temp;
+  if(area(poly->head(), poly->tail(), poly->getNext()->tail()) < 0.00000)
+    return 0;
+  for(temp = poly->getNext(); temp != poly; temp = temp->getNext())
+    {
+      if(area(temp->head(), temp->tail(), temp->getNext()->tail()) < 0.00000)
+	return 0;
+    }
+  return 1;
+}
+
+Int DBG_is_U_monotone(directedLine* poly)
+{
+  Int n_changes = 0;
+  Int prev_sign;
+  Int cur_sign;
+   directedLine* temp;
+  cur_sign = compV2InX(poly->tail(), poly->head());
+
+  n_changes = (compV2InX(poly->getPrev()->tail(), poly->getPrev()->head())
+	       != cur_sign);
+
+  for(temp = poly->getNext(); temp != poly; temp = temp->getNext())
+    {
+      prev_sign = cur_sign;
+      cur_sign = compV2InX(temp->tail(), temp->head());
+
+      if(cur_sign != prev_sign)
+	n_changes++;
+    }
+
+  if(n_changes ==2) return 1;
+  else return 0;
+}
+
+/*if u-monotone, and there is a long horizontal edge*/
+Int DBG_is_U_direction(directedLine* poly)
+{
+/*
+  if(! DBG_is_U_monotone(poly))
+    return 0;
+*/
+  Int V_count = 0;
+  Int U_count = 0;
+  directedLine* temp;
+  if( fabs(poly->head()[0] - poly->tail()[0]) <= fabs(poly->head()[1]-poly->tail()[1]))
+    V_count += poly->get_npoints();
+  else
+    U_count += poly->get_npoints();
+  /*
+  else if(poly->head()[1] == poly->tail()[1])
+    U_count += poly->get_npoints();
+    */
+  for(temp = poly->getNext(); temp != poly; temp = temp->getNext())
+    {
+      if( fabs(temp->head()[0] - temp->tail()[0]) <= fabs(temp->head()[1]-temp->tail()[1]))
+	V_count += temp->get_npoints();
+      else
+	U_count += temp->get_npoints();
+      /*
+      if(temp->head()[0] == temp->tail()[0])
+	V_count += temp->get_npoints();
+      else if(temp->head()[1] == temp->tail()[1])
+	U_count += temp->get_npoints();
+	*/
+    }
+
+  if(U_count > V_count) return 1;
+  else return 0;
+}
+
+/*given two line segments, determine whether
+ *they intersect each other or not.
+ *return 1 if they do,
+ *return 0 otherwise
+ */
+Int DBG_edgesIntersect(directedLine* l1, directedLine* l2)
+{
+  if(l1->getNext() == l2)
+    {
+      if(area(l1->head(), l1->tail(), l2->tail()) == 0) //colinear
+	{
+	  if( (l1->tail()[0] - l1->head()[0])*(l2->tail()[0]-l2->head()[0]) +
+	     (l1->tail()[1] - l1->head()[1])*(l2->tail()[1]-l2->head()[1]) >=0)
+	    return 0; //not intersect
+	  else
+	    return 1;
+	}
+      //else we use the normal code
+    }
+  else if(l1->getPrev() == l2)
+    {
+      if(area(l2->head(), l2->tail(), l1->tail()) == 0) //colinear
+	{
+	  if( (l2->tail()[0] - l2->head()[0])*(l1->tail()[0]-l1->head()[0]) +
+	     (l2->tail()[1] - l2->head()[1])*(l1->tail()[1]-l1->head()[1]) >=0)
+	    return 0; //not intersect
+	  else
+	    return 1;
+	}
+      //else we use the normal code
+    }
+  else //the two edges are not connected
+    {
+      if((l1->head()[0] == l2->head()[0] &&
+	 l1->head()[1] == l2->head()[1]) ||
+	 (l1->tail()[0] == l2->tail()[0] &&
+	 l1->tail()[1] == l2->tail()[1]))
+	return 1;
+
+    }
+
+
+  if(
+     (
+      area(l1->head(), l1->tail(), l2->head())
+      *
+      area(l1->head(), l1->tail(), l2->tail())
+      < 0
+      )
+     &&
+     (
+      area(l2->head(), l2->tail(), l1->head())
+      *area(l2->head(), l2->tail(), l1->tail())
+      < 0
+      )
+     )
+    return 1;
+  else
+    return 0;
+}
+
+/*whether AB and CD intersect
+ *return 1 if they do
+ *retur 0 otheriwse
+ */
+Int DBG_edgesIntersectGen(Real A[2], Real B[2], Real C[2], Real D[2])
+{
+  if(
+     (
+      area(A, B, C) * area(A,B,D) <0
+      )
+     &&
+     (
+      area(C,D,A) * area(C,D,B) < 0
+      )
+     )
+    return 1;
+  else
+    return 0;
+}
+
+/*determien whether    (A,B) interesect chain[start] to [end]
+ */
+Int DBG_intersectChain(vertexArray* chain, Int start, Int end, Real A[2], Real B[2])
+{
+  Int i;
+  for(i=start; i<=end-2; i++)
+    if(DBG_edgesIntersectGen(chain->getVertex(i), chain->getVertex(i+1), A, B))
+      return 1;
+
+  return 0;
+}
+
+/*determine whether a polygon intersect itself or not
+ *return 1 is it does,
+ *	 0 otherwise
+ */
+Int DBG_polygonSelfIntersect(directedLine* poly)
+{
+  directedLine* temp1;
+  directedLine* temp2;
+  temp1=poly;
+  for(temp2=temp1->getNext(); temp2 != temp1; temp2=temp2->getNext())
+    {
+      if(DBG_edgesIntersect(temp1, temp2))
+	{
+	  return 1;
+	}
+
+    }
+
+  for(temp1=poly->getNext(); temp1 != poly; temp1 = temp1->getNext())
+    for(temp2=temp1->getNext(); temp2 != temp1; temp2=temp2->getNext())
+      {
+	if(DBG_edgesIntersect(temp1, temp2))
+	  {
+	    return 1;
+	  }
+      }
+  return 0;
+}
+
+/*check whether a line segment intersects a  polygon
+ */
+Int DBG_edgeIntersectPoly(directedLine* edge, directedLine* poly)
+{
+  directedLine* temp;
+  if(DBG_edgesIntersect(edge, poly))
+    return 1;
+  for(temp=poly->getNext(); temp != poly; temp=temp->getNext())
+    if(DBG_edgesIntersect(edge, temp))
+      return 1;
+  return 0;
+}
+
+/*check whether two polygons intersect
+ */
+Int DBG_polygonsIntersect(directedLine* p1, directedLine* p2)
+{
+  directedLine* temp;
+  if(DBG_edgeIntersectPoly(p1, p2))
+    return 1;
+  for(temp=p1->getNext(); temp!= p1; temp = temp->getNext())
+    if(DBG_edgeIntersectPoly(temp, p2))
+      return 1;
+  return 0;
+}
+
+/*check whether there are polygons intersecting each other in
+ *a list of polygons
+ */
+Int DBG_polygonListIntersect(directedLine* pList)
+{
+  directedLine *temp;
+  for(temp=pList; temp != NULL; temp = temp->getNextPolygon())
+    if(DBG_polygonSelfIntersect(temp))
+      return 1;
+  directedLine* temp2;
+  for(temp=pList; temp!=NULL; temp=temp->getNextPolygon())
+    {
+      for(temp2=temp->getNextPolygon(); temp2 != NULL; temp2=temp2->getNextPolygon())
+	if(DBG_polygonsIntersect(temp, temp2))
+	  return 1;
+    }
+
+  return 0;
+}
+
+
+Int DBG_isCounterclockwise(directedLine* poly)
+{
+  return (poly->polyArea() > 0);
+}
+
+/*ray: v0 with direction (dx,dy).
+ *edge: v1-v2.
+ * the extra point v10[2] is given for the information at
+ *v1. Basically this edge is connectd to edge
+ * v10-v1. If v1 is on the ray,
+ * then we need v10  to determine whether this ray intersects
+ * the edge or not (that is, return 1 or return 0).
+ * If v1 is on the ray, then if v2 and v10 are on the same side of the ray,
+ * we return 0, otherwise return 1.
+ *For v2, if v2 is on the ray, we always return 0.
+ *Notice that v1 and v2 are not symmetric. So the edge is directed!!!
+ * The purpose for this convention is such that: a point is inside a polygon
+ * if and only if it intersets with odd number of edges.
+ */
+Int DBG_rayIntersectEdge(Real v0[2], Real dx, Real dy, Real v10[2], Real v1[2], Real v2[2])
+{
+/*
+if( (v1[1] >= v0[1] && v2[1]<= v0[1] )
+  ||(v2[1] >= v0[1] && v1[1]<= v0[1] )
+   )
+  printf("rayIntersectEdge, *********\n");
+*/
+
+  Real denom = (v2[0]-v1[0])*(-dy) - (v2[1]-v1[1]) * (-dx);
+  Real nomRay = (v2[0]-v1[0]) * (v0[1] - v1[1]) - (v2[1]-v1[1])*(v0[0]-v1[0]);
+  Real nomEdge = (v0[0]-v1[0]) * (-dy) - (v0[1]-v1[1])*(-dx);
+
+
+  /*if the ray is parallel to the edge, return 0: not intersect*/
+  if(denom == 0.0)
+    return 0;
+
+  /*if v0 is on the edge, return 0: not intersect*/
+  if(nomRay == 0.0)
+    return 0;
+
+  /*if v1 is on the positive ray, and the neighbor of v1 crosses the ray
+   *return 1: intersect
+   */
+  if(nomEdge == 0)
+    { /*v1 is on the positive or negative ray*/
+
+/*
+      printf("v1 is on the ray\n");
+*/
+
+      if(dx*(v1[0]-v0[0])>=0 && dy*(v1[1]-v0[1])>=0) /*v1 on positive ray*/
+	{
+	  if(area(v0, v1, v10) * area(v0, v1, v2) >0)
+	    return 0;
+	  else
+	    return 1;
+	}
+      else /*v1 on negative ray*/
+	return 0;
+    }
+
+  /*if v2 is on the ray, always return 0: not intersect*/
+  if(nomEdge == denom) {
+/*    printf("v2 is on the ray\n");*/
+    return 0;
+  }
+
+  /*finally */
+  if(denom*nomRay>0 && denom*nomEdge>0 && nomEdge/denom <=1.0)
+    return 1;
+  return 0;
+}
+
+
+/*return the number of intersections*/
+Int DBG_rayIntersectPoly(Real v0[2], Real dx, Real dy, directedLine* poly)
+{
+  directedLine* temp;
+  Int count=0;
+  if(DBG_rayIntersectEdge(v0, dx, dy, poly->getPrev()->head(), poly->head(), poly->tail()))
+    count++;
+
+  for(temp=poly->getNext(); temp != poly; temp = temp->getNext())
+    if(DBG_rayIntersectEdge(v0, dx, dy, temp->getPrev()->head(), temp->head(), temp->tail()))
+      count++;
+/*printf("ray intersect poly: count=%i\n", count);*/
+  return count;
+}
+
+Int DBG_pointInsidePoly(Real v[2], directedLine* poly)
+{
+/*
+printf("enter pointInsidePoly , v=(%f,%f)\n", v[0], v[1]);
+printf("the polygon is\n");
+poly->printList();
+*/
+  /*for debug purpose*/
+  assert( (DBG_rayIntersectPoly(v,1,0,poly) % 2 )
+	 == (DBG_rayIntersectPoly(v,1,Real(0.1234), poly) % 2 )
+	 );
+  if(DBG_rayIntersectPoly(v, 1, 0, poly) % 2 == 1)
+    return 1;
+  else
+    return 0;
+}
+
+/*return the number of polygons which contain thie polygon
+ * as a subset
+ */
+Int DBG_enclosingPolygons(directedLine* poly, directedLine* list)
+{
+  directedLine* temp;
+  Int count=0;
+/*
+printf("%i\n", DBG_pointInsidePoly(poly->head(),
+				   list->getNextPolygon()
+				   ->getNextPolygon()
+				   ->getNextPolygon()
+				   ->getNextPolygon()
+));
+*/
+
+  for(temp = list; temp != NULL; temp = temp->getNextPolygon())
+    {
+      if(poly != temp)
+	if(DBG_pointInsidePoly(poly->head(), temp))
+	  count++;
+/*	printf("count=%i\n", count);*/
+    }
+  return count;
+}
+
+void  DBG_reverse(directedLine* poly)
+{
+  if(poly->getDirection() == INCREASING)
+    poly->putDirection(DECREASING);
+  else
+    poly->putDirection(INCREASING);
+
+  directedLine* oldNext = poly->getNext();
+  poly->putNext(poly->getPrev());
+  poly->putPrev(oldNext);
+
+  directedLine* temp;
+  for(temp=oldNext; temp!=poly; temp = oldNext)
+    {
+      if(temp->getDirection() == INCREASING)
+	temp->putDirection(DECREASING);
+      else
+	temp->putDirection(INCREASING);
+
+      oldNext = temp->getNext();
+      temp->putNext(temp->getPrev());
+      temp->putPrev(oldNext);
+    }
+  printf("reverse done\n");
+}
+
+Int DBG_checkConnectivity(directedLine *polygon)
+{
+  if(polygon == NULL) return 1;
+  directedLine* temp;
+  if(polygon->head()[0] != polygon->getPrev()->tail()[0] ||
+     polygon->head()[1] != polygon->getPrev()->tail()[1])
+    return 0;
+  for(temp=polygon->getNext(); temp != polygon; temp=temp->getNext())
+    {
+      if(temp->head()[0] != temp->getPrev()->tail()[0] ||
+	 temp->head()[1] != temp->getPrev()->tail()[1])
+	return 0;
+    }
+  return 1;
+}
+
+/*print out error message.
+ *If it cannot modify the polygon list to make it satify the
+ *requirements, return 1.
+ *otherwise modify the polygon list, and return 0
+ */
+Int DBG_check(directedLine *polyList)
+{
+  directedLine* temp;
+  if(polyList == NULL) return 0;
+
+  /*if there are intersections, print out error message
+   */
+  if(DBG_polygonListIntersect(polyList))
+    {
+      fprintf(stderr, "DBG_check: there are self intersections, don't know to modify the polygons\n");
+    return 1;
+    }
+
+  /*check the connectivity of each polygon*/
+  for(temp = polyList; temp!= NULL; temp = temp ->getNextPolygon())
+    {
+      if(! DBG_checkConnectivity(temp))
+	{
+	  fprintf(stderr, "DBG_check, polygon not connected\n");
+	  return 1;
+	}
+    }
+
+  /*check the orientation of each polygon*/
+  for(temp = polyList; temp!= NULL; temp = temp ->getNextPolygon())
+    {
+
+
+      Int correctDir;
+
+      if( DBG_enclosingPolygons(temp, polyList) % 2 == 0)
+	correctDir = 1; /*counterclockwise*/
+      else
+	correctDir = 0; /*clockwise*/
+
+      Int actualDir = DBG_isCounterclockwise(temp);
+
+      if(correctDir != actualDir)
+	{
+	  fprintf(stderr, "DBG_check: polygon with incorrect orientations. reversed\n");
+
+	  DBG_reverse(temp);
+	}
+
+    }
+  return 0;
+}
+
+/**************handle self intersections*****************/
+//determine whether e interects [begin, end] or not
+static directedLine* DBG_edgeIntersectChainD(directedLine *e,
+			       directedLine *begin, directedLine *end)
+{
+  directedLine *temp;
+  for(temp=begin; temp != end; temp = temp->getNext())
+    {
+      if(DBG_edgesIntersect(e, temp))
+	 return temp;
+    }
+  if(DBG_edgesIntersect(e, end))
+    return end;
+  return NULL;
+}
+
+//given a polygon, cut the edges off and finally obtain a
+//a polygon without intersections. The cut-off edges are
+//dealloated. The new polygon is returned.
+directedLine* DBG_cutIntersectionPoly(directedLine *polygon, int& cutOccur)
+{
+  directedLine *begin, *end, *next;
+  begin = polygon;
+  end = polygon;
+  cutOccur = 0;
+  while( (next = end->getNext()) != begin)
+    {
+      directedLine *interc = NULL;
+      if( (interc = DBG_edgeIntersectChainD(next, begin, end)))
+	{
+	  int fixed = 0;
+	  if(DBG_edgesIntersect(next, interc->getNext()))
+	     {
+	       //trying to fix it
+	       Real buf[2];
+	       int i;
+	       Int n=5;
+	       buf[0] = interc->tail()[0];
+	       buf[1] = interc->tail()[1];
+
+	       for(i=1; i<n; i++)
+		 {
+		   Real r = ((Real)i) / ((Real) n);
+		   Real u = (1-r) * interc->head()[0] + r * interc->tail()[0];
+		   Real v = (1-r) * interc->head()[1] + r * interc->tail()[1];
+		   interc->tail()[0] = interc->getNext()->head()[0] = u;
+		   interc->tail()[1] = interc->getNext()->head()[1] = v;
+		   if( (! DBG_edgesIntersect(next, interc)) &&
+		      (! DBG_edgesIntersect(next, interc->getNext())))
+		     break; //we fixed it
+		 }
+	       if(i==n) // we didn't fix it
+		 {
+		   fixed = 0;
+		   //back to original
+		   interc->tail()[0] = interc->getNext()->head()[0] = buf[0];
+		   interc->tail()[1] = interc->getNext()->head()[1] = buf[1];
+		 }
+	       else
+		 {
+		   fixed = 1;
+		 }
+	     }
+	  if(fixed == 0)
+	    {
+	      cutOccur = 1;
+	      begin->deleteSingleLine(next);
+
+	      if(begin != end)
+		{
+		  if(DBG_polygonSelfIntersect(begin))
+		    {
+		      directedLine* newEnd = end->getPrev();
+		      begin->deleteSingleLine(end);
+		      end = newEnd;
+		    }
+		}
+	    }
+	  else
+	    {
+	      end = end->getNext();
+	    }
+	}
+      else
+	{
+	  end = end->getNext();
+	}
+    }
+  return begin;
+}
+
+//given a polygon, cut the edges off and finally obtain a
+//a polygon without intersections. The cut-off edges are
+//dealloated. The new polygon is returned.
+#if 0 // UNUSED
+static directedLine* DBG_cutIntersectionPoly_notwork(directedLine *polygon)
+{
+  directedLine *crt;//current polygon
+  directedLine *begin;
+  directedLine *end;
+  directedLine *temp;
+  crt = polygon;
+  int find=0;
+  while(1)
+    {
+//printf("loop\n");
+      //if there are less than 3 edges, we should stop
+      if(crt->getPrev()->getPrev() == crt)
+	return NULL;
+
+      if(DBG_edgesIntersect(crt, crt->getNext()) ||
+	(crt->head()[0] == crt->getNext()->tail()[0] &&
+	crt->head()[1] == crt->getNext()->tail()[1])
+	 )
+	{
+	  find = 1;
+	  crt=crt->deleteChain(crt, crt->getNext());
+	}
+      else
+	{
+	  //now we know crt and crt->getNext do not intersect
+	  begin = crt;
+	  end = crt->getNext();
+//printf("begin=(%f,%f)\n", begin->head()[0], begin->head()[1]);
+//printf("end=(%f,%f)\n", end->head()[0], end->head()[1]);
+	  for(temp=end->getNext(); temp!=begin; temp= temp->getNext())
+	    {
+//printf("temp=(%f,%f)\n", temp->head()[0], temp->head()[1]);
+	       directedLine *intersect = DBG_edgeIntersectChainD(temp, begin, end);
+	       if(intersect != NULL)
+		{
+		  crt = crt->deleteChain(intersect, temp);
+		  find=1;
+		  break; //the for loop
+		}
+	      else
+		{
+		  end = temp;
+		}
+	    }
+	}
+      if(find == 0)
+	return crt;
+      else
+	find = 0;    //go to next loop
+}
+}
+#endif
+
+directedLine* DBG_cutIntersectionAllPoly(directedLine* list)
+{
+  directedLine* temp;
+  directedLine* tempNext=NULL;
+  directedLine* ret = NULL;
+  int cutOccur=0;
+  for(temp=list; temp != NULL; temp = tempNext)
+    {
+      directedLine *left;
+      tempNext = temp->getNextPolygon();
+
+      left = DBG_cutIntersectionPoly(temp, cutOccur);
+      if(left != NULL)
+	ret=left->insertPolygon(ret);
+    }
+  return ret;
+}
+
+sampledLine*  DBG_collectSampledLinesAllPoly(directedLine *polygonList)
+{
+  directedLine *temp;
+  sampledLine* tempHead = NULL;
+  sampledLine* tempTail = NULL;
+  sampledLine* cHead = NULL;
+  sampledLine* cTail = NULL;
+
+  if(polygonList == NULL)
+    return NULL;
+
+  DBG_collectSampledLinesPoly(polygonList, cHead, cTail);
+
+  assert(cHead);
+  assert(cTail);
+  for(temp = polygonList->getNextPolygon(); temp != NULL; temp = temp->getNextPolygon())
+    {
+      DBG_collectSampledLinesPoly(temp, tempHead, tempTail);
+      cTail->insert(tempHead);
+      cTail = tempTail;
+    }
+  return cHead;
+}
+
+void  DBG_collectSampledLinesPoly(directedLine *polygon, sampledLine*& retHead, sampledLine*& retTail)
+{
+  directedLine *temp;
+  retHead = NULL;
+  retTail = NULL;
+  if(polygon == NULL)
+    return;
+
+  retHead = retTail = polygon->getSampledLine();
+  for(temp = polygon->getNext(); temp != polygon; temp=temp->getNext())
+    {
+      retHead = temp->getSampledLine()->insert(retHead);
+    }
+}
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/polyDBG.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/polyDBG.h
new file mode 100644
index 000000000..74843d888
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/polyDBG.h
@@ -0,0 +1,68 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _POLYDBG_H
+#define _POLYDBG_H
+
+#include "definitions.h"
+#include "directedLine.h"
+#include "monoTriangulation.h"
+
+Int DBG_edgesIntersectGen(Real A[2], Real B[2], Real C[2], Real D[2]);
+Int DBG_intersectChain(vertexArray* chain, Int start, Int end, Real A[2], Real B[2]);
+  
+
+Int DBG_edgesIntersect(directedLine* l1, directedLine* l2);
+Int DBG_polygonSelfIntersect(directedLine* poly);
+Int DBG_edgeIntersectPoly(directedLine* edge, directedLine* poly);
+Int DBG_polygonsIntersect(directedLine* p1, directedLine* p2);
+Int DBG_polygonListIntersect(directedLine* pList);
+
+Int DBG_isCounterclockwise(directedLine* poly);
+Int DBG_rayIntersectEdge(Real v0[2], Real dx, Real dy, Real v10[2], Real v1[2], Real v2[2]);
+Int DBG_pointInsidePoly(Real v[2], directedLine* poly);
+Int DBG_enclosingPolygons(directedLine* poly, directedLine* list);
+void  DBG_reverse(directedLine* poly);
+Int DBG_check(directedLine *polyList);
+
+Int DBG_isConvex(directedLine *poly);
+Int DBG_is_U_direction(directedLine *poly);
+Int DBG_is_U_monotone(directedLine* poly);
+
+directedLine* DBG_cutIntersectionAllPoly(directedLine* list);
+directedLine* DBG_cutIntersectionPoly(directedLine *polygon, int& cutOccur);
+
+sampledLine*  DBG_collectSampledLinesAllPoly(directedLine *polygonList);
+
+void  DBG_collectSampledLinesPoly(directedLine *polygon, sampledLine*& retHead, sampledLine*& retTail);
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/polyUtil.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/polyUtil.cc
new file mode 100644
index 000000000..f9a27f402
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/polyUtil.cc
@@ -0,0 +1,90 @@
+/*
+** 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 "polyUtil.h"
+
+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;
+
+/*  return (B[0]-A[0])*(C[1]-A[1]) - (C[0]-A[0])*(B[1]-A[1]);*/
+}
+
+/*given a directed line A->B, and a point P, 
+ *determine whether P is to the left of AB.
+ *the line A->B (imagine it has beedn extended both 
+ *end to the infinity) divides the plan into two 
+ *half planes. When we walk from A to B, one
+ *half is to the left and the other half is to the right.
+ *return 1 if P is to the left.
+ *if P is on AB, 0 is returned.
+ */
+Int pointLeftLine(Real A[2], Real B[2],  Real P[2])
+{
+  if(area(A, B, P) >0) return 1;
+  else return 0;
+}
+
+/*given two directed line: A -> B -> C, and another point P.
+ *determine whether P is to the left hand side of A->B->C.
+ *Think of BA and BC extended as two rays. So that the plane is
+ * divided into two parts. One part is to the left we  walk from A 
+ *to B and to C, the other part is to the right.
+ * In order for P to be the left, P must be either to the left 
+ *of 
+ */
+Int pointLeft2Lines(Real A[2], Real B[2], Real C[2], Real P[2])
+{
+  Int C_left_AB = (area(A, B, C)>0);
+  Int P_left_AB = (area(A, B, P)>0);
+  Int P_left_BC = (area(B, C, P)>0);
+
+  if(C_left_AB)
+    {
+      return (P_left_AB && P_left_BC);
+    }
+  else
+    return  (P_left_AB || P_left_BC);
+}
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/polyUtil.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/polyUtil.h
new file mode 100644
index 000000000..1ca2ebcc0
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/polyUtil.h
@@ -0,0 +1,47 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _POLYUTIL_H
+#define _POLYUTIL_H
+
+#include "definitions.h"
+#ifdef __cplusplus
+extern "C" {
+#endif
+Real area(Real A[2], Real B[2], Real C[2]);
+
+Int pointLeftLine(Real A[2], Real B[2],  Real P[2]);
+Int pointLeft2Lines(Real A[2], Real B[2], Real C[2], Real P[2]);
+#ifdef __cplusplus
+}
+#endif
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/primitiveStream.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/primitiveStream.cc
new file mode 100644
index 000000000..26d05342f
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/primitiveStream.cc
@@ -0,0 +1,190 @@
+/*
+** 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 <assert.h>
+#include <GL/gl.h> 
+
+#include "primitiveStream.h"
+
+Int primStream::num_triangles()
+{
+  Int i;
+  Int ret=0;
+  for(i=0; i<index_lengths; i++)
+    {
+      ret += lengths[i]-2;
+    }
+  return ret;
+}
+
+	  
+
+/*the begining of inserting a new primitive. 
+ *reset counter to be 0.
+ */
+void primStream::begin()
+{
+  counter = 0;
+}
+
+void primStream::insert(Real u, Real v)
+{
+  /*if the space cannot hold u and v,
+   *we have to expand the array
+   */
+  if(index_vertices+1 >= size_vertices) {
+    Real* temp = (Real*) malloc (sizeof(Real) * (2*size_vertices + 2));
+    assert(temp);
+    
+    /*copy*/
+    for(Int i=0; i<index_vertices; i++)
+      temp[i] = vertices[i];
+    
+    free(vertices);
+    vertices = temp;
+    size_vertices = 2*size_vertices + 2;
+  }
+
+  vertices[index_vertices++] = u;
+  vertices[index_vertices++] = v;
+  counter++;
+}
+
+/*the end of a primitive.
+ *increase index_lengths 
+ */
+void primStream::end(Int type)
+{
+  Int i;
+  /*if there is no vertex in this primitive, 
+   *nothing needs to be done
+   */
+  if(counter == 0) return ;
+
+  if(index_lengths >= size_lengths){
+    Int* temp = (Int*) malloc(sizeof(Int) * (2*size_lengths + 2));
+    assert(temp);
+    Int* tempTypes = (Int*) malloc(sizeof(Int) * (2*size_lengths + 2));
+    assert(tempTypes);
+    
+    /*copy*/
+    for(i=0; i<index_lengths; i++){
+      temp[i] = lengths[i];
+      tempTypes[i] = types[i];
+    }
+    
+    free(lengths);
+    free(types);
+    lengths = temp;
+    types = tempTypes;
+    size_lengths = 2*size_lengths + 2;
+  }
+  lengths[index_lengths] = counter;
+  types[index_lengths] = type;
+  index_lengths++;
+}
+
+void primStream::print()
+{
+  Int i,j,k;
+  printf("index_lengths=%i,size_lengths=%i\n", index_lengths, size_lengths);
+  printf("index_vertices=%i,size_vertices=%i\n", index_vertices, size_vertices);
+  k=0;
+  for(i=0; i<index_lengths; i++)
+    {
+      if(types[i] == PRIMITIVE_STREAM_FAN)
+	printf("primitive-FAN:\n");
+      else 
+	printf("primitive-STRIP:\n");
+      for(j=0; j<lengths[i]; j++)
+	{
+	  printf("(%f,%f) ", vertices[k], vertices[k+1]);
+	  k += 2;	  
+	}
+      printf("\n");
+    }
+}
+
+primStream::primStream(Int sizeLengths, Int sizeVertices)
+{
+  lengths = (Int*)malloc (sizeof(Int) * sizeLengths);
+  assert(lengths);
+  types = (Int*)malloc (sizeof(Int) * sizeLengths);
+  assert(types);
+  
+  vertices = (Real*) malloc(sizeof(Real) * sizeVertices);
+  assert(vertices);
+  
+  index_lengths = 0;
+  index_vertices = 0;
+  size_lengths = sizeLengths;
+  size_vertices = sizeVertices; 
+}
+
+primStream::~primStream()
+{
+  free(lengths);
+  free(types);
+  free(vertices);
+}
+
+void primStream::draw()
+{
+  Int i,j,k;
+  k=0;
+  for(i=0; i<index_lengths; i++)
+    {
+      switch(types[i]){
+      case PRIMITIVE_STREAM_FAN:
+	glBegin(GL_TRIANGLE_FAN);
+	break;
+      case PRIMITIVE_STREAM_STRIP:
+	glBegin(GL_TRIANGLE_STRIP);
+	break;
+      }
+      
+      for(j=0; j<lengths[i]; j++){
+	glVertex2fv(vertices+k);
+	k += 2;
+      }
+      glEnd();
+    }
+}
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/primitiveStream.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/primitiveStream.h
new file mode 100644
index 000000000..b4174f146
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/primitiveStream.h
@@ -0,0 +1,109 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+/*we do not use the constans GL_... so that this file is independent of 
+ *<GL/gl.h>
+ */
+
+#ifndef _PRIMITIVE_STREAM_H
+#define _PRIMITIVE_STREAM_H
+
+enum {PRIMITIVE_STREAM_FAN, PRIMITIVE_STREAM_STRIP};
+
+#include "definitions.h"
+
+class primStream {
+  Int *lengths; /*length[i]=number of vertices of ith primitive*/
+  Int *types; /*each primive has a type: FAN or STREAM*/
+  Real *vertices; /*the size >= 2 * num_vertices, each vertex (u,v)*/
+
+  /*the following size information are used for dynamic arrays*/
+  Int index_lengths; /*the current available entry*/
+  Int size_lengths; /*the allocated size of the array: lengths*/
+  Int index_vertices;
+  Int size_vertices;
+
+  /*the vertex is inserted one by one. counter is used to 
+   *count the number of vertices which have been inserted so far in 
+   *the current primitive
+   */
+  Int counter;
+
+public:  
+  primStream(Int sizeLengths, Int sizeVertices);
+  ~primStream();
+
+  Int get_n_prims() //num of primitives
+    {
+      return index_lengths;
+    }
+  Int get_type(Int i)  //the type of ith primitive
+    {
+      return  types[i];
+    }
+  Int get_length(Int i) //the length of the ith primitive
+    {
+      return lengths[i];
+    }
+  Real* get_vertices() {return vertices;}
+
+  /*the begining of inserting a new primitive. 
+   *reset counter to be 0.
+   */
+  void begin();
+  void insert(Real u, Real v);
+  void insert(Real v[2]) {insert(v[0], v[1]);}
+  void end(Int type);
+  
+  Int num_triangles();
+  
+  void triangle(Real A[2], Real B[2], Real C[2])
+    {
+      begin();
+      insert(A);
+      insert(B);
+      insert(C);
+      end(PRIMITIVE_STREAM_FAN);
+    }
+  void print();
+  void draw(); /*using GL to draw the primitives*/
+};
+
+
+
+
+
+
+  
+
+#endif
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/quicksort.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/quicksort.cc
new file mode 100644
index 000000000..9d0b290b3
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/quicksort.cc
@@ -0,0 +1,77 @@
+/*
+** 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>
+
+
+static void swap(void *v[], int i, int j)
+{
+  void *temp;
+  temp = v[i];
+  v[i] = v[j];
+  v[j] = temp;
+}
+
+/*as an example to use this function to
+ *sort integers, you need to supply the function
+ *int comp(int *i1, int *i2)
+ *{
+ *  if( *i1 < * i2) return -1;
+ *  else return 1;
+ *}
+ *and an array of pointers to integers: 
+ * int *v[100] (allocate space for where  each v[i] points to).
+ *then you can call:
+ * quicksort( (void**)v, left, right, (int (*)(void *, void *))comp)
+ */
+void quicksort(void *v[], int left, int right,
+	       int (*comp) (void *, void *))
+{
+  int i, last;
+  if(left >= right) /*do nothing if array contains */
+    return;         /*fewer than two elements*/
+  
+  swap(v, left, (left+right)/2);
+  last = left;
+  for(i=left+1; i<=right; i++)
+    if((*comp)(v[i], v[left])<0)
+      swap(v, ++last, i);
+  swap(v, left, last);
+  quicksort(v, left, last-1, comp);
+  quicksort(v, last+1, right, comp);
+}
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/quicksort.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/quicksort.h
new file mode 100644
index 000000000..3a8dcd6a2
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/quicksort.h
@@ -0,0 +1,42 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _QUICKSORT_H
+#define _QUICKSORT_H
+
+#include <stdlib.h>
+#include <stdio.h>
+
+void quicksort(void *v[], int left, int right,
+	       int (*comp) (void *, void *));
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/rectBlock.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/rectBlock.cc
new file mode 100644
index 000000000..f457b1573
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/rectBlock.cc
@@ -0,0 +1,196 @@
+/*
+** 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 "glimports.h"
+#include "zlassert.h"
+#include <GL/gl.h>
+
+#include "rectBlock.h"
+
+rectBlock::rectBlock(gridBoundaryChain* left, gridBoundaryChain* right, Int beginVline, Int endVline)
+{
+  Int i;
+
+
+  upGridLineIndex = left->getVlineIndex(beginVline);
+
+  lowGridLineIndex = left->getVlineIndex(endVline);
+
+  Int n = upGridLineIndex-lowGridLineIndex+1; //number of grid lines
+  leftIndices = (Int*) malloc(sizeof(Int) * n);
+  assert(leftIndices);
+  rightIndices = (Int*) malloc(sizeof(Int) * n);
+  assert(rightIndices);
+  for(i=0; i<n; i++)
+    {
+
+      leftIndices[i] = left->getInnerIndex(i+beginVline);
+      rightIndices[i] = right->getInnerIndex(i+beginVline);
+    }
+}
+
+
+rectBlock::~rectBlock()
+{
+  free(leftIndices);
+  free(rightIndices);
+}
+
+void rectBlock::print()
+{
+  Int i;
+  printf("block:\n");
+  for(i=upGridLineIndex; i >= lowGridLineIndex; i--)
+    {
+      printf("gridline %i, (%i,%i)\n", i, leftIndices[upGridLineIndex-i], rightIndices[upGridLineIndex-i]);
+    }
+}
+
+
+
+void rectBlock::draw(Real* u_values, Real* v_values)
+{
+  Int i,j,k;
+  //upgrid line to bot grid line
+#ifdef DEBUG
+printf("upGridLineIndex=%i, lowGridLineIndex=%i\n", upGridLineIndex, lowGridLineIndex);
+#endif
+  for(k=0, i=upGridLineIndex; i > lowGridLineIndex; i--, k++)
+    {
+      glBegin(GL_QUAD_STRIP);
+
+      for(j=leftIndices[k+1]; j<= rightIndices[k+1]; j++)
+	{
+	  glVertex2f(u_values[j], v_values[i]);
+	  glVertex2f(u_values[j], v_values[i-1]);
+	}
+      glEnd();
+    }  
+}
+
+
+Int rectBlock::num_quads()
+{
+  Int ret=0;
+  Int k,i;
+  for(k=0, i=upGridLineIndex; i>lowGridLineIndex; i--, k++)
+    {
+      ret += (rightIndices[k+1]-leftIndices[k+1]);
+    }
+  return ret;
+}
+
+Int rectBlockArray::num_quads()
+{
+  Int ret=0;
+  for(Int i=0; i<n_elements; i++)
+    ret += array[i]->num_quads();
+  return ret;
+}
+
+rectBlockArray::rectBlockArray(Int s)
+{
+  Int i;
+  n_elements = 0;
+  size = s;
+  array = (rectBlock**) malloc(sizeof(rectBlock*) * s);
+  assert(array);
+//initialization
+  for(i=0; i<s; i++)
+    array[i] = NULL;
+}
+
+rectBlockArray::~rectBlockArray()
+{
+  Int i;
+  for(i=0; i<size; i++)
+    {
+      if(array[i] != NULL)
+	delete array[i];
+    }
+  free(array);
+}
+
+//put to the end of the array, check the size
+void rectBlockArray::insert(rectBlock* newBlock)
+{
+  Int i;
+  if(n_elements == size) //full
+    {
+      rectBlock** temp = (rectBlock**) malloc(sizeof(rectBlock) * (2*size+1));
+      assert(temp);
+      //initialization
+      for(i=0; i<2*size+1; i++)
+	temp[i] = NULL;
+      
+      for(i=0; i<n_elements; i++)
+	temp[i] = array[i];
+      
+      free(array);
+      array = temp;
+      size = 2*size +  1;
+    }
+  
+  array[n_elements++] = newBlock;
+}
+
+void rectBlockArray::print()
+{
+  Int i;
+  for(i=0; i<n_elements; i++)
+    array[i]->print();
+}
+
+void rectBlockArray::draw(Real* u_values, Real* v_values)
+{
+  Int i;
+  for(i=0; i<n_elements; i++)
+    array[i]->draw(u_values, v_values);
+}
+
+
+
+
+
+
+
+
+
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/rectBlock.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/rectBlock.h
new file mode 100644
index 000000000..8dbd7eb81
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/rectBlock.h
@@ -0,0 +1,82 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _RECTBLOCK_H
+#define _RECTBLOCK_H
+
+#include "definitions.h"
+#include "gridWrap.h"
+
+class rectBlock{
+  Int upGridLineIndex;
+  Int lowGridLineIndex;
+  Int* leftIndices; //up to bottome
+  Int* rightIndices; //up to bottom
+public:
+  //the arrays are copies.
+  rectBlock(gridBoundaryChain* left, gridBoundaryChain* right, Int beginVline, Int endVline);
+  ~rectBlock(); //free the two arrays
+
+  Int get_upGridLineIndex() {return upGridLineIndex;}
+  Int get_lowGridLineIndex() {return lowGridLineIndex;}
+  Int* get_leftIndices() {return leftIndices;}
+  Int* get_rightIndices() {return rightIndices;}
+
+  Int num_quads();
+
+  void print();
+  void draw(Real* u_values, Real* v_values);
+};
+
+
+class rectBlockArray{
+  rectBlock** array;
+  Int n_elements;
+  Int size;
+public:
+  rectBlockArray(Int s);
+  ~rectBlockArray();//delete avarything including the blocks
+  
+  Int get_n_elements() {return n_elements;}
+  rectBlock* get_element(Int i) {return array[i];}
+  void insert(rectBlock* newBlock); //only take the pointer, not ther cotent
+
+  Int num_quads();
+
+  void print();
+  void draw(Real* u_values, Real* v_values);
+};
+  
+
+
+#endif
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleComp.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleComp.cc
new file mode 100644
index 000000000..861c71bb3
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleComp.cc
@@ -0,0 +1,371 @@
+/*
+** 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 "glimports.h"
+#include "sampleComp.h"
+#include "sampleCompTop.h"
+#include "sampleCompBot.h"
+#include "sampleCompRight.h"
+
+
+
+#define max(a,b) ((a>b)? a:b)
+#define min(a,b) ((a>b)? b:a)
+
+void sampleConnectedComp(Real* topVertex, Real* botVertex,
+		    vertexArray* leftChain, 
+		    Int leftStartIndex, Int leftEndIndex,
+		    vertexArray* rightChain,
+		    Int rightStartIndex, Int rightEndIndex,
+		    gridBoundaryChain* leftGridChain,
+		    gridBoundaryChain* rightGridChain,
+		    Int gridIndex1, Int gridIndex2,
+		    Int up_leftCornerWhere,
+		    Int up_leftCornerIndex,
+		    Int up_rightCornerWhere,
+		    Int up_rightCornerIndex,
+		    Int down_leftCornerWhere,
+		    Int down_leftCornerIndex,
+		    Int down_rightCornerWhere,
+		    Int down_rightCornerIndex,
+		    primStream* pStream,
+		    rectBlockArray* rbArray
+		    )
+{
+
+ sampleCompLeft(topVertex, botVertex,
+		leftChain,
+		leftStartIndex,	leftEndIndex,
+		rightChain,
+		rightStartIndex, rightEndIndex,
+		leftGridChain,
+		gridIndex1,
+		gridIndex2,
+		up_leftCornerWhere,
+		up_leftCornerIndex,
+		down_leftCornerWhere,
+		down_leftCornerIndex,
+		pStream);
+
+
+ sampleCompRight(topVertex, botVertex,
+		 leftChain,
+		 leftStartIndex, leftEndIndex,
+		 rightChain,
+		 rightStartIndex,
+		 rightEndIndex,
+		 rightGridChain,
+		 gridIndex1, gridIndex2,
+		 up_rightCornerWhere,
+		 up_rightCornerIndex,
+		 down_rightCornerWhere,
+		 down_rightCornerIndex,
+		 pStream);
+		 
+
+ sampleCompTop(topVertex,
+		     leftChain,
+		     leftStartIndex,
+		     rightChain,
+		     rightStartIndex,
+		     leftGridChain,
+		     rightGridChain,
+		     gridIndex1,
+		     up_leftCornerWhere,
+		     up_leftCornerIndex,
+		     up_rightCornerWhere,
+		     up_rightCornerIndex,
+		     pStream);
+
+ sampleCompBot(botVertex,
+		     leftChain,
+		     leftEndIndex,
+		     rightChain,
+		     rightEndIndex,
+		     leftGridChain,
+		     rightGridChain,
+		     gridIndex2,
+		     down_leftCornerWhere,
+		     down_leftCornerIndex,
+		     down_rightCornerWhere,
+		     down_rightCornerIndex,
+		     pStream);
+
+
+ //the center
+
+ rbArray->insert(new rectBlock(leftGridChain, rightGridChain, gridIndex1, gridIndex2));
+
+	
+}
+
+/*notice that we need rightChain because the 
+ *corners could be on the rightChain.
+ *here comp means component.
+ */
+void sampleCompLeft(Real* topVertex, Real* botVertex,
+		    vertexArray* leftChain,
+		    Int leftStartIndex, Int leftEndIndex,
+		    vertexArray* rightChain,
+		    Int rightStartIndex, Int rightEndIndex,
+		    gridBoundaryChain* leftGridChain,
+		    Int gridIndex1, Int gridIndex2,
+		    Int up_leftCornerWhere,
+		    Int up_leftCornerIndex,
+		    Int down_leftCornerWhere,
+		    Int down_leftCornerIndex,
+		    primStream* pStream)
+{
+  /*find out whether there is a trim vertex which is
+   *inbetween the top and bot grid lines or not.
+   */
+  Int midIndex1;
+  Int midIndex2;
+  Int gridMidIndex1 = 0, gridMidIndex2 = 0;
+  //midIndex1: array[i] <= v, array[i-1] > v
+  //midIndex2: array[i] >= v, array[i+1] < v
+  // v(gridMidIndex1) >= v(midindex1) > v(gridMidIndex1+1)
+  // v(gridMidIndex2-1) >= v(midIndex2) > v(gridMidIndex2) ??
+  midIndex1 = leftChain->findIndexBelowGen(
+					   leftGridChain->get_v_value(gridIndex1),
+					   leftStartIndex,
+					   leftEndIndex);
+
+  midIndex2 = -1; /*initilization*/
+  if(midIndex1<= leftEndIndex && gridIndex1<gridIndex2)
+    if(leftChain->getVertex(midIndex1)[1] >= leftGridChain->get_v_value(gridIndex2))
+      {
+	midIndex2 = leftChain->findIndexAboveGen(
+						 leftGridChain->get_v_value(gridIndex2),
+						 midIndex1, //midIndex1 <= midIndex2.
+						 leftEndIndex);
+	gridMidIndex1  = leftGridChain->lookfor(leftChain->getVertex(midIndex1)[1],
+						gridIndex1, gridIndex2);
+	gridMidIndex2 = 1+leftGridChain->lookfor(leftChain->getVertex(midIndex2)[1],
+					       gridMidIndex1, gridIndex2);	
+      }
+
+
+  /*to interprete the corner information*/
+  Real* cornerTop;
+  Real* cornerBot;
+  Int cornerLeftStart;
+  Int cornerLeftEnd;
+  Int cornerRightUpEnd;
+  Int cornerRightDownStart;
+  if(up_leftCornerWhere == 0) /*left corner is on left chain*/
+    {
+      cornerTop = leftChain->getVertex(up_leftCornerIndex);
+      cornerLeftStart = up_leftCornerIndex+1;
+      cornerRightUpEnd = -1; /*no right*/
+    }
+  else if(up_leftCornerWhere == 1) /*left corner is on top*/
+    {
+      cornerTop = topVertex;
+      cornerLeftStart = leftStartIndex;
+      cornerRightUpEnd = -1; /*no right*/
+    }
+  else /*left corner is on right chain*/
+    {
+      cornerTop = topVertex;
+      cornerLeftStart = leftStartIndex;
+      cornerRightUpEnd = up_leftCornerIndex;
+    }
+  
+  if(down_leftCornerWhere == 0) /*left corner is on left chain*/
+    {
+      cornerBot = leftChain->getVertex(down_leftCornerIndex);
+      cornerLeftEnd = down_leftCornerIndex-1;
+      cornerRightDownStart = rightEndIndex+1; /*no right*/
+    }
+  else if(down_leftCornerWhere == 1) /*left corner is on bot*/
+    {
+      cornerBot = botVertex;
+      cornerLeftEnd = leftEndIndex;
+      cornerRightDownStart = rightEndIndex+1; /*no right*/
+    }
+  else /*left corner is on the right chian*/
+    {
+      cornerBot = botVertex;
+      cornerLeftEnd = leftEndIndex;
+      cornerRightDownStart = down_leftCornerIndex;
+    }
+      
+
+
+
+  /*sample*/
+  if(midIndex2 >= 0) /*there is a trim point inbewteen grid lines*/
+    {
+
+      sampleLeftSingleTrimEdgeRegionGen(cornerTop, leftChain->getVertex(midIndex1),
+					leftChain,
+					cornerLeftStart,
+					midIndex1-1,
+					leftGridChain,
+					gridIndex1,
+					gridMidIndex1,
+					rightChain,
+					rightStartIndex,
+					cornerRightUpEnd,
+					0, //no right down section
+					-1,
+					pStream);
+
+      sampleLeftSingleTrimEdgeRegionGen(leftChain->getVertex(midIndex2),
+					cornerBot,
+					leftChain,
+					midIndex2+1,
+					cornerLeftEnd,
+					leftGridChain,
+					gridMidIndex2,
+					gridIndex2,
+					rightChain,
+					0, //no right up section
+					-1,
+					cornerRightDownStart,
+					rightEndIndex,
+					pStream);
+
+
+      sampleLeftStripRecF(leftChain,
+			  midIndex1,
+			  midIndex2,
+			  leftGridChain,
+			  gridMidIndex1,
+			  gridMidIndex2,
+			  pStream);
+    }
+  else
+    {
+      sampleLeftSingleTrimEdgeRegionGen(cornerTop, cornerBot,
+					leftChain,
+					cornerLeftStart,
+					cornerLeftEnd,
+					leftGridChain,
+					gridIndex1,
+					gridIndex2,
+					rightChain,
+					rightStartIndex,
+					cornerRightUpEnd,
+					cornerRightDownStart,
+					rightEndIndex,
+					pStream);
+    }					 
+}
+		    
+void sampleLeftSingleTrimEdgeRegionGen(Real topVert[2], Real botVert[2],
+				       vertexArray* leftChain,
+				       Int leftStart,
+				       Int leftEnd,
+				       gridBoundaryChain* gridChain,
+				       Int gridBeginIndex,
+				       Int gridEndIndex,
+				       vertexArray* rightChain,
+				       Int rightUpBegin,
+				       Int rightUpEnd,
+				       Int rightDownBegin,
+				       Int rightDownEnd,
+				       primStream* pStream)
+{
+  Int i,j,k;
+
+  /*creat an array to store all the up and down secments of the right chain,
+   *and the left end grid points
+   *
+   *although vertex array is a dynamic array, but to gain efficiency,
+   *it is better to initiliza the exact array size
+   */
+  vertexArray vArray(gridEndIndex-gridBeginIndex+1 +
+		     max(0,rightUpEnd - rightUpBegin+1)+
+		     max(0,rightDownEnd - rightDownBegin+1));
+  
+  /*append the vertices on the up section of thr right chain*/
+  for(i=rightUpBegin; i<= rightUpEnd; i++)
+    vArray.appendVertex(rightChain->getVertex(i));
+  
+  /*append the vertices of the left extremal grid points,
+   *and at the same time, perform triangulation for the stair cases
+   */
+  vArray.appendVertex(gridChain->get_vertex(gridBeginIndex));
+
+  for(k=1, i=gridBeginIndex+1; i<=gridEndIndex; i++, k++)
+    {
+      vArray.appendVertex(gridChain->get_vertex(i));
+
+      /*output the fan of the grid points of the (i)th and (i-1)th grid line.
+       */
+      if(gridChain->getUlineIndex(i) < gridChain->getUlineIndex(i-1))
+	{
+	  pStream->begin();	  
+	  pStream->insert(gridChain->get_vertex(i-1));
+	  for(j=gridChain->getUlineIndex(i); j<= gridChain->getUlineIndex(i-1); j++)
+	    pStream->insert(gridChain->getGrid()->get_u_value(j), gridChain->get_v_value(i));
+	  pStream->end(PRIMITIVE_STREAM_FAN);
+	}
+      else if(gridChain->getUlineIndex(i) > gridChain->getUlineIndex(i-1))
+	{
+	  pStream->begin();
+	  pStream->insert(gridChain->get_vertex(i));
+	  for(j=gridChain->getUlineIndex(i); j>= gridChain->getUlineIndex(i-1); j--)
+	    pStream->insert(gridChain->getGrid()->get_u_value(j), gridChain->get_v_value(i-1));
+	  pStream->end(PRIMITIVE_STREAM_FAN);
+	}
+      /*otherwisem, the two are equal, so there is no fan to outout*/	  
+    }
+
+  /*then append all the vertices on the down section of the right chain*/
+  for(i=rightDownBegin; i<= rightDownEnd; i++)
+    vArray.appendVertex(rightChain->getVertex(i));  
+
+  monoTriangulationRecGen(topVert, botVert,
+			  leftChain, leftStart, leftEnd,
+			  &vArray, 0, vArray.getNumElements()-1,
+			  pStream);
+		     
+}
+
+
+
+
+
+
+
+
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleComp.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleComp.h
new file mode 100644
index 000000000..a3c179025
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleComp.h
@@ -0,0 +1,86 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _SAMPLECOMP_H
+#define _SAMPLECOMP_H
+
+#include "sampleMonoPoly.h"
+#include "rectBlock.h"
+
+void sampleConnectedComp(Real* topVertex, Real* botVertex,
+		    vertexArray* leftChain, 
+		    Int leftStartIndex, Int botLeftIndex,
+		    vertexArray* rightChain,
+		    Int rightStartIndex, Int botRightIndex,
+		    gridBoundaryChain* leftGridChain,
+		    gridBoundaryChain* rightGridChain,
+		    Int gridIndex1, Int gridIndex2,
+		    Int up_leftCornerWhere,
+		    Int up_leftCornerIndex,
+		    Int up_rightCornerWhere,
+		    Int up_rightCornerIndex,
+		    Int down_leftCornerWhere,
+		    Int down_leftCornerIndex,
+		    Int down_rightCornerWhere,
+		    Int down_rightCornerIndex,
+		    primStream* pStream,
+		    rectBlockArray* rbArray
+		    );
+
+void sampleCompLeft(Real* topVertex, Real* botVertex,
+		    vertexArray* leftChain,
+		    Int leftStartIndex, Int leftEndIndex,
+		    vertexArray* rightChain,
+		    Int rightStartIndex, Int rightEndIndex,
+		    gridBoundaryChain* leftGridChain,
+		    Int gridIndex1, Int gridIndex2,
+		    Int up_leftCornerWhere,
+		    Int up_leftCornerIndex,
+		    Int down_leftCornerWhere,
+		    Int down_leftCornerIndex,
+		    primStream* pStream);
+
+void sampleLeftSingleTrimEdgeRegionGen(Real topVert[2], Real botVert[2],
+				       vertexArray* leftChain,
+				       Int leftStart,
+				       Int leftEnd,
+				       gridBoundaryChain* gridChain,
+				       Int gridBegindex,
+				       Int gridEndIndex,
+				       vertexArray* rightChain,
+				       Int rightUpBegin,
+				       Int rightUpEnd,
+				       Int rightDownBegin,
+				       Int rightDownEnd,
+				       primStream* pStream);
+		    
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompBot.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompBot.cc
new file mode 100644
index 000000000..e12f88bab
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompBot.cc
@@ -0,0 +1,844 @@
+/*
+** 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 "zlassert.h"
+#include "sampleCompBot.h"
+#include "sampleCompRight.h"
+
+#define max(a,b) ((a>b)? a:b)
+
+//return: index_mono, index_pass
+//from [pass, mono] is strictly U-monotone
+//from [corner, pass] is <u
+// vertex[pass][0] >= u
+//if everybost is <u, then pass = end+1.
+//otherwise both mono and pass are meanng full and we have corner<=pass<=mono<=end
+void findBotLeftSegment(vertexArray* leftChain, 
+			Int leftEnd,
+			Int leftCorner,
+			Real u,
+			Int& ret_index_mono,
+			Int& ret_index_pass)
+{
+  Int i;
+
+  assert(leftCorner <= leftEnd);
+  for(i=leftCorner; i<= leftEnd; i++)
+    if(leftChain->getVertex(i)[0] >= u)
+      break;
+  ret_index_pass = i;
+  if(ret_index_pass <= leftEnd)
+    {
+      for(i=ret_index_pass; i< leftEnd; i++)
+	{
+	  if(leftChain->getVertex(i+1)[0] <= leftChain->getVertex(i)[0])
+	    break;
+	}
+      ret_index_mono = i;
+    }
+
+}
+
+void findBotRightSegment(vertexArray* rightChain, 
+			 Int rightEnd,
+			 Int rightCorner,
+			 Real u,
+			 Int& ret_index_mono,
+			 Int& ret_index_pass)
+{
+  Int i;
+  assert(rightCorner <= rightEnd);
+  for(i=rightCorner; i<= rightEnd; i++)
+    if(rightChain->getVertex(i)[0] <= u)
+      break;
+
+
+
+  ret_index_pass = i;
+
+  if(ret_index_pass <= rightEnd)
+    {
+      for(i=ret_index_pass; i< rightEnd; i++)
+	{
+	  if(rightChain->getVertex(i+1)[0] >= rightChain->getVertex(i)[0])
+	    break;
+	}
+      ret_index_mono = i;
+    }
+}
+
+
+void sampleBotRightWithGridLinePost(Real* botVertex,
+				    vertexArray* rightChain,
+				    Int rightEnd,
+				    Int segIndexMono,
+				    Int segIndexPass,
+				    Int rightCorner,
+				    gridWrap* grid,
+				    Int gridV,
+				    Int leftU,
+				    Int rightU,
+				    primStream* pStream)
+{
+  //the possible section which is to the right of rightU
+  if(segIndexPass > rightCorner) //from corner to pass-1 is > u.
+    {
+      Real *tempBot;
+      if(segIndexPass <= rightEnd) //there is a point to the left of u
+	tempBot = rightChain->getVertex(segIndexPass);
+      else   //nothing is to the left of u.
+	tempBot = botVertex; 
+      Real tempTop[2];
+      tempTop[0] = grid->get_u_value(rightU);
+      tempTop[1] = grid->get_v_value(gridV);
+      
+      monoTriangulation2(tempTop, tempBot,
+			 rightChain,
+			 rightCorner,
+			 segIndexPass-1,
+			 0, // a decrease chain
+			 pStream);
+    }
+
+  //the possible section which is strictly Umonotone
+  if(segIndexPass <= rightEnd) //segIndex pass and mono exist
+    {
+      //if there are grid points which are to the left of botVertex
+      //then we should use botVertex to form a fan with these points to
+      //optimize the triangulation
+      int do_optimize = 1;
+      if(botVertex[0] <= grid->get_u_value(leftU))
+	do_optimize = 0;
+      else
+	{
+	  //we also have to make sure that botVertex is the left most vertex on the chain
+	  int i;
+	  for(i=segIndexMono; i<=rightEnd; i++)
+	    if(rightChain->getVertex(i)[0] <= botVertex[0])
+	      {
+		do_optimize = 0;
+		break;
+	      }
+	}
+
+      if(do_optimize)
+	{
+	  //find midU so that grid->get_u_value(midU) <= botVertex[0]
+	  //and               grid->get_u_value(midU) >  botVertex[0]
+	  int midU = leftU;
+	  while(grid->get_u_value(midU) <= botVertex[0])
+	    {
+	      midU++;
+	      if(midU > rightU)
+		break;
+	    }
+	  midU--;
+
+	  grid->outputFanWithPoint(gridV, leftU, midU, botVertex, pStream);
+	  stripOfFanRight(rightChain, segIndexMono, segIndexPass, grid, gridV, midU, rightU, pStream, 1);	  
+	  Real tempTop[2];
+	  tempTop[0] = grid->get_u_value(midU);
+	  tempTop[1] = grid->get_v_value(gridV);
+	  monoTriangulation2(tempTop, botVertex, rightChain, segIndexMono, rightEnd, 0, pStream);
+	}
+      else //not optimize
+	{
+	  stripOfFanRight(rightChain, segIndexMono, segIndexPass, grid, gridV, leftU, rightU, pStream, 1);
+	  Real tempTop[2];
+	  tempTop[0] = grid->get_u_value(leftU);
+	  tempTop[1] = grid->get_v_value(gridV);
+	  monoTriangulation2(tempTop, botVertex, rightChain, segIndexMono, rightEnd, 0, pStream);
+	}
+    }
+  else //the botVertex forms a fan witht eh grid points
+    grid->outputFanWithPoint(gridV, leftU, rightU, botVertex, pStream);
+}
+      
+void sampleBotRightWithGridLine(Real* botVertex, 
+				vertexArray* rightChain,
+				Int rightEnd,
+				Int rightCorner,
+				gridWrap* grid,
+				Int gridV,
+				Int leftU,
+				Int rightU,
+				primStream* pStream)
+{
+  //if right chaain is empty, then there is only one bot vertex with
+  //one grid line
+  if(rightEnd<rightCorner){
+    grid->outputFanWithPoint(gridV, leftU, rightU, botVertex, pStream);
+    return;
+  }
+
+  Int segIndexMono, segIndexPass;
+  findBotRightSegment(rightChain,
+		      rightEnd,
+		      rightCorner,
+		      grid->get_u_value(rightU),
+		      segIndexMono,
+		      segIndexPass);
+
+  sampleBotRightWithGridLinePost(botVertex, 
+				 rightChain,
+				 rightEnd,
+				 segIndexMono,
+				 segIndexPass,
+				 rightCorner,
+				 grid,
+				 gridV,
+				 leftU,
+				 rightU,
+				 pStream);
+}
+  
+ 
+void sampleBotLeftWithGridLinePost(Real* botVertex,
+				   vertexArray* leftChain,
+				   Int leftEnd,
+				   Int segIndexMono,
+				   Int segIndexPass,
+				   Int leftCorner,
+				   gridWrap* grid,
+				   Int gridV,
+				   Int leftU, 
+				   Int rightU,
+				   primStream* pStream)
+{
+
+  //the possible section which is to the left of leftU
+  if(segIndexPass > leftCorner) //at least leftCorner is to the left of leftU
+    {
+      Real *tempBot; 
+      if(segIndexPass <= leftEnd) //from corner to pass-1 is <u
+	tempBot = leftChain->getVertex(segIndexPass);
+      else //nothing is to the rigth of u
+	tempBot = botVertex;
+      Real tempTop[2];
+      tempTop[0] = grid->get_u_value(leftU);
+      tempTop[1] = grid->get_v_value(gridV);
+      monoTriangulation2(tempTop, tempBot, leftChain, leftCorner, segIndexPass-1,
+			 1, //a increase chain,
+			 pStream);
+    }
+  //the possible section which is strictly Umonotone
+  if(segIndexPass <= leftEnd) //segIndexpass and mono exist
+    {
+      stripOfFanLeft(leftChain, segIndexMono, segIndexPass, grid, gridV, leftU, rightU, pStream, 1);
+      Real tempTop[2];
+      tempTop[0] = grid->get_u_value(rightU);
+      tempTop[1] = grid->get_v_value(gridV);
+
+      monoTriangulation2(tempTop, botVertex, leftChain, segIndexMono, leftEnd, 
+			 1,  //increase chain
+			 pStream);
+    }
+  else //the botVertex forms a fan with the grid points
+    {
+      grid->outputFanWithPoint(gridV, leftU, rightU, botVertex, pStream);
+    }
+
+}
+
+void sampleBotLeftWithGridLine(Real* botVertex,
+			       vertexArray* leftChain,
+			       Int leftEnd,
+			       Int leftCorner,
+			       gridWrap* grid,
+			       Int gridV,
+			       Int leftU,
+			       Int rightU,
+			       primStream* pStream)
+{
+
+  //if leftChain is empty, then there is only one botVertex with one grid line
+  if(leftEnd< leftCorner){
+    grid->outputFanWithPoint(gridV, leftU, rightU, botVertex, pStream);
+    return;
+  }
+
+  Int segIndexPass, segIndexMono;
+  findBotLeftSegment(leftChain, leftEnd, leftCorner, grid->get_u_value(leftU), segIndexMono, segIndexPass);
+
+  sampleBotLeftWithGridLinePost(botVertex,
+			    leftChain,
+			    leftEnd,
+			    segIndexMono,
+			    segIndexPass,
+			    leftCorner,
+			    grid,
+			    gridV,
+			    leftU, rightU, pStream);
+}
+
+//return 1 if separator exists, 0 otherwise
+Int findBotSeparator(vertexArray* leftChain,
+		     Int leftEnd,
+		     Int leftCorner,
+		     vertexArray* rightChain,
+		     Int rightEnd,
+		     Int rightCorner,
+		     Int& ret_sep_left,
+		     Int& ret_sep_right)
+{
+  Int oldLeftI, oldRightI, newLeftI, newRightI;
+  Int i,j,k;
+  Real leftMax /*= leftChain->getVertex(leftCorner)[0]*/;
+  Real rightMin /*= rightChain->getVertex(rightCorner)[0]*/;
+  if(leftChain->getVertex(leftCorner)[1] < rightChain->getVertex(rightCorner)[1])//leftlower
+    {
+      oldLeftI = leftCorner-1;
+      oldRightI = rightCorner;
+      leftMax = leftChain->getVertex(leftCorner)[0] - Real(1.0) ; //initilize to be left of leftCorner
+      rightMin = rightChain->getVertex(rightCorner)[0]; 
+    }
+  else //rightlower
+    {
+      oldLeftI = leftCorner;
+      oldRightI = rightCorner-1;
+      leftMax = leftChain->getVertex(leftCorner)[0];
+      rightMin = rightChain->getVertex(rightCorner)[0] + Real(1.0);
+    }
+
+  //i: the current working leftChain Index
+  //j: the curent working right chian index
+  //if(left(i) is lower than right(j), then the two chains above right(j) are separated.
+  //else the two chains below left(i) are separated.
+  i = leftCorner;
+  j = rightCorner;
+  while(1)
+    {
+      newLeftI = oldLeftI;
+      newRightI = oldRightI;
+      if(i> leftEnd) //left chain is doen , go through remaining right chain
+	{
+	  for(k=j+1; k<= rightEnd; k++)
+	    {
+	      if(rightChain->getVertex(k)[0] > leftMax) //no conflict
+		{
+		  //update oldRightI if necessary
+		  if(rightChain->getVertex(k)[0] < rightMin)
+		    {
+		      rightMin = rightChain->getVertex(k)[0];
+		      oldRightI = k;
+		    }
+		}
+	      else //there is a conflict
+		break; //the for-loop, above right(k+1) is separated: oldLeftI, oldRightI
+	    }
+	  break; //the while loop
+	}
+      else if(j > rightEnd) //right Chain is doen
+	{
+	  for(k=i+1; k<= leftEnd; k++)
+	    {
+	      if(leftChain->getVertex(k)[0] < rightMin) //no conflict
+		{
+		  //update oldLeftI if necessary
+		  if(leftChain->getVertex(k)[0] > leftMax)
+		    {
+		      leftMax =  leftChain->getVertex(k)[0];
+		      oldLeftI = k;
+		    }
+		}
+	      else //there is a conflict
+		break; //the for-loop, above left(k+1) is separated: oldLeftI, oldRightI
+	    }
+	  break; //the while loop
+	}
+      else if(leftChain->getVertex(i)[1] < rightChain->getVertex(j)[1]) //left lower
+	{
+
+	  if(leftChain->getVertex(i)[0] > leftMax) //update leftMax amd newLeftI
+	    {
+	      leftMax = leftChain->getVertex(i)[0];
+	      newLeftI = i;
+	    }
+	  for(k=j+1; k<= rightEnd; k++) //update rightMin and newRightI;
+	    {
+	      if(rightChain->getVertex(k)[1] < leftChain->getVertex(i)[1]) //right gets lower
+		break;
+	      if(rightChain->getVertex(k)[0] < rightMin)
+		{
+		  rightMin = rightChain->getVertex(k)[0];
+		  newRightI = k;
+		}
+	    }
+	  j = k; //next working j, since j will he lower than i in next loop
+	  if(leftMax >= rightMin) //there is a conflict
+	    break;
+	  else //still no conflict
+	    {
+	      oldLeftI = newLeftI;
+	      oldRightI = newRightI;
+
+	    }
+	}
+      else //right lower
+	{
+	  if(rightChain->getVertex(j)[0] < rightMin)
+	    {
+	      rightMin = rightChain->getVertex(j)[0];
+	      newRightI = j;
+	    }
+	  for(k=i+1; k<= leftEnd; k++)
+	    {
+	      if(leftChain->getVertex(k)[1] < rightChain->getVertex(j)[1])
+		break;
+	      if(leftChain->getVertex(k)[0] > leftMax)
+		{
+		  leftMax = leftChain->getVertex(k)[0];
+		  newLeftI = k;
+		}
+	    }
+	  i=k; //nexct working i, since i will be lower than j next loop
+	  if(leftMax >= rightMin) //there is conflict
+	    break;
+	  else //still no conflict
+	    {
+	      oldLeftI = newLeftI;
+	      oldRightI = newRightI;
+	    }
+	}
+    }//end of while loop
+  //now oldLeftI and oldRight I are the desired separator index notice that they are not 
+  //necessarily valid 
+  if(oldLeftI < leftCorner || oldRightI < rightCorner)
+    return 0; //no separator
+  else
+    {
+      ret_sep_left = oldLeftI;
+      ret_sep_right = oldRightI;
+      return 1;
+    }
+}
+
+void sampleCompBot(Real* botVertex,
+		   vertexArray* leftChain,
+		   Int leftEnd,
+		   vertexArray* rightChain,
+		   Int rightEnd,
+		   gridBoundaryChain* leftGridChain,
+		   gridBoundaryChain* rightGridChain,
+		   Int gridIndex,
+		   Int down_leftCornerWhere,
+		   Int down_leftCornerIndex,
+		   Int down_rightCornerWhere,
+		   Int down_rightCornerIndex,
+		   primStream* pStream)
+{
+
+  if(down_leftCornerWhere == 1 && down_rightCornerWhere == 1) //the bot is botVertex with possible grid points
+    {
+
+      leftGridChain->getGrid()->outputFanWithPoint(leftGridChain->getVlineIndex(gridIndex),
+						   leftGridChain->getUlineIndex(gridIndex),
+						  rightGridChain->getUlineIndex(gridIndex),
+						   botVertex,
+						   pStream);
+      return;
+    }
+  else if(down_leftCornerWhere != 0)
+    {
+
+      Real* tempBot;
+      Int tempRightEnd;
+      if(down_leftCornerWhere == 1){
+	tempRightEnd = rightEnd;
+	tempBot = botVertex;
+      }
+      else
+	{
+	  tempRightEnd = down_leftCornerIndex-1;
+	  tempBot = rightChain->getVertex(down_leftCornerIndex);
+	}
+
+      sampleBotRightWithGridLine(tempBot,
+				 rightChain, 
+				 tempRightEnd,
+				 down_rightCornerIndex,
+				 rightGridChain->getGrid(),
+				 leftGridChain->getVlineIndex(gridIndex),
+				 leftGridChain->getUlineIndex(gridIndex),
+				 rightGridChain->getUlineIndex(gridIndex),
+				 pStream);
+    }
+  else if(down_rightCornerWhere != 2)
+    {
+
+      Real* tempBot;
+      Int tempLeftEnd;
+      if(down_rightCornerWhere == 1){
+	tempLeftEnd = leftEnd;
+	tempBot = botVertex;
+      }
+      else //right corner is on left chain
+	{
+	  tempLeftEnd = down_rightCornerIndex-1;
+	  tempBot = leftChain->getVertex(down_rightCornerIndex);	  
+	}
+
+
+      sampleBotLeftWithGridLine(tempBot, leftChain, tempLeftEnd, down_leftCornerIndex, 
+				leftGridChain->getGrid(),
+				leftGridChain->getVlineIndex(gridIndex),
+				leftGridChain->getUlineIndex(gridIndex),
+				rightGridChain->getUlineIndex(gridIndex),
+				pStream);
+
+    }
+  else //down_leftCornereWhere == 0, down_rightCornerwhere == 2
+    {
+      sampleCompBotSimple(botVertex, 
+			  leftChain,
+			  leftEnd,
+			  rightChain,
+			  rightEnd,
+			  leftGridChain,
+			  rightGridChain,
+			  gridIndex,
+			  down_leftCornerWhere,
+			  down_leftCornerIndex,
+			  down_rightCornerWhere,
+			  down_rightCornerIndex,
+			  pStream);
+      
+      return;
+
+#ifdef NOT_REACHABLE
+      //the following code is trying to do some optimization, but not quite working. so it is not reachable, but leave it here for reference
+      Int sep_left, sep_right;
+      if(findBotSeparator(leftChain, leftEnd, down_leftCornerIndex,
+			  rightChain, rightEnd, down_rightCornerIndex,
+			  sep_left, sep_right)
+	 )//separator exiosts
+	{
+
+	  if(leftChain->getVertex(sep_left)[0] >= leftGridChain->get_u_value(gridIndex) &&
+	     rightChain->getVertex(sep_right)[0] <= rightGridChain->get_u_value(gridIndex))
+	    {
+	      Int gridSep;
+	      Int segLeftMono, segLeftPass, segRightMono, segRightPass;
+	      findBotLeftSegment(leftChain,
+				 sep_left,
+				 down_leftCornerIndex,
+				 leftGridChain->get_u_value(gridIndex),
+				 segLeftMono,
+				 segLeftPass);
+	      findBotRightSegment(rightChain,
+				  sep_right,
+				  down_rightCornerIndex,
+				  rightGridChain->get_u_value(gridIndex),
+				  segRightMono,
+				  segRightPass);
+	      if(leftChain->getVertex(segLeftMono)[1] <= rightChain->getVertex(segRightMono)[1])
+		{
+		  gridSep = rightGridChain->getUlineIndex(gridIndex);
+		  while(leftGridChain->getGrid()->get_u_value(gridSep) > leftChain->getVertex(segLeftMono)[0])
+		    gridSep--;
+		}
+	      else 
+		{
+		  gridSep = leftGridChain->getUlineIndex(gridIndex);
+		  while(leftGridChain->getGrid()->get_u_value(gridSep) < rightChain->getVertex(segRightMono)[0])
+		    gridSep++;
+		}
+
+	      sampleBotLeftWithGridLinePost(leftChain->getVertex(segLeftMono),
+					    leftChain,
+					    segLeftMono-1,
+					    segLeftMono-1,
+					    segLeftPass,
+					    down_leftCornerIndex,
+					    leftGridChain->getGrid(),
+					    leftGridChain->getVlineIndex(gridIndex),
+					    leftGridChain->getUlineIndex(gridIndex),
+					    gridSep,
+					    pStream);
+	      sampleBotRightWithGridLinePost(rightChain->getVertex(segRightMono),
+					     rightChain,
+					     segRightMono-1,
+					     segRightMono-1,
+					     segRightPass,
+					     down_rightCornerIndex,
+					     rightGridChain->getGrid(),
+					     rightGridChain->getVlineIndex(gridIndex),
+					     gridSep,
+					     rightGridChain->getUlineIndex(gridIndex),
+					     pStream);
+	      Real tempTop[2];
+	      tempTop[0] = leftGridChain->getGrid()->get_u_value(gridSep);
+	      tempTop[1] = leftGridChain->get_v_value(gridIndex);
+	      monoTriangulationRecGen(tempTop, botVertex,
+				      leftChain, segLeftMono, leftEnd,
+				      rightChain, segRightMono, rightEnd,
+				      pStream);
+	    }//end if both sides have vertices inside the gridboundary points
+	  else if(leftChain->getVertex(sep_left)[0] >= leftGridChain->get_u_value(gridIndex)) //left n right out
+	    
+	    {
+	      Int segLeftMono, segLeftPass;
+	      findBotLeftSegment(leftChain,
+				 sep_left,
+				 down_leftCornerIndex,
+				 leftGridChain->get_u_value(gridIndex),
+				 segLeftMono,
+				 segLeftPass);				 
+              assert(segLeftPass <= sep_left); //make sure there is a point to the right of u.
+              monoTriangulation2(leftGridChain->get_vertex(gridIndex),
+				 leftChain->getVertex(segLeftPass),
+				 leftChain,
+				 down_leftCornerIndex,
+				 segLeftPass-1,
+				 1, //a increase chain
+				 pStream);
+              stripOfFanLeft(leftChain, segLeftMono, segLeftPass, 
+			     leftGridChain->getGrid(),
+			     leftGridChain->getVlineIndex(gridIndex),
+			     leftGridChain->getUlineIndex(gridIndex),
+			     rightGridChain->getUlineIndex(gridIndex),
+			     pStream,1 );
+/*
+	      sampleBotLeftWithGridLinePost(leftChain->getVertex(segLeftMono),
+					    leftChain,
+					    segLeftMono-1,
+					    segLeftMono-1,
+					    segLeftPass,
+					    down_leftCornerIndex,
+					    leftGridChain->getGrid(),
+					    leftGridChain->getVlineIndex(gridIndex),
+					    leftGridChain->getUlineIndex(gridIndex),
+					    rightGridChain->getUlineIndex(gridIndex),
+					    pStream);					    
+*/
+	      
+	      monoTriangulationRecGen(rightGridChain->get_vertex(gridIndex),
+				      botVertex,
+				      leftChain, segLeftMono, leftEnd,
+				      rightChain, down_rightCornerIndex, rightEnd,
+				      pStream);
+	    }//end left in right out
+	  else if(rightChain->getVertex(sep_right)[0] <= rightGridChain->get_u_value(gridIndex))//left out right in
+	    {	      
+	      Int segRightMono, segRightPass;
+	      findBotRightSegment(rightChain, sep_right, down_rightCornerIndex,
+				  rightGridChain->get_u_value(gridIndex),
+				  segRightMono,
+				  segRightPass);
+
+              assert(segRightPass <= sep_right); //make sure there is a point to the left of u.
+              monoTriangulation2(rightGridChain->get_vertex(gridIndex),
+				 rightChain->getVertex(segRightPass),
+				 rightChain,
+				 down_rightCornerIndex,
+				 segRightPass-1,
+				 0, // a decrease chain
+				 pStream);
+
+              stripOfFanRight(rightChain, segRightMono, segRightPass, 
+			      rightGridChain->getGrid(),
+			      rightGridChain->getVlineIndex(gridIndex),
+			      leftGridChain->getUlineIndex(gridIndex),
+			      rightGridChain->getUlineIndex(gridIndex),     
+			      pStream, 1);
+
+
+	      monoTriangulationRecGen(leftGridChain->get_vertex(gridIndex),
+				      botVertex,
+				      leftChain, down_leftCornerIndex, leftEnd,
+				      rightChain, segRightMono, rightEnd,
+				      pStream);	    	
+
+	    }//end left out right in
+	  else //left out, right out
+	    {
+	      sampleCompBotSimple(botVertex, 
+				 leftChain,
+				 leftEnd,
+				 rightChain,
+				 rightEnd,
+				 leftGridChain,
+				 rightGridChain,
+				 gridIndex,
+				 down_leftCornerWhere,
+				 down_leftCornerIndex,
+				 down_rightCornerWhere,
+				 down_rightCornerIndex,
+				 pStream);
+	    
+	    }//end leftout right out
+	}//end if separator exists
+      else //no separator
+	{
+
+	  sampleCompBotSimple(botVertex, 
+			     leftChain,
+			     leftEnd,
+			     rightChain,
+			     rightEnd,
+			     leftGridChain,
+			     rightGridChain,
+			     gridIndex,
+			     down_leftCornerWhere,
+			     down_leftCornerIndex,
+			     down_rightCornerWhere,
+			     down_rightCornerIndex,
+			     pStream);
+	}
+#endif
+    }//end id 0 2
+}//end if the functin
+
+				 
+void sampleCompBotSimple(Real* botVertex,
+		   vertexArray* leftChain,
+		   Int leftEnd,
+		   vertexArray* rightChain,
+		   Int rightEnd,
+		   gridBoundaryChain* leftGridChain,
+		   gridBoundaryChain* rightGridChain,
+		   Int gridIndex,
+		   Int down_leftCornerWhere,
+		   Int down_leftCornerIndex,
+		   Int down_rightCornerWhere,
+		   Int down_rightCornerIndex,
+		   primStream* pStream)  
+{
+  //the plan is to use monotriangulation algorithm.
+  Int i,k;
+  Real* ActualTop;
+  Real* ActualBot;
+  Int ActualLeftStart, ActualLeftEnd;
+  Int ActualRightStart, ActualRightEnd;
+  
+  //creat an array to store the points on the grid line
+  gridWrap* grid = leftGridChain->getGrid();
+  Int gridV = leftGridChain->getVlineIndex(gridIndex);
+  Int gridLeftU = leftGridChain->getUlineIndex(gridIndex);
+  Int gridRightU = rightGridChain->getUlineIndex(gridIndex);
+  Real2* gridPoints = (Real2*) malloc(sizeof(Real2) * (gridRightU - gridLeftU +1));
+  assert(gridPoints);
+
+  for(k=0, i=gridRightU; i>= gridLeftU; i--, k++)
+    {
+      gridPoints[k][0] = grid->get_u_value(i);
+      gridPoints[k][1] = grid->get_v_value(gridV);
+    }
+
+  if(down_rightCornerWhere != 0) //rightCorner is not on lef
+    ActualLeftEnd = leftEnd;
+  else
+    ActualLeftEnd = down_rightCornerIndex-1; //down_rightCornerIndex will be th actualBot
+  
+  if(down_leftCornerWhere != 0) //left corner is not on let chian
+    ActualLeftStart = leftEnd+1; //meaning that there is no actual left section
+  else
+    ActualLeftStart = down_leftCornerIndex;
+  
+  vertexArray ActualLeftChain(max(0, ActualLeftEnd - ActualLeftStart +1) + gridRightU - gridLeftU +1);
+  
+  for(i=0; i<gridRightU - gridLeftU +1 ; i++)
+    ActualLeftChain.appendVertex(gridPoints[i]);
+  for(i=ActualLeftStart; i<= ActualLeftEnd; i++)
+    ActualLeftChain.appendVertex(leftChain->getVertex(i));
+  
+  //determine ActualRightStart
+  if(down_rightCornerWhere != 2) //right is not on right
+    ActualRightStart = rightEnd +1; //meaning no section on right
+  else
+    ActualRightStart = down_rightCornerIndex;
+  
+  //determine actualrightEnd
+  if(down_leftCornerWhere != 2) //left is not on right
+    {
+
+      ActualRightEnd = rightEnd;
+    }
+  else //left corner is on right 
+    {
+      ActualRightEnd = down_leftCornerIndex-1; //down_leftCornerIndex will be the bot
+
+    }
+
+  //actual bot
+  if(down_rightCornerWhere == 2) 
+    {
+      if(down_leftCornerWhere == 2)
+	ActualBot = rightChain->getVertex(down_leftCornerIndex);
+      else
+	ActualBot = botVertex;
+    }
+  else if(down_rightCornerWhere == 1) //right corner bot
+    ActualBot = botVertex;
+  else //down_rightCornerWhere == 0
+    ActualBot = leftChain->getVertex(down_rightCornerIndex);
+  
+  ActualTop = gridPoints[0];
+/*
+printf("in bot simple, actual leftChain is \n");
+ActualLeftChain.print();
+printf("Actual Top = %f,%f\n", ActualTop[0],ActualTop[1]);
+printf("Actual Bot = %f,%f\n", ActualBot[0],ActualBot[1]);
+printf("Actual right start = %i, end=%i\n",ActualRightStart,   ActualRightEnd);
+*/
+  if(rightChain->getVertex(ActualRightStart)[1] == ActualTop[1])
+    monoTriangulationRecGenOpt(rightChain->getVertex(ActualRightStart),
+			    ActualBot,
+			    &ActualLeftChain,
+			    0, 
+			    ActualLeftChain.getNumElements()-1,
+			    rightChain,
+			    ActualRightStart+1,
+			    ActualRightEnd,
+			    pStream);
+  else
+    monoTriangulationRecGenOpt(ActualTop, ActualBot, 
+			  &ActualLeftChain,
+			  1, //the first one is the top vertex
+			  ActualLeftChain.getNumElements()-1,
+			  rightChain,
+			  ActualRightStart,
+			  ActualRightEnd,
+			  pStream);
+  free(gridPoints);
+}
+  
+  
+				 
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompBot.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompBot.h
new file mode 100644
index 000000000..7b982794c
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompBot.h
@@ -0,0 +1,138 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _SAMPLECOMPBOT_H
+#define _SAMPLECOMPBOT_H
+
+#include "sampleMonoPoly.h"
+
+void findBotLeftSegment(vertexArray* leftChain, 
+			Int leftEnd,
+			Int leftCorner,
+			Real u,
+			Int& ret_index_mono,
+			Int& ret_index_pass);
+
+void findBotRightSegment(vertexArray* rightChain, 
+			 Int rightEnd,
+			 Int rightCorner,
+			 Real u,
+			 Int& ret_index_mono,
+			 Int& ret_index_pass);
+
+
+void sampleBotRightWithGridLinePost(Real* botVertex,
+				    vertexArray* rightChain,
+				    Int rightEnd,
+				    Int segIndexMono,
+				    Int segIndexPass,
+				    Int rightCorner,
+				    gridWrap* grid,
+				    Int gridV,
+				    Int leftU,
+				    Int rightU,
+				    primStream* pStream);
+
+
+void sampleBotRightWithGridLine(Real* botVertex, 
+				vertexArray* rightChain,
+				Int rightEnd,
+				Int rightCorner,
+				gridWrap* grid,
+				Int gridV,
+				Int leftU,
+				Int rightU,
+				primStream* pStream);
+
+
+void sampleBotLeftWithGridLinePost(Real* botVertex,
+				   vertexArray* leftChain,
+				   Int leftEnd,
+				   Int segIndexMono,
+				   Int segIndexPass,
+				   Int leftCorner,
+				   gridWrap* grid,
+				   Int gridV,
+				   Int leftU, 
+				   Int rightU,
+				   primStream* pStream);
+
+
+void sampleBotLeftWithGridLine(Real* botVertex,
+			       vertexArray* leftChain,
+			       Int leftEnd,
+			       Int leftCorner,
+			       gridWrap* grid,
+			       Int gridV,
+			       Int leftU,
+			       Int rightU,
+			       primStream* pStream);
+
+
+Int findBotSeparator(vertexArray* leftChain,
+		     Int leftEnd,
+		     Int leftCorner,
+		     vertexArray* rightChain,
+		     Int rightEnd,
+		     Int rightCorner,
+		     Int& ret_sep_left,
+		     Int& ret_sep_right);
+
+void sampleCompBot(Real* botVertex,
+		   vertexArray* leftChain,
+		   Int leftEnd,
+		   vertexArray* rightChain,
+		   Int rightEnd,
+		   gridBoundaryChain* leftGridChain,
+		   gridBoundaryChain* rightGridChain,
+		   Int gridIndex,
+		   Int down_leftCornerWhere,
+		   Int down_leftCornerIndex,
+		   Int down_rightCornerWhere,
+		   Int down_rightCornerIndex,
+		   primStream* pStream);
+
+void sampleCompBotSimple(Real* botVertex,
+		   vertexArray* leftChain,
+		   Int leftEnd,
+		   vertexArray* rightChain,
+		   Int rightEnd,
+		   gridBoundaryChain* leftGridChain,
+		   gridBoundaryChain* rightGridChain,
+		   Int gridIndex,
+		   Int down_leftCornerWhere,
+		   Int down_leftCornerIndex,
+		   Int down_rightCornerWhere,
+		   Int down_rightCornerIndex,
+		   primStream* pStream);
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompRight.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompRight.cc
new file mode 100644
index 000000000..d01e50018
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompRight.cc
@@ -0,0 +1,644 @@
+/*
+** 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 "sampleCompRight.h"
+
+#define max(a,b) ((a>b)? a:b)
+#define min(a,b) ((a>b)? b:a)
+
+
+
+#ifdef NOT_TAKEOUT
+
+/*notice that we need leftChain because the 
+ *corners could be on the leftChain.
+ */
+void sampleCompRight(Real* topVertex, Real* botVertex,
+		    vertexArray* leftChain,
+		    Int leftStartIndex, Int leftEndIndex,
+		    vertexArray* rightChain,
+		    Int rightStartIndex, Int rightEndIndex,
+		    gridBoundaryChain* rightGridChain,
+		    Int gridIndex1, Int gridIndex2,
+		    Int up_rightCornerWhere,
+		    Int up_rightCornerIndex,
+		    Int down_rightCornerWhere,
+		    Int down_rightCornerIndex,
+		    primStream* pStream)
+{
+  /*find out whether there is a trim vertex  which is
+   *inbetween the top and bot grid lines or not.
+   */
+  Int midIndex1;
+  Int midIndex2;
+  Int gridMidIndex1 = 0, gridMidIndex2 = 0;
+  //midIndex1: array[i] <= v, array[i+1] > v
+  //midIndex2: array[i] >= v,  array[i+1] < v
+  midIndex1 = rightChain->findIndexBelowGen(rightGridChain->get_v_value(gridIndex1),
+					    rightStartIndex,
+					    rightEndIndex);
+  midIndex2 = -1; //initilization
+  if(midIndex1 <= rightEndIndex && gridIndex1 < gridIndex2)
+    if(rightChain->getVertex(midIndex1)[1] >= rightGridChain->get_v_value(gridIndex2))
+      {
+	//midIndex2 must exist:
+	midIndex2 = rightChain->findIndexAboveGen(rightGridChain->get_v_value(gridIndex2),
+						  midIndex1, //midIndex1<=midIndex2
+						  rightEndIndex);
+	//find gridMidIndex1 so that either it=gridIndex1 when the gridline is 
+	// at the same height as trim vertex midIndex1, or it is the last one 
+	//which is strictly above midIndex1.
+	{
+	  Real temp = rightChain->getVertex(midIndex1)[1];
+	  if(rightGridChain->get_v_value(gridIndex1) == temp)
+	    gridMidIndex1 = gridIndex1;
+	  else
+	    {
+	    gridMidIndex1 = gridIndex1;
+	    while(rightGridChain->get_v_value(gridMidIndex1) > temp)
+	      gridMidIndex1++;
+	    gridMidIndex1--;
+	    }
+	}//end of find gridMindIndex1
+	//find gridMidIndex2 so that it is the (first one below or equal 
+	//midIndex) last one above or equal midIndex2
+	{
+	  Real temp = rightChain->getVertex(midIndex2)[1];
+	  for(gridMidIndex2 = gridMidIndex1+1; gridMidIndex2 <= gridIndex2; gridMidIndex2++)
+	    if(rightGridChain->get_v_value(gridMidIndex2) <= temp)
+	      break;
+
+	  assert(gridMidIndex2 <= gridIndex2);
+	}//end of find gridMidIndex2
+      }
+
+
+  
+  //to interprete the corner information
+  Real* cornerTop;
+  Real* cornerBot;
+  Int cornerRightStart;
+  Int cornerRightEnd;
+  Int cornerLeftUpEnd;
+  Int cornerLeftDownStart;
+  if(up_rightCornerWhere == 2) //right corner is on right chain
+    {
+      cornerTop = rightChain->getVertex(up_rightCornerIndex);
+      cornerRightStart = up_rightCornerIndex+1;
+      cornerLeftUpEnd = -1; //no left
+    }
+  else if(up_rightCornerWhere == 1) //right corner is on top
+    {
+      cornerTop = topVertex;
+      cornerRightStart = rightStartIndex;
+      cornerLeftUpEnd = -1; //no left
+    }
+  else //right corner is on left chain
+    {
+      cornerTop = topVertex;
+      cornerRightStart = rightStartIndex;
+      cornerLeftUpEnd = up_rightCornerIndex;
+    }
+  
+  if(down_rightCornerWhere == 2) //right corner is on right chan
+    {
+      cornerBot = rightChain->getVertex(down_rightCornerIndex);
+      cornerRightEnd = down_rightCornerIndex-1;
+      cornerLeftDownStart = leftEndIndex+1; //no left
+    }
+  else if (down_rightCornerWhere == 1) //right corner is at bot
+    {
+      cornerBot = botVertex;
+      cornerRightEnd = rightEndIndex;
+      cornerLeftDownStart = leftEndIndex+1; //no left     
+    }
+  else //right corner is on the left chain
+    {
+      cornerBot = botVertex;
+      cornerRightEnd = rightEndIndex;
+      cornerLeftDownStart = down_rightCornerIndex;
+    }
+
+  //sample
+  if(midIndex2 >= 0) //there is a trm point between grid lines
+    {
+
+      sampleRightSingleTrimEdgeRegionGen(cornerTop, rightChain->getVertex(midIndex1),
+					 rightChain,
+					 cornerRightStart,
+					 midIndex1-1,
+					 rightGridChain,
+					 gridIndex1,
+					 gridMidIndex1,
+					 leftChain,
+					 leftStartIndex,
+					 cornerLeftUpEnd,
+					 0, //no left down section,
+					 -1,
+					 pStream);
+
+      sampleRightSingleTrimEdgeRegionGen(rightChain->getVertex(midIndex2),
+					 cornerBot,
+					 rightChain,
+					 midIndex2+1,
+					 cornerRightEnd,
+					 rightGridChain,
+					 gridMidIndex2,
+					 gridIndex2,
+					 leftChain,
+					 0, //no left up section
+					 -1,
+					 cornerLeftDownStart,
+					 leftEndIndex,
+					 pStream);
+
+      sampleRightStripRecF(rightChain,
+			   midIndex1,
+			   midIndex2,
+			   rightGridChain,
+			   gridMidIndex1,
+			   gridMidIndex2,
+			   pStream);
+
+    }
+  else
+    {
+      sampleRightSingleTrimEdgeRegionGen(cornerTop, cornerBot,
+					 rightChain,
+					 cornerRightStart,
+					 cornerRightEnd,
+					 rightGridChain,
+					 gridIndex1,
+					 gridIndex2,
+					 leftChain,
+					 leftStartIndex,
+					 cornerLeftUpEnd,
+					 cornerLeftDownStart,
+					 leftEndIndex,
+					 pStream);
+    }
+}
+
+void sampleRightSingleTrimEdgeRegionGen(Real topVertex[2], Real botVertex[2],
+					 vertexArray* rightChain,
+					 Int rightStart,
+					 Int rightEnd,
+					 gridBoundaryChain* gridChain,
+					 Int gridBeginIndex,
+					 Int gridEndIndex,
+					 vertexArray* leftChain,
+					 Int leftUpBegin,
+					 Int leftUpEnd,
+					 Int leftDownBegin,
+					 Int leftDownEnd,
+					 primStream* pStream)
+{
+  Int i,k;
+   /*creat an array to store all the up and down secments of the left chain,
+   *and the right end grid points
+   *
+   *although vertex array is a dynamic array, but to gain efficiency,
+   *it is better to initiliza the exact array size
+   */
+  vertexArray vArray(gridEndIndex-gridBeginIndex+1 +
+		     max(0,leftUpEnd - leftUpBegin+1)+
+		     max(0,leftDownEnd - leftDownBegin+1));
+  //append the vertices on the up section of the left chain
+  for(i=leftUpBegin; i<= leftUpEnd; i++)
+    vArray.appendVertex(leftChain->getVertex(i));
+  
+  //append the vertices of the right extremal grid points,
+  //and at the same time, perform triangulation for the stair cases
+  vArray.appendVertex(gridChain->get_vertex(gridBeginIndex));
+  
+  for(k=1, i=gridBeginIndex+1; i<= gridEndIndex; i++, k++)
+    {
+      vArray.appendVertex(gridChain->get_vertex(i));
+      
+      //output the fan of the grid points of the (i)th and (i-1)th grid line.
+      gridChain->rightEndFan(i, pStream);
+    }
+  
+  //append all the vertices on the down section of the left chain
+  for(i=leftDownBegin; i<= leftDownEnd; i++)
+    vArray.appendVertex(leftChain->getVertex(i));
+  monoTriangulationRecGen(topVertex, botVertex,
+			  &vArray, 0, vArray.getNumElements()-1,
+			  rightChain, rightStart, rightEnd,
+			  pStream);
+}
+  
+void sampleRightSingleTrimEdgeRegion(Real upperVert[2], Real lowerVert[2],
+				     gridBoundaryChain* gridChain,
+				     Int beginIndex,
+				     Int endIndex,
+				     primStream* pStream)
+{
+  Int i,k;
+  vertexArray vArray(endIndex-beginIndex+1);
+  vArray.appendVertex(gridChain->get_vertex(beginIndex));
+  for(k=1, i=beginIndex+1; i<= endIndex; i++, k++)
+    {
+      vArray.appendVertex(gridChain->get_vertex(i));
+      //output the fan of the grid points of the (i)_th and i-1th gridLine
+      gridChain->rightEndFan(i, pStream);
+    }
+  monoTriangulation2(upperVert, lowerVert, &vArray, 0, endIndex-beginIndex, 
+		     1, //increase chain (to the left)
+		     pStream);
+}
+		      
+
+/*the gridlines from rightGridChainStartIndex to 
+ *rightGridChainEndIndex are assumed to form a 
+ *connected componenet
+ *the trm vertex of topRightIndex is assumed to be below
+ *or equal the first gridLine, and the trm vertex of
+ *botRightIndex is assumed to be above or equal the last gridline
+ **there could be multipe trm vertices equal to the last gridline, but
+ **only one could be equal to top gridline. shape: ____| (recall that
+ **for left chain recF, we allow shape: |----
+ *if botRightIndex<topRightIndex, then no connected componenet exists, and 
+ *no triangles are generated.
+ *Othewise, botRightIndex>= topRightIndex, there is at least one triangles to 
+ *output
+ */
+void sampleRightStripRecF(vertexArray* rightChain,
+		     Int topRightIndex,
+		     Int botRightIndex,
+		     gridBoundaryChain* rightGridChain,
+		     Int rightGridChainStartIndex,
+		     Int rightGridChainEndIndex,	
+		     primStream* pStream
+		     )
+{
+
+  //sstop conditionL: if topRightIndex > botRightIndex, then stop
+  if(topRightIndex > botRightIndex)
+    return;
+  
+  //if there is only one grid line, return
+  if(rightGridChainStartIndex >= rightGridChainEndIndex)
+    return;
+
+
+  assert(rightChain->getVertex(topRightIndex)[1] <= rightGridChain->get_v_value(rightGridChainStartIndex) &&
+	 rightChain->getVertex(botRightIndex)[1] >= rightGridChain->get_v_value(rightGridChainEndIndex));
+
+  //firstfind the first trim vertex which is strictly below the second top
+  //grid line: index1. 
+  Real secondGridChainV = rightGridChain->get_v_value(rightGridChainStartIndex+1);
+  Int index1 = topRightIndex;
+  while(rightChain->getVertex(index1)[1] >= secondGridChainV){
+    index1++;
+    if(index1 >  botRightIndex)
+      break;
+  }
+  //now rightChain->getVertex(index1-1)[1] >= secondGridChainV and
+  //rightChain->getVertex(index1)[1] < secondGridChainV and
+  //we should include index1-1 to perform a gridStep
+    index1--;
+
+  //now we have rightChain->getVertex(index1)[1] >= secondGridChainV, and
+  //rightChain->getVertex(index1+1)[1] < secondGridChainV
+  sampleRightOneGridStep(rightChain, topRightIndex, index1, rightGridChain, rightGridChainStartIndex, pStream);
+
+  //if rightChain->getVertex(index1)[1] ==secondGridChainV then we can 
+  //recurvesively to the rest
+  if(rightChain->getVertex(index1)[1] == secondGridChainV)
+    {
+
+      
+      sampleRightStripRecF(rightChain, index1, botRightIndex, rightGridChain, rightGridChainStartIndex+1, rightGridChainEndIndex, pStream);
+    }
+  else if(index1 < botRightIndex)
+    {
+      //otherwise, we have rightChain->getVertex(index1)[1] > secondV
+      //let the next trim vertex be nextTrimVertex, (which should be strictly
+      //below the second grid line). Find the last grid line index2 which is STRICTLY ABOVE
+      //nextTrimVertex.
+      //sample one trm edge region.
+      Real *uppervert, *lowervert;
+      uppervert = rightChain->getVertex(index1);
+      lowervert = rightChain->getVertex(index1+1); //okay since index1<botRightindex
+      Int index2 = rightGridChainStartIndex+1;
+      while(rightGridChain->get_v_value(index2) > lowervert[1])
+	{
+	  index2++;
+	  if(index2 > rightGridChainEndIndex)
+	    break;
+	}
+      index2--;
+      
+      sampleRightSingleTrimEdgeRegion(uppervert, lowervert, rightGridChain, rightGridChainStartIndex+1, index2, pStream);
+      
+      //recursion
+      sampleRightStripRecF(rightChain, index1+1, botRightIndex, rightGridChain, index2, rightGridChainEndIndex, pStream);
+    }
+}
+
+//the degenerate case of sampleRightOneGridStep
+void sampleRightOneGridStepNoMiddle(vertexArray* rightChain,
+				    Int beginRightIndex,
+				    Int endRightIndex,
+				    gridBoundaryChain* rightGridChain,
+				    Int rightGridChainStartIndex,
+				    primStream* pStream)
+{
+  /*since there is no middle, there is at most one point which is on the 
+   *second grid line, there could be multiple points on the first (top)
+   *grid line.
+   */
+  rightGridChain->rightEndFan(rightGridChainStartIndex+1, pStream);
+  monoTriangulation2(rightGridChain->get_vertex(rightGridChainStartIndex),
+		     rightGridChain->get_vertex(rightGridChainStartIndex+1),
+		     rightChain,
+		     beginRightIndex,
+		     endRightIndex,
+		     0, //decrease chain
+		     pStream);
+}
+
+//sampling the right area in between two grid lines
+//shape: _________|
+void sampleRightOneGridStep(vertexArray* rightChain, 
+			    Int beginRightIndex,
+			    Int endRightIndex,
+			    gridBoundaryChain* rightGridChain,
+			    Int rightGridChainStartIndex,
+			    primStream* pStream)
+{
+  if(checkMiddle(rightChain, beginRightIndex, endRightIndex,
+		 rightGridChain->get_v_value(rightGridChainStartIndex),
+		 rightGridChain->get_v_value(rightGridChainStartIndex+1))<0)
+    {
+      sampleRightOneGridStepNoMiddle(rightChain, beginRightIndex, endRightIndex, rightGridChain, rightGridChainStartIndex, pStream);
+      return;
+    }
+
+  //copy into a polygn
+  {
+    directedLine* poly = NULL;
+    sampledLine* sline;
+    directedLine* dline;
+    gridWrap* grid = rightGridChain->getGrid();
+    float vert1[2];
+    float vert2[2];
+    Int i;
+    
+    Int innerInd = rightGridChain->getInnerIndex(rightGridChainStartIndex+1);
+    Int upperInd = rightGridChain->getUlineIndex(rightGridChainStartIndex);
+    Int lowerInd = rightGridChain->getUlineIndex(rightGridChainStartIndex+1);
+    Real upperV = rightGridChain->get_v_value(rightGridChainStartIndex);
+    Real lowerV = rightGridChain->get_v_value(rightGridChainStartIndex+1);
+    
+    //the upper gridline
+    vert1[1]=vert2[1]=upperV;
+    for(i=upperInd;
+	i>innerInd;
+	i--)
+      {
+	vert1[0]=grid->get_u_value(i);
+	vert2[0]=grid->get_u_value(i-1);
+	sline = new sampledLine(vert1, vert2);
+	dline = new directedLine(INCREASING, sline);
+	if(poly == NULL)
+	  poly = dline;
+	else
+	  poly->insert(dline);
+      }
+    
+    //the vertical grid line segment
+    vert1[0]=vert2[0] = grid->get_u_value(innerInd);
+    vert1[1]=upperV;
+    vert2[1]=lowerV;
+    sline=new sampledLine(vert1, vert2);
+    dline=new directedLine(INCREASING, sline);
+    if(poly == NULL)
+      poly = dline;
+    else
+      poly->insert(dline);
+    
+    //the lower grid line
+    vert1[1]=vert2[1]=lowerV;
+    for(i=innerInd; i<lowerInd; i++)
+      {
+	vert1[0] = grid->get_u_value(i);
+	vert2[0] = grid->get_u_value(i+1);
+	sline = new sampledLine(vert1, vert2);
+	dline = new directedLine(INCREASING, sline);
+	poly->insert(dline);       
+      }
+
+    //the edge connecting lower grid to right chain
+    vert1[0]=grid->get_u_value(lowerInd);
+    sline = new sampledLine(vert1, rightChain->getVertex(endRightIndex));
+    dline = new directedLine(INCREASING, sline);
+    poly->insert(dline);
+    
+    
+    //the right Chain
+    for(i=endRightIndex; i>beginRightIndex; i--)
+      {
+	sline = new sampledLine(rightChain->getVertex(i), rightChain->getVertex(i-1));
+	dline = new directedLine(INCREASING, sline);
+	poly->insert(dline);
+      }
+
+    //the edge connecting right chain with upper grid
+    vert2[1]=upperV;
+    vert2[0]=grid->get_u_value(upperInd);
+    sline = new sampledLine(rightChain->getVertex(beginRightIndex), vert2);
+    dline = new directedLine(INCREASING, sline);
+    poly->insert(dline);    
+    monoTriangulationOpt(poly, pStream);
+    //clean up
+    poly->deleteSinglePolygonWithSline();
+
+    return;
+  }
+	   
+  //this following code cannot be reached, but leave it for debuggig purpose.
+  Int i;
+  //find the maximal U-monotone chain of beginRightIndex, beginRightIndex+1,...
+  i=beginRightIndex;
+  Real prevU = rightChain->getVertex(i)[0];
+  for(i=beginRightIndex+1; i<= endRightIndex; i++){
+    Real thisU = rightChain->getVertex(i)[0];
+    if(thisU < prevU)
+      prevU = thisU;
+    else
+      break;
+  }
+  //from beginRightIndex to i-1 is strictly U-monotne
+  //if(i-1==beginRightIndex and the vertex of rightchain is on the first 
+  //gridline, then we should use 2 vertices  on the right chain. Of we only 
+  //use one (begin), we would output degenrate triangles.
+  if(i-1 == beginRightIndex && rightChain->getVertex(beginRightIndex)[1] == rightGridChain->get_v_value(rightGridChainStartIndex))
+    i++;
+  
+  Int j = endRightIndex -1;
+  if(rightGridChain->getInnerIndex(rightGridChainStartIndex+1) < rightGridChain->getUlineIndex(rightGridChainStartIndex+1))
+    {
+      j = rightChain->findDecreaseChainFromEnd(i-1/*beginRightIndex*/, endRightIndex);
+      Int temp = endRightIndex;
+      //now from j+1 to end is strictly U-monotone.
+      //if j+1 is on the last grid line, then we wat to skip to the vertex   
+      //whcih is strictly above the second grid line. This vertex must exist 
+      //since there is a middle vertex
+      if(j+1 == endRightIndex)
+	{
+	  while(rightChain->getVertex(j+1)[1] == rightGridChain->get_v_value(rightGridChainStartIndex+1))
+	    j--;
+
+	  monoTriangulation2(rightChain->getVertex(j+1),
+			     rightGridChain->get_vertex(rightGridChainStartIndex+1),
+			     rightChain,
+			     j+2,
+			     endRightIndex,
+			     0, //a decrease chain
+			     pStream);
+
+	  temp = j+1;
+	}
+
+      stripOfFanRight(rightChain, temp, j+1, rightGridChain->getGrid(),
+		      rightGridChain->getVlineIndex(rightGridChainStartIndex+1),
+		      rightGridChain->getInnerIndex(rightGridChainStartIndex+1),
+		      rightGridChain->getUlineIndex(rightGridChainStartIndex+1),
+		      pStream,
+		      0 //the grid line is below the trim line
+		      );
+
+    }
+
+
+  stripOfFanRight(rightChain, i-1, beginRightIndex, rightGridChain->getGrid(),
+		  rightGridChain->getVlineIndex(rightGridChainStartIndex),
+		  rightGridChain->getInnerIndex(rightGridChainStartIndex+1),
+		  rightGridChain->getUlineIndex(rightGridChainStartIndex),
+		  pStream,
+		  1 //the grid line is above the trm lines
+		  );
+
+  //monotone triangulate the remaining rightchain together with the
+  //two vertices on the two grid v-lines
+  Real vert[2][2];
+  vert[0][0] = vert[1][0] = rightGridChain->getInner_u_value(rightGridChainStartIndex+1);
+  vert[0][1] = rightGridChain->get_v_value(rightGridChainStartIndex);
+  vert[1][1] = rightGridChain->get_v_value(rightGridChainStartIndex+1);
+
+  monoTriangulation2(&vert[0][0], 
+		     &vert[1][0],
+		     rightChain,
+		     i-1,
+		     j+1,
+		     0, ///a decreae chain
+		     pStream);
+}
+		  
+#endif    
+
+void stripOfFanRight(vertexArray* rightChain, 
+		    Int largeIndex,
+		    Int smallIndex,
+		    gridWrap* grid,
+		    Int vlineIndex,
+		    Int ulineSmallIndex,
+		    Int ulineLargeIndex,
+		    primStream* pStream,
+		    Int gridLineUp /*1 if the grid line is above the trim lines*/
+		     )
+{
+  assert(largeIndex >= smallIndex);
+
+  Real grid_v_value;
+  grid_v_value = grid->get_v_value(vlineIndex);
+
+  Real2* trimVerts=(Real2*) malloc(sizeof(Real2)* (largeIndex-smallIndex+1));
+  assert(trimVerts);
+
+
+  Real2* gridVerts=(Real2*) malloc(sizeof(Real2)* (ulineLargeIndex-ulineSmallIndex+1));
+  assert(gridVerts);
+
+  Int k,i;
+  if(! gridLineUp) /*trim line is above grid line, so trim vertices are going right when index increases*/
+    for(k=0, i=smallIndex; i<=largeIndex; i++, k++)
+      {
+      trimVerts[k][0] = rightChain->getVertex(i)[0];
+      trimVerts[k][1] = rightChain->getVertex(i)[1];
+    }
+  else
+    for(k=0, i=largeIndex; i>=smallIndex; i--, k++)
+      {
+	trimVerts[k][0] = rightChain->getVertex(i)[0];
+	trimVerts[k][1] = rightChain->getVertex(i)[1];
+      }
+
+  for(k=0, i=ulineSmallIndex; i<= ulineLargeIndex; i++, k++)
+    {
+      gridVerts[k][0] = grid->get_u_value(i);
+      gridVerts[k][1] = grid_v_value;
+    }
+
+  if(gridLineUp)
+    triangulateXYMono(
+		      ulineLargeIndex-ulineSmallIndex+1, gridVerts,
+		      largeIndex-smallIndex+1, trimVerts,
+		      pStream);
+  else
+    triangulateXYMono(largeIndex-smallIndex+1, trimVerts,
+		      ulineLargeIndex-ulineSmallIndex+1, gridVerts,
+		      pStream);
+  free(trimVerts);
+  free(gridVerts);
+}
+
+
+
+
+
+
+
+
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompRight.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompRight.h
new file mode 100644
index 000000000..4670b87ca
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompRight.h
@@ -0,0 +1,117 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _SAMPLECOMPRIGHT_H
+#define _SAMPLECOMPRIGHT_H
+
+#define NOT_TAKEOUT
+
+#include "sampleMonoPoly.h"
+void stripOfFanRight(vertexArray* rightChain, 
+		    Int largeIndex,
+		    Int smallIndex,
+		    gridWrap* grid,
+		    Int vlineIndex,
+		    Int ulineSmallIndex,
+		    Int ulineLargeIndex,
+		    primStream* pStream,
+		    Int gridLineUp /*1 if grid line is above the trim lines */
+		     );
+
+#ifdef NOT_TAKEOUT
+void sampleRightStripRecF(vertexArray* rightChain,
+		     Int topRightIndex,
+		     Int botRightIndex,
+		     gridBoundaryChain* rightGridChain,
+		     Int rightGridChainStartIndex,
+		     Int rightGridChainEndIndex,	
+		     primStream* pStream
+		     );
+//the degenerate case of sampleRightOneGridStep
+void sampleRightOneGridStepNoMiddle(vertexArray* rightChain,
+				    Int beginRightIndex,
+				    Int endRightIndex,
+				    gridBoundaryChain* rightGridChain,
+				    Int rightGridChainStartIndex,
+				    primStream* pStream);
+//sampling the right area in between two grid lines
+//shape: _________|
+void sampleRightOneGridStep(vertexArray* rightChain, 
+			    Int beginRightIndex,
+			    Int endRightIndex,
+			    gridBoundaryChain* rightGridChain,
+			    Int rightGridChainStartIndex,
+			    primStream* pStream);
+void sampleRightSingleTrimEdgeRegion(Real upperVert[2], Real lowerVert[2],
+				     gridBoundaryChain* gridChain,
+				     Int beginIndex,
+				     Int endIndex,
+				     primStream* pStream);
+//the degenerate case of sampleRightOneGridStep
+void sampleRightOneGridStepNoMiddle(vertexArray* rightChain,
+				    Int beginRightIndex,
+				    Int endRightIndex,
+				    gridBoundaryChain* rightGridChain,
+				    Int rightGridChainStartIndex,
+				    primStream* pStream);
+
+void sampleCompRight(Real* topVertex, Real* botVertex,
+                    vertexArray* leftChain,
+                    Int leftStartIndex, Int leftEndIndex,
+                    vertexArray* rightChain,
+                    Int rightStartIndex, Int rightEndIndex,
+                    gridBoundaryChain* rightGridChain,
+                    Int gridIndex1, Int gridIndex2,
+                    Int up_leftCornerWhere,
+                    Int up_leftCornerIndex,
+                    Int down_leftCornerWhere,
+                    Int down_leftCornerIndex,
+                    primStream* pStream);
+
+void sampleRightSingleTrimEdgeRegionGen(Real topVert[2], Real botVert[2],
+                                       vertexArray* rightChain,
+                                       Int rightStart,
+                                       Int rightEnd,
+                                       gridBoundaryChain* gridChain,
+                                       Int gridBegindex,
+                                       Int gridEndIndex,
+                                       vertexArray* leftChain,
+                                       Int leftUpBegin,
+                                       Int leftUpEnd,
+                                       Int leftDownBegin,
+                                       Int leftDownEnd,
+                                       primStream* pStream);
+#endif
+
+#endif
+
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompTop.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompTop.cc
new file mode 100644
index 000000000..b7b929623
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompTop.cc
@@ -0,0 +1,1030 @@
+/*
+** 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 <math.h>
+#include "zlassert.h"
+#include "sampleCompTop.h"
+#include "sampleCompRight.h"
+
+#define max(a,b) ((a>b)? a:b)
+
+//return : index_small, and index_large,
+//from [small, large] is strictly U-monotne,
+//from [large+1, end] is <u
+//and vertex[large][0] is >= u
+//if eveybody is <u, the large = start-1.
+//otherwise both large and small are meaningful and we have start<=small<=large<=end
+void findTopLeftSegment(vertexArray* leftChain,
+                        Int leftStart,
+                        Int leftEnd,
+                        Real u,
+                        Int& ret_index_small,
+                        Int& ret_index_large
+                        )
+{
+  Int i;
+  assert(leftStart <= leftEnd);
+  for(i=leftEnd; i>= leftStart; i--)
+    {
+      if(leftChain->getVertex(i)[0] >= u)
+        break;
+    }
+  ret_index_large = i;
+  if(ret_index_large >= leftStart)
+    {
+      for(i=ret_index_large; i>leftStart; i--)
+        {
+          if(leftChain->getVertex(i-1)[0] <= leftChain->getVertex(i)[0])
+            break;
+        }
+      ret_index_small = i;
+    }
+}
+
+void findTopRightSegment(vertexArray* rightChain,
+                         Int rightStart,
+                         Int rightEnd,
+                         Real u,
+                         Int& ret_index_small,
+                         Int& ret_index_large)
+{
+  Int i;
+  assert(rightStart<=rightEnd);
+  for(i=rightEnd; i>=rightStart; i--)
+    {
+      if(rightChain->getVertex(i)[0] <= u)
+        break;
+    }
+  ret_index_large = i;
+  if(ret_index_large >= rightStart)
+    {
+      for(i=ret_index_large; i>rightStart;i--)
+        {
+          if(rightChain->getVertex(i-1)[0] >= rightChain->getVertex(i)[0])           
+	    break;
+        }
+      ret_index_small = i;
+    }
+}
+
+
+void sampleTopRightWithGridLinePost(Real* topVertex,
+				   vertexArray* rightChain,
+				   Int rightStart,
+				   Int segIndexSmall,
+				   Int segIndexLarge,
+				   Int rightEnd,
+				   gridWrap* grid,
+				   Int gridV,
+				   Int leftU,
+				   Int rightU,
+				   primStream* pStream)
+{
+  //the possible section which is to the right of rightU
+  if(segIndexLarge < rightEnd)
+    {
+      Real *tempTop;
+      if(segIndexLarge >= rightStart)
+        tempTop = rightChain->getVertex(segIndexLarge);
+      else
+        tempTop = topVertex;
+      Real tempBot[2];
+      tempBot[0] = grid->get_u_value(rightU);
+      tempBot[1] = grid->get_v_value(gridV);
+monoTriangulationRecGenOpt(tempTop, tempBot,
+			   NULL, 1,0,
+			   rightChain, segIndexLarge+1, rightEnd,
+			   pStream);
+/*
+      monoTriangulation2(tempTop, tempBot,
+                         rightChain,
+                         segIndexLarge+1,
+                         rightEnd,
+                         0, //a decrease  chian
+                         pStream);
+*/
+
+    }
+  
+  //the possible section which is strictly Umonotone
+  if(segIndexLarge >= rightStart)
+    {
+      stripOfFanRight(rightChain, segIndexLarge, segIndexSmall, grid, gridV, leftU, rightU, pStream, 0);
+      Real tempBot[2];
+      tempBot[0] = grid->get_u_value(leftU);
+      tempBot[1] = grid->get_v_value(gridV);
+      monoTriangulation2(topVertex, tempBot, rightChain, rightStart, segIndexSmall, 0, pStream);
+    }
+  else //the topVertex forms a fan with the grid points
+    grid->outputFanWithPoint(gridV, leftU, rightU, topVertex, pStream);
+}
+
+void sampleTopRightWithGridLine(Real* topVertex,
+                                vertexArray* rightChain,
+                                Int rightStart,
+                                Int rightEnd,
+                                gridWrap* grid,
+                                Int gridV,
+                                Int leftU,
+                                Int rightU,
+                                primStream* pStream
+                                )
+{
+  //if right chian is empty, then there is only one topVertex with one grid line
+  if(rightEnd < rightStart){
+    grid->outputFanWithPoint(gridV, leftU, rightU, topVertex, pStream);
+    return;
+  }
+
+  Int segIndexSmall, segIndexLarge;
+  findTopRightSegment(rightChain,
+                      rightStart,
+                      rightEnd,
+                      grid->get_u_value(rightU),
+                      segIndexSmall,
+                      segIndexLarge
+                      );
+  sampleTopRightWithGridLinePost(topVertex, rightChain,
+				 rightStart,
+				 segIndexSmall,
+				 segIndexLarge,
+				 rightEnd,
+				 grid,
+				 gridV,
+				 leftU,
+				 rightU,
+				 pStream);
+}
+
+
+void sampleTopLeftWithGridLinePost(Real* topVertex,
+				   vertexArray* leftChain,
+				   Int leftStart,
+				   Int segIndexSmall,
+				   Int segIndexLarge,
+				   Int leftEnd,
+				   gridWrap* grid,
+				   Int gridV,
+				   Int leftU,
+				   Int rightU,
+				   primStream* pStream)
+{
+  //the possible section which is to the left of leftU
+
+  if(segIndexLarge < leftEnd)
+    {
+      Real *tempTop;
+      if(segIndexLarge >= leftStart)
+        tempTop = leftChain->getVertex(segIndexLarge);
+      else
+        tempTop = topVertex;
+      Real tempBot[2];
+      tempBot[0] = grid->get_u_value(leftU);
+      tempBot[1] = grid->get_v_value(gridV);
+
+      monoTriangulation2(tempTop, tempBot,
+                         leftChain,
+                         segIndexLarge+1,
+                         leftEnd,
+                         1, //a increase  chian
+                         pStream);
+    }
+
+  //the possible section which is strictly Umonotone
+  if(segIndexLarge >= leftStart)
+    {
+      //if there are grid points which are to the right of topV,
+      //then we should use topVertex to form a fan with these points to
+      //optimize the triangualtion
+      int do_optimize=1;
+      if(topVertex[0] >= grid->get_u_value(rightU))
+	do_optimize = 0;
+      else
+	{
+	  //we also have to make sure that topVertex are the right most vertex
+          //on the chain.
+	  int i;
+	  for(i=leftStart; i<=segIndexSmall; i++)
+	    if(leftChain->getVertex(i)[0] >= topVertex[0])
+	      {
+		do_optimize = 0;
+		break;
+	      }
+	}
+
+      if(do_optimize)
+	{
+	  //find midU so that grid->get_u_value(midU) >= topVertex[0]
+	  //and               grid->get_u_value(midU-1) < topVertex[0]
+	  int midU=rightU;
+	  while(grid->get_u_value(midU) >= topVertex[0])
+	    {
+	      midU--;
+	      if(midU < leftU)
+		break;
+	    }
+	  midU++;
+
+	  grid->outputFanWithPoint(gridV, midU, rightU, topVertex, pStream);
+	  stripOfFanLeft(leftChain, segIndexLarge, segIndexSmall, grid, gridV, leftU, midU, pStream, 0);
+	  Real tempBot[2];
+	  tempBot[0] = grid->get_u_value(midU);
+	  tempBot[1] = grid->get_v_value(gridV);
+	  monoTriangulation2(topVertex, tempBot, leftChain, leftStart, segIndexSmall, 1, pStream);      
+	}
+      else //not optimize
+	{
+
+	  stripOfFanLeft(leftChain, segIndexLarge, segIndexSmall, grid, gridV, leftU, rightU, pStream, 0);
+	  Real tempBot[2];
+	  tempBot[0] = grid->get_u_value(rightU);
+	  tempBot[1] = grid->get_v_value(gridV);
+	  monoTriangulation2(topVertex, tempBot, leftChain, leftStart, segIndexSmall, 1, pStream);
+	}
+    }
+  else //the topVertex forms a fan with the grid points
+    grid->outputFanWithPoint(gridV, leftU, rightU, topVertex, pStream);  
+}				   
+				   
+
+void sampleTopLeftWithGridLine(Real* topVertex,
+                                vertexArray* leftChain,
+                                Int leftStart,
+                                Int leftEnd,
+                                gridWrap* grid,
+                                Int gridV,
+                                Int leftU,
+                                Int rightU,
+                                primStream* pStream
+                                )
+{
+  Int segIndexSmall, segIndexLarge;
+  //if left chain is empty, then there is only one top vertex with one grid 
+  //  line
+  if(leftEnd < leftStart) {
+    grid->outputFanWithPoint(gridV, leftU, rightU, topVertex, pStream);
+    return;
+  }
+  findTopLeftSegment(leftChain,
+                      leftStart,
+                      leftEnd,
+                      grid->get_u_value(leftU),
+                      segIndexSmall,
+                      segIndexLarge
+                      );
+  sampleTopLeftWithGridLinePost(topVertex,
+				leftChain,
+				leftStart,
+				segIndexSmall,
+				segIndexLarge,
+				leftEnd,
+				grid,
+				gridV,
+			        leftU,
+				rightU,
+				pStream);   
+}
+ 
+                
+//return 1 if saprator exits, 0 otherwise
+Int findTopSeparator(vertexArray* leftChain,
+		     Int leftStartIndex,
+		     Int leftEndIndex,
+		     vertexArray* rightChain,
+		     Int rightStartIndex,
+		     Int rightEndIndex,
+		     Int& ret_sep_left,
+		     Int& ret_sep_right)
+{
+  
+  Int oldLeftI, oldRightI, newLeftI, newRightI;
+  Int i,j,k;
+  Real leftMax /*= leftChain->getVertex(leftEndIndex)[0]*/;
+  Real rightMin /*= rightChain->getVertex(rightEndIndex)[0]*/;
+  if(leftChain->getVertex(leftEndIndex)[1] > rightChain->getVertex(rightEndIndex)[1]) //left higher
+    {
+      oldLeftI = leftEndIndex+1;
+      oldRightI = rightEndIndex;
+      leftMax =  leftChain->getVertex(leftEndIndex)[0] - Real(1.0); //initilza to left of leftU
+      rightMin = rightChain->getVertex(rightEndIndex)[0];
+    }
+  else
+    {
+      oldLeftI = leftEndIndex;
+      oldRightI = rightEndIndex+1;
+      leftMax =  leftChain->getVertex(leftEndIndex)[0]; 
+      rightMin = rightChain->getVertex(rightEndIndex)[0] + Real(1.0);      
+    }
+  
+  //i: the current working leftChain index, 
+  //j: the current working rightChain index,
+  //if left(i) is higher than right(j), then the two chains beloew right(j) are separated.
+  //else the two chains below left(i) are separeated.
+  i=leftEndIndex; 
+  j=rightEndIndex;
+  while(1)
+    {
+      newLeftI = oldLeftI;
+      newRightI = oldRightI;
+
+      if(i<leftStartIndex) //left chain is done, go through remining right chain.
+	{
+	  for(k=j-1; k>= rightStartIndex; k--)
+	    {
+	      if(rightChain->getVertex(k)[0] > leftMax) //no conflict
+		{
+		  //update oldRightI if necessary
+		  if(rightChain->getVertex(k)[0] < rightMin)
+		    {
+		      rightMin = rightChain->getVertex(k)[0];
+		      oldRightI = k;
+		    }
+		}
+	      else  //there is a conflict
+		break; //the for-loop. below right(k-1) is seperated: oldLeftI, oldRightI.
+	    }
+	  break; //the while loop
+	}
+      else if(j<rightStartIndex) //rightChain is done
+	{
+	  for(k=i-1; k>= leftStartIndex; k--)
+	    {
+	      if(leftChain->getVertex(k)[0] < rightMin) //no conflict
+		{
+		  //update oldLeftI if necessary
+		  if(leftChain->getVertex(k)[0] > leftMax)
+		    {
+		      leftMax = leftChain->getVertex(k)[0];
+		      oldLeftI = k;
+		    }
+		}
+	      else //there is a conflict
+		break; //the for loop
+	    }
+	  break; //the while loop
+	}
+      else if(leftChain->getVertex(i)[1] > rightChain->getVertex(j)[1]) //left hgiher
+	{
+	  if(leftChain->getVertex(i)[0] > leftMax) //update leftMax and newLeftI.
+	    {
+	      leftMax = leftChain->getVertex(i)[0];	     
+	      newLeftI = i;
+	    }
+	  for(k=j-1; k>= rightStartIndex; k--) //update rightMin and newRightI.
+	    {
+	      if(rightChain->getVertex(k)[1] > leftChain->getVertex(i)[1])
+		break;
+	      if(rightChain->getVertex(k)[0] < rightMin)
+		{
+		  rightMin = rightChain->getVertex(k)[0];
+		  newRightI = k;
+		}
+	    }
+	  j = k; //next working j, since j will be higher than i in next loop
+	  if(leftMax >= rightMin) //there is a conflict
+	    break;
+	  else //still no conflict
+	    {
+	      oldLeftI = newLeftI;
+	      oldRightI = newRightI;
+	    }
+	}
+      else //right higher
+	{
+	  if(rightChain->getVertex(j)[0] < rightMin)
+	    {
+	      rightMin = rightChain->getVertex(j)[0];
+	      newRightI = j;
+	    }
+	  for(k=i-1; k>= leftStartIndex; k--)
+	    {
+	      if(leftChain->getVertex(k)[1] > rightChain->getVertex(j)[1])
+		break;
+	      if(leftChain->getVertex(k)[0] > leftMax)
+		{
+		  leftMax = leftChain->getVertex(k)[0];
+		  newLeftI = k;
+		}
+	    }
+	  i = k; //next working i, since i will be higher than j next loop
+	  
+	  if(leftMax >= rightMin) //there is a conflict
+	    break;
+	  else //still no conflict
+	    {
+	      oldLeftI = newLeftI;
+	      oldRightI = newRightI;
+	    }
+	}
+    }//end of while loop
+  //now oldLeftI and oldRightI are the desired separeator index, notice that there are not necessarily valid
+  if(oldLeftI > leftEndIndex || oldRightI > rightEndIndex)
+    return 0;
+  else
+    {
+      ret_sep_left = oldLeftI;
+      ret_sep_right = oldRightI;
+      return 1;
+    }
+}
+
+        
+void sampleCompTop(Real* topVertex,
+                   vertexArray* leftChain,
+                   Int leftStartIndex,
+                   vertexArray* rightChain,
+                   Int rightStartIndex,
+                   gridBoundaryChain* leftGridChain,
+                   gridBoundaryChain* rightGridChain,
+                   Int gridIndex1,
+                   Int up_leftCornerWhere,
+                   Int up_leftCornerIndex,
+                   Int up_rightCornerWhere,
+                   Int up_rightCornerIndex,
+                   primStream* pStream)
+{
+  if(up_leftCornerWhere == 1 && up_rightCornerWhere == 1) //the top is topVertex with possible grid points
+    {
+      leftGridChain->getGrid()->outputFanWithPoint(leftGridChain->getVlineIndex(gridIndex1),
+						   leftGridChain->getUlineIndex(gridIndex1),
+						   rightGridChain->getUlineIndex(gridIndex1),
+						   topVertex,
+						   pStream);
+      return;
+    }
+
+  else if(up_leftCornerWhere != 0)
+    {
+      Real* tempTop;
+      Int tempRightStart;
+      if(up_leftCornerWhere == 1){
+	tempRightStart = rightStartIndex;
+	tempTop = topVertex;
+      }
+      else
+	{
+	  tempRightStart = up_leftCornerIndex+1;
+	  tempTop = rightChain->getVertex(up_leftCornerIndex);
+	}
+      sampleTopRightWithGridLine(tempTop, rightChain, tempRightStart, up_rightCornerIndex,
+				 rightGridChain->getGrid(),
+				 leftGridChain->getVlineIndex(gridIndex1),
+				 leftGridChain->getUlineIndex(gridIndex1),
+				 rightGridChain->getUlineIndex(gridIndex1),
+				 pStream);
+    }
+  else if(up_rightCornerWhere != 2)
+    {
+      Real* tempTop;
+      Int tempLeftStart;
+      if(up_rightCornerWhere == 1)
+	{
+	  tempLeftStart = leftStartIndex;
+	  tempTop = topVertex;
+	}
+      else //0
+	{
+	  tempLeftStart = up_rightCornerIndex+1;
+	  tempTop = leftChain->getVertex(up_rightCornerIndex);
+	}
+/*
+      sampleTopLeftWithGridLine(tempTop, leftChain, tempLeftStart, up_leftCornerIndex,
+				leftGridChain->getGrid(),
+				 leftGridChain->getVlineIndex(gridIndex1),
+				 leftGridChain->getUlineIndex(gridIndex1),
+				 rightGridChain->getUlineIndex(gridIndex1),
+				 pStream);
+*/
+      sampleCompTopSimple(topVertex,
+			  leftChain,
+			  leftStartIndex,
+			  rightChain,
+			  rightStartIndex,
+			  leftGridChain,
+			  rightGridChain,
+			  gridIndex1,
+			  up_leftCornerWhere,
+			  up_leftCornerIndex,
+			  up_rightCornerWhere,
+			  up_rightCornerIndex,
+			  pStream);	      	      
+    }
+  else //up_leftCornerWhere == 0, up_rightCornerWhere == 2.
+    {
+      sampleCompTopSimple(topVertex,
+			  leftChain,
+			  leftStartIndex,
+			  rightChain,
+			  rightStartIndex,
+			  leftGridChain,
+			  rightGridChain,
+			  gridIndex1,
+			  up_leftCornerWhere,
+			  up_leftCornerIndex,
+			  up_rightCornerWhere,
+			  up_rightCornerIndex,
+			  pStream);	      	      
+      return;
+#ifdef NOT_REACHABLE //code is not reachable, for test purpose only
+      //the following code is trying to do some optimization, but not quite working, also see sampleCompBot.C:
+      Int sep_left, sep_right;
+      if(findTopSeparator(leftChain,
+			  leftStartIndex,
+			  up_leftCornerIndex,
+			  rightChain,
+			  rightStartIndex,
+			  up_rightCornerIndex,
+			  sep_left,
+			  sep_right)
+	 ) //separator exists
+	{
+
+	  if( leftChain->getVertex(sep_left)[0] >= leftGridChain->get_u_value(gridIndex1) &&
+	     rightChain->getVertex(sep_right)[0] <= rightGridChain->get_u_value(gridIndex1))
+	    {
+	      Int gridSep;
+	      Int segLeftSmall, segLeftLarge, segRightSmall, segRightLarge;
+	      Int valid=1; //whether the gridStep is valid or not.
+	      findTopLeftSegment(leftChain,
+				 sep_left,
+				 up_leftCornerIndex,
+				 leftGridChain->get_u_value(gridIndex1),
+				 segLeftSmall,
+				 segLeftLarge);
+	      findTopRightSegment(rightChain,
+				 sep_right,
+				 up_rightCornerIndex,
+				 rightGridChain->get_u_value(gridIndex1),
+				 segRightSmall,
+				 segRightLarge);
+	      if(leftChain->getVertex(segLeftSmall)[1] >= rightChain->getVertex(segRightSmall)[1])
+		{
+		  gridSep = rightGridChain->getUlineIndex(gridIndex1);
+		  while(leftGridChain->getGrid()->get_u_value(gridSep) > leftChain->getVertex(segLeftSmall)[0])
+		    gridSep--;
+		  if(segLeftSmall<segLeftLarge)
+		    if(leftGridChain->getGrid()->get_u_value(gridSep) < leftChain->getVertex(segLeftSmall+1)[0])
+		      {
+			valid = 0;
+		      }
+		}
+	      else
+		{
+		  gridSep = leftGridChain->getUlineIndex(gridIndex1);
+		  while(leftGridChain->getGrid()->get_u_value(gridSep) < rightChain->getVertex(segRightSmall)[0])
+		    gridSep++;
+		  if(segRightSmall<segRightLarge)
+		    if(leftGridChain->getGrid()->get_u_value(gridSep) > rightChain->getVertex(segRightSmall+1)[0])
+		      {
+			valid = 0;
+		      }
+		}		
+		  
+	      if(! valid)
+		{
+		  sampleCompTopSimple(topVertex,
+				      leftChain,
+				      leftStartIndex,
+				      rightChain,
+				      rightStartIndex,
+				      leftGridChain,
+				      rightGridChain,
+				      gridIndex1,
+				      up_leftCornerWhere,
+				      up_leftCornerIndex,
+				      up_rightCornerWhere,
+				      up_rightCornerIndex,
+				      pStream);	      	      
+		}
+	      else
+		{
+		  sampleTopLeftWithGridLinePost(leftChain->getVertex(segLeftSmall),
+						leftChain,
+						segLeftSmall+1,
+						segLeftSmall+1,
+						segLeftLarge,
+						up_leftCornerIndex,
+						leftGridChain->getGrid(),
+						leftGridChain->getVlineIndex(gridIndex1),
+						leftGridChain->getUlineIndex(gridIndex1),
+						gridSep,
+						pStream);
+		  sampleTopRightWithGridLinePost(rightChain->getVertex(segRightSmall),
+						 rightChain,
+						 segRightSmall+1,
+						 segRightSmall+1,
+						 segRightLarge,
+						 up_rightCornerIndex,
+						 leftGridChain->getGrid(),
+						 leftGridChain->getVlineIndex(gridIndex1),
+						 gridSep,
+						 rightGridChain->getUlineIndex(gridIndex1),
+						 pStream);
+		  Real tempBot[2];
+		  tempBot[0] = leftGridChain->getGrid()->get_u_value(gridSep);
+		  tempBot[1] = leftGridChain->get_v_value(gridIndex1);
+		  monoTriangulationRecGen(topVertex, tempBot,
+					  leftChain, leftStartIndex, segLeftSmall,
+					  rightChain, rightStartIndex, segRightSmall,
+					  pStream);
+		}
+	    }//end if both sides have vetices inside the gridboundary points
+	  else if(leftChain->getVertex(sep_left)[0] >= leftGridChain->get_u_value(gridIndex1)) //left is in, right is nout
+	    {
+
+	      Int segLeftSmall, segLeftLarge;
+	      findTopLeftSegment(leftChain,
+				 sep_left,
+				 up_leftCornerIndex,
+				 leftGridChain->get_u_value(gridIndex1),
+				 segLeftSmall,
+				 segLeftLarge);	      
+	      assert(segLeftLarge >= sep_left); 
+              monoTriangulation2(leftChain->getVertex(segLeftLarge),
+				 leftGridChain->get_vertex(gridIndex1),
+				 leftChain,
+				 segLeftLarge+1,
+				 up_leftCornerIndex,
+				 1, //a increase chain,
+				 pStream);
+
+	      stripOfFanLeft(leftChain, segLeftLarge, segLeftSmall, 
+			     leftGridChain->getGrid(),
+			     leftGridChain->getVlineIndex(gridIndex1),
+			     leftGridChain->getUlineIndex(gridIndex1),
+			     rightGridChain->getUlineIndex(gridIndex1),
+			     pStream, 0);
+
+
+	      monoTriangulationRecGen(topVertex, rightGridChain->get_vertex(gridIndex1),
+				      leftChain, leftStartIndex, segLeftSmall,
+				      rightChain, rightStartIndex, up_rightCornerIndex,
+				      pStream);	    
+	    }//end left in right out
+	  else if(rightChain->getVertex(sep_right)[0] <= rightGridChain->get_u_value(gridIndex1))
+	    {
+	      Int segRightSmall, segRightLarge;
+	      findTopRightSegment(rightChain,
+				 sep_right,
+				 up_rightCornerIndex,
+				 rightGridChain->get_u_value(gridIndex1),
+				 segRightSmall,
+				 segRightLarge);
+	      assert(segRightLarge>=sep_right);
+	      monoTriangulation2(rightChain->getVertex(segRightLarge),
+				 rightGridChain->get_vertex(gridIndex1),
+				 rightChain,
+				 segRightLarge+1,
+				 up_rightCornerIndex,
+				 0, //a decrease chain
+				 pStream);
+	      stripOfFanRight(rightChain, segRightLarge, segRightSmall,
+			      rightGridChain->getGrid(),
+			      rightGridChain->getVlineIndex(gridIndex1),
+			      leftGridChain->getUlineIndex(gridIndex1),
+			      rightGridChain->getUlineIndex(gridIndex1),
+			      pStream, 0);
+
+
+	      monoTriangulationRecGen(topVertex, leftGridChain->get_vertex(gridIndex1),
+				      leftChain, leftStartIndex, up_leftCornerIndex,
+				      rightChain, rightStartIndex,segRightSmall,
+				      pStream);
+
+	    }//end left out rigth in
+	  else //left out , right out
+	    {
+
+	      sampleCompTopSimple(topVertex,
+				  leftChain,
+				  leftStartIndex,
+				  rightChain,
+				  rightStartIndex,
+				  leftGridChain,
+				  rightGridChain,
+				  gridIndex1,
+				  up_leftCornerWhere,
+				  up_leftCornerIndex,
+				  up_rightCornerWhere,
+				  up_rightCornerIndex,
+				  pStream);	      	      
+	    }//end leftout, right out
+	}//end if separator exixts.
+      else //no separator
+	{
+
+	  sampleCompTopSimple(topVertex,
+			    leftChain,
+			      leftStartIndex,
+			      rightChain,
+			      rightStartIndex,
+			      leftGridChain,
+			      rightGridChain,
+			      gridIndex1,
+			    up_leftCornerWhere,
+			      up_leftCornerIndex,
+			      up_rightCornerWhere,
+			      up_rightCornerIndex,
+			    pStream);
+	}
+#endif
+    }//end if 0,2
+}//end if the function
+
+		   
+static void sampleCompTopSimpleOpt(gridWrap* grid,
+				   Int gridV,
+				   Real* topVertex, Real* botVertex,
+				   vertexArray* inc_chain, Int inc_current, Int inc_end,
+				   vertexArray* dec_chain, Int dec_current, Int dec_end,
+				   primStream* pStream)
+{
+  if(gridV <= 0 || dec_end<dec_current || inc_end <inc_current)
+    {
+      monoTriangulationRecGenOpt(topVertex, botVertex,
+				 inc_chain, inc_current, inc_end,
+				 dec_chain, dec_current, dec_end,
+				 pStream);
+      return;
+    }
+  if(grid->get_v_value(gridV+1) >= topVertex[1])
+    {
+      monoTriangulationRecGenOpt(topVertex, botVertex,
+				 inc_chain, inc_current, inc_end,
+				 dec_chain, dec_current, dec_end,
+				 pStream);
+      return;
+    }      
+ Int i,j,k;
+  Real currentV = grid->get_v_value(gridV+1);
+  if(inc_chain->getVertex(inc_end)[1] <= currentV &&
+     dec_chain->getVertex(dec_end)[1] < currentV)
+    {
+      //find i bottom up so that inc_chain[i]<= curentV and inc_chain[i-1] > currentV, 
+      //find j botom up so that dec_chain[j] < currentV and dec_chain[j-1] >= currentV
+      for(i=inc_end; i >= inc_current; i--) 
+	{
+	  if(inc_chain->getVertex(i)[1] > currentV)
+	    break;
+	}
+      i++;
+      for(j=dec_end; j >= dec_current; j--)
+	{
+	  if(dec_chain->getVertex(j)[1] >= currentV)
+	    break;
+	}
+      j++;
+     if(inc_chain->getVertex(i)[1] <= dec_chain->getVertex(j)[1])
+       {
+	 //find the k so that dec_chain[k][1] < inc_chain[i][1]
+	 for(k=j; k<=dec_end; k++)
+	   {
+	     if(dec_chain->getVertex(k)[1] < inc_chain->getVertex(i)[1])
+	       break;
+	   }
+         //we know that dec_chain[j][1] >= inc_chian[i][1]
+	 //we know that dec_chain[k-1][1]>=inc_chain[i][1]
+         //we know that dec_chian[k][1] < inc_chain[i][1]
+         //find l in [j, k-1] so that dec_chain[l][0] 0 is closest to
+         // inc_chain[i]
+         int l;
+         Real tempI = Real(j);
+         Real tempMin = (Real)fabs(inc_chain->getVertex(i)[0] - dec_chain->getVertex(j)[0]);
+         for(l=j+1; l<= k-1; l++)
+	   {
+	     if(fabs(inc_chain->getVertex(i)[0] - dec_chain->getVertex(l)[0])
+		<= tempMin)
+	       {
+		 tempMin = (Real)fabs(inc_chain->getVertex(i)[0] - dec_chain->getVertex(l)[0]);
+		 tempI = (Real)l;
+	       }
+	   }
+	 //inc_chain[i] and dec_chain[tempI] are connected.
+	 monoTriangulationRecGenOpt(dec_chain->getVertex((int)tempI),
+				    botVertex,
+				    inc_chain, i, inc_end,
+				    dec_chain, (int)(tempI+1), dec_end,
+				    pStream);
+	 //recursively do the rest
+	 sampleCompTopSimpleOpt(grid,
+				gridV+1,
+				topVertex, inc_chain->getVertex(i),
+				inc_chain, inc_current, i-1,
+				dec_chain, dec_current, (int)tempI,
+				pStream);
+       }
+      else
+	{
+	  //find the k so that inc_chain[k][1] <= dec_chain[j][1]
+	  for(k=i; k<=inc_end; k++)
+	    {
+	      if(inc_chain->getVertex(k)[1] <= dec_chain->getVertex(j)[1])
+		break;
+	    }
+	  //we know that inc_chain[i] > dec_chain[j]
+	  //we know that inc_chain[k-1][1] > dec_chain[j][1]
+	  //we know that inc_chain[k][1] <= dec_chain[j][1]
+	  //so we find l between [i,k-1] so that 
+	  //inc_chain[l][0] is the closet to dec_chain[j][0]
+	  int tempI = i;
+	  int l;
+	  Real tempMin = (Real)fabs(inc_chain->getVertex(i)[0] - dec_chain->getVertex(j)[0]);
+	  for(l=i+1; l<=k-1; l++)
+	    {
+	      if(fabs(inc_chain->getVertex(l)[0] - dec_chain->getVertex(j)[0]) <= tempMin)
+		{
+		  tempMin = (Real)fabs(inc_chain->getVertex(l)[0] - dec_chain->getVertex(j)[0]);
+		  tempI = l;
+		}
+	    }				 	      
+
+	  //inc_chain[tempI] and dec_chain[j] are connected
+
+	  monoTriangulationRecGenOpt(inc_chain->getVertex(tempI),
+				     botVertex,
+				     inc_chain, tempI+1, inc_end,
+				     dec_chain, j, dec_end,
+				     pStream);
+
+	  //recurvesily do the rest
+	  sampleCompTopSimpleOpt(grid, gridV+1,
+				 topVertex, dec_chain->getVertex(j),
+				 inc_chain, inc_current, tempI,
+				 dec_chain, dec_current, j-1,
+				 pStream);
+	}	    				   	       
+    }
+  else //go to the next higher gridV
+    {
+      sampleCompTopSimpleOpt(grid,
+			     gridV+1,
+			     topVertex, botVertex,
+			     inc_chain, inc_current, inc_end,
+			     dec_chain, dec_current, dec_end,
+			     pStream);
+    }
+}
+			  
+void sampleCompTopSimple(Real* topVertex,
+                   vertexArray* leftChain,
+                   Int leftStartIndex,
+                   vertexArray* rightChain,
+                   Int rightStartIndex,
+                   gridBoundaryChain* leftGridChain,
+                   gridBoundaryChain* rightGridChain,
+                   Int gridIndex1,
+                   Int up_leftCornerWhere,
+                   Int up_leftCornerIndex,
+                   Int up_rightCornerWhere,
+                   Int up_rightCornerIndex,
+                   primStream* pStream)
+{
+  //the plan is to use monotriangulation algortihm.
+  Int i,k;
+  Real* ActualTop;
+  Real* ActualBot;
+  Int ActualLeftStart, ActualLeftEnd;
+  Int ActualRightStart, ActualRightEnd;
+  
+  //creat an array to store the points on the grid line
+  gridWrap* grid = leftGridChain->getGrid();
+  Int gridV = leftGridChain->getVlineIndex(gridIndex1);
+  Int gridLeftU = leftGridChain->getUlineIndex(gridIndex1);
+  Int gridRightU = rightGridChain->getUlineIndex(gridIndex1);
+
+  Real2* gridPoints = (Real2*) malloc(sizeof(Real2) * (gridRightU - gridLeftU +1));
+  assert(gridPoints);
+  
+  for(k=0, i=gridRightU; i>= gridLeftU; i--, k++)
+    {
+      gridPoints[k][0] = grid->get_u_value(i);
+      gridPoints[k][1] = grid->get_v_value(gridV);
+    }
+
+  if(up_leftCornerWhere != 2)
+    ActualRightStart = rightStartIndex;
+  else
+    ActualRightStart = up_leftCornerIndex+1; //up_leftCornerIndex will be the ActualTop
+  
+  if(up_rightCornerWhere != 2) //right corner is not on right chain
+    ActualRightEnd = rightStartIndex-1; //meaning that there is no actual rigth section
+  else
+    ActualRightEnd = up_rightCornerIndex;
+  
+  vertexArray ActualRightChain(max(0, ActualRightEnd-ActualRightStart+1) + gridRightU-gridLeftU+1);
+
+  for(i=ActualRightStart; i<= ActualRightEnd; i++)
+    ActualRightChain.appendVertex(rightChain->getVertex(i));
+  for(i=0; i<gridRightU-gridLeftU+1; i++)
+    ActualRightChain.appendVertex(gridPoints[i]);    
+
+  //determine ActualLeftEnd
+  if(up_leftCornerWhere != 0)
+    ActualLeftEnd = leftStartIndex-1;
+  else
+    ActualLeftEnd = up_leftCornerIndex;
+  
+  if(up_rightCornerWhere != 0)
+    ActualLeftStart = leftStartIndex;
+  else
+    ActualLeftStart = up_rightCornerIndex+1; //up_rightCornerIndex will be the actual top
+  
+  if(up_leftCornerWhere == 0) 
+    {
+      if(up_rightCornerWhere == 0)
+	ActualTop = leftChain->getVertex(up_rightCornerIndex);
+      else
+	ActualTop = topVertex;
+    }
+  else if(up_leftCornerWhere == 1) 
+    ActualTop = topVertex;
+  else  //up_leftCornerWhere == 2
+    ActualTop = rightChain->getVertex(up_leftCornerIndex);
+  
+  ActualBot = gridPoints[gridRightU - gridLeftU];
+  
+
+
+
+  if(leftChain->getVertex(ActualLeftEnd)[1] == ActualBot[1])
+    {
+/*
+    monoTriangulationRecGenOpt(ActualTop, leftChain->getVertex(ActualLeftEnd),
+			    leftChain,
+			    ActualLeftStart, ActualLeftEnd-1,
+			    &ActualRightChain,
+			    0,
+			    ActualRightChain.getNumElements()-1,
+			    pStream);
+*/
+   
+    sampleCompTopSimpleOpt(grid, gridV,
+			   ActualTop, leftChain->getVertex(ActualLeftEnd),
+			    leftChain,
+			    ActualLeftStart, ActualLeftEnd-1,
+			    &ActualRightChain,
+			    0,
+			    ActualRightChain.getNumElements()-1,
+			    pStream);
+    
+  }
+  else
+    {
+/*
+    monoTriangulationRecGenOpt(ActualTop, ActualBot, leftChain,
+			  ActualLeftStart, ActualLeftEnd,
+			  &ActualRightChain,
+			  0, ActualRightChain.getNumElements()-2, //the last is the bot.
+			  pStream);
+*/
+   	  
+    sampleCompTopSimpleOpt(grid, gridV,
+			   ActualTop, ActualBot, leftChain,
+			  ActualLeftStart, ActualLeftEnd,
+			  &ActualRightChain,
+			  0, ActualRightChain.getNumElements()-2, //the last is the bot.
+			  pStream);
+
+   
+  }
+
+  free(gridPoints);
+      
+}		  
+						   
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompTop.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompTop.h
new file mode 100644
index 000000000..95598d63a
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleCompTop.h
@@ -0,0 +1,67 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _SAMPLECOMPTOP_H
+#define _SAMPLECOMPTOP_H
+
+#include "sampleMonoPoly.h"
+
+void sampleCompTop(Real* topVertex,
+                   vertexArray* leftChain,
+                   Int leftStartIndex,
+                   vertexArray* rightChain,
+                   Int rightStartIndex,
+                   gridBoundaryChain* leftGridChain,
+                   gridBoundaryChain* rightGridChain,
+                   Int gridIndex1,
+                   Int up_leftCornerWhere,
+                   Int up_leftCornerIndex,
+                   Int up_rightCornerWhere,
+                   Int up_rightCornerIndex,
+                   primStream* pStream);
+
+void sampleCompTopSimple(Real* topVertex,
+                   vertexArray* leftChain,
+                   Int leftStartIndex,
+                   vertexArray* rightChain,
+                   Int rightStartIndex,
+                   gridBoundaryChain* leftGridChain,
+                   gridBoundaryChain* rightGridChain,
+                   Int gridIndex1,
+                   Int up_leftCornerWhere,
+                   Int up_leftCornerIndex,
+                   Int up_rightCornerWhere,
+                   Int up_rightCornerIndex,
+                   primStream* pStream);
+
+#endif
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleMonoPoly.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleMonoPoly.cc
new file mode 100644
index 000000000..051f24108
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleMonoPoly.cc
@@ -0,0 +1,2427 @@
+/*
+** 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 <math.h>
+
+#ifndef max
+#define max(a,b) ((a>b)? a:b)
+#endif
+#ifndef min
+#define min(a,b) ((a>b)? b:a)
+#endif
+
+#include <GL/gl.h>
+
+#include "glimports.h"
+#include "zlassert.h"
+#include "sampleMonoPoly.h"
+#include "sampleComp.h"
+#include "polyDBG.h"
+#include "partitionX.h"
+
+
+#define ZERO 0.00001
+
+//#define  MYDEBUG
+
+//#define SHORTEN_GRID_LINE
+//see work/newtess/internal/test/problems
+
+
+/*split a polygon so that each vertex correcpond to one edge
+ *the head of the first edge of the returned plygon must be the head of the first
+ *edge of the origianl polygon. This is crucial for the code in sampleMonoPoly function
+ */
+ directedLine*  polygonConvert(directedLine* polygon)
+{
+  int i;
+  directedLine* ret;
+  sampledLine* sline;
+  sline = new sampledLine(2);
+  sline->setPoint(0, polygon->getVertex(0));
+  sline->setPoint(1, polygon->getVertex(1));
+  ret=new directedLine(INCREASING, sline);
+  for(i=1; i<= polygon->get_npoints()-2; i++)
+    {
+      sline = new sampledLine(2);
+      sline->setPoint(0, polygon->getVertex(i));
+      sline->setPoint(1, polygon->getVertex(i+1));
+      ret->insert(new directedLine(INCREASING, sline));
+    }
+
+  for(directedLine *temp = polygon->getNext(); temp != polygon; temp = temp->getNext())
+    {
+      for(i=0; i<= temp->get_npoints()-2; i++)
+	{
+	  sline = new sampledLine(2);
+	  sline->setPoint(0, temp->getVertex(i));
+	  sline->setPoint(1, temp->getVertex(i+1));
+	  ret->insert(new directedLine(INCREASING, sline));
+	}
+    }
+  return ret;
+}
+
+void triangulateConvexPolyVertical(directedLine* topV, directedLine* botV, primStream *pStream)
+{
+  Int i,j;
+  Int n_leftVerts;
+  Int n_rightVerts;
+  Real** leftVerts;
+  Real** rightVerts;
+  directedLine* tempV;
+  n_leftVerts = 0;
+  for(tempV = topV; tempV != botV; tempV = tempV->getNext())
+    {
+      n_leftVerts += tempV->get_npoints();
+    }
+  n_rightVerts=0;
+  for(tempV = botV; tempV != topV; tempV = tempV->getNext())
+    {
+      n_rightVerts += tempV->get_npoints();
+    }
+
+  Real2* temp_leftVerts = (Real2 *) malloc(sizeof(Real2) * n_leftVerts);
+  assert(temp_leftVerts);
+  Real2* temp_rightVerts = (Real2 *) malloc(sizeof(Real2) * n_rightVerts);
+  assert(temp_rightVerts);
+
+  leftVerts = (Real**) malloc(sizeof(Real2*) * n_leftVerts);
+  assert(leftVerts);
+  rightVerts = (Real**) malloc(sizeof(Real2*) * n_rightVerts);
+  assert(rightVerts);
+  for(i=0; i<n_leftVerts; i++)
+    leftVerts[i] = temp_leftVerts[i];
+  for(i=0; i<n_rightVerts; i++)
+    rightVerts[i] = temp_rightVerts[i];
+
+  i=0;
+  for(tempV = topV; tempV != botV; tempV = tempV->getNext())
+    {
+      for(j=1; j<tempV->get_npoints(); j++)
+	{
+	  leftVerts[i][0] = tempV->getVertex(j)[0];
+	  leftVerts[i][1] = tempV->getVertex(j)[1];
+	  i++;
+	}
+    }
+  n_leftVerts = i;
+  i=0;
+  for(tempV = topV->getPrev(); tempV != botV->getPrev(); tempV = tempV->getPrev())
+    {
+      for(j=tempV->get_npoints()-1; j>=1; j--)
+	{
+	  rightVerts[i][0] = tempV->getVertex(j)[0];
+	  rightVerts[i][1] = tempV->getVertex(j)[1];
+	  i++;
+	}
+    }
+  n_rightVerts = i;
+  triangulateXYMonoTB(n_leftVerts, leftVerts, n_rightVerts, rightVerts, pStream);
+  free(leftVerts);
+  free(rightVerts);
+  free(temp_leftVerts);
+  free(temp_rightVerts);
+}  
+
+void triangulateConvexPolyHoriz(directedLine* leftV, directedLine* rightV, primStream *pStream)
+{
+  Int i,j;
+  Int n_lowerVerts;
+  Int n_upperVerts;
+  Real2 *lowerVerts;
+  Real2 *upperVerts;
+  directedLine* tempV;
+  n_lowerVerts=0;
+  for(tempV = leftV; tempV != rightV; tempV = tempV->getNext())
+    {
+      n_lowerVerts += tempV->get_npoints();
+    }
+  n_upperVerts=0;
+  for(tempV = rightV; tempV != leftV; tempV = tempV->getNext())
+    {
+      n_upperVerts += tempV->get_npoints();
+    }
+  lowerVerts = (Real2 *) malloc(sizeof(Real2) * n_lowerVerts);
+  assert(n_lowerVerts);
+  upperVerts = (Real2 *) malloc(sizeof(Real2) * n_upperVerts);
+  assert(n_upperVerts);
+  i=0;
+  for(tempV = leftV; tempV != rightV; tempV = tempV->getNext())
+    {
+      for(j=0; j<tempV->get_npoints(); j++)
+	{
+	  lowerVerts[i][0] = tempV->getVertex(j)[0];
+	  lowerVerts[i][1] = tempV->getVertex(j)[1];
+	  i++;
+	}
+    }
+  i=0;
+  for(tempV = leftV->getPrev(); tempV != rightV->getPrev(); tempV = tempV->getPrev())
+    {
+      for(j=tempV->get_npoints()-1; j>=0; j--)
+	{
+	  upperVerts[i][0] = tempV->getVertex(j)[0];
+	  upperVerts[i][1] = tempV->getVertex(j)[1];
+	  i++;
+	}
+    }
+  triangulateXYMono(n_upperVerts, upperVerts, n_lowerVerts, lowerVerts, pStream);
+  free(lowerVerts);
+  free(upperVerts);
+}  
+void triangulateConvexPoly(directedLine* polygon, Int ulinear, Int vlinear, primStream* pStream)
+{
+  /*find left, right, top , bot
+    */
+  directedLine* tempV;
+  directedLine* topV;
+  directedLine* botV;
+  directedLine* leftV;
+  directedLine* rightV;
+  topV = botV = polygon;
+
+  for(tempV = polygon->getNext(); tempV != polygon; tempV = tempV->getNext())
+    {
+      if(compV2InY(topV->head(), tempV->head())<0) {
+
+	topV = tempV;
+      }
+      if(compV2InY(botV->head(), tempV->head())>0) {
+
+	botV = tempV;
+      }
+    }
+  //find leftV
+  for(tempV = topV; tempV != botV; tempV = tempV->getNext())
+    {
+      if(tempV->tail()[0] >= tempV->head()[0])
+	break;
+    }
+  leftV = tempV;
+  //find rightV
+  for(tempV = botV; tempV != topV; tempV = tempV->getNext())
+    {
+      if(tempV->tail()[0] <= tempV->head()[0])
+	break;
+    }
+  rightV = tempV;
+  if(vlinear)
+    {
+      triangulateConvexPolyHoriz( leftV, rightV, pStream);
+    }
+  else if(ulinear)
+    {
+      triangulateConvexPolyVertical(topV, botV, pStream);
+    }
+  else
+    {
+      if(DBG_is_U_direction(polygon))
+	{
+	  triangulateConvexPolyHoriz( leftV, rightV, pStream);
+	}
+      else
+	triangulateConvexPolyVertical(topV, botV, pStream);
+    }
+}	      
+
+/*for debug purpose*/
+void drawCorners(
+		 Real* topV, Real* botV,		 
+		 vertexArray* leftChain,
+		 vertexArray* rightChain,
+		 gridBoundaryChain* leftGridChain,
+		 gridBoundaryChain* rightGridChain,
+		 Int gridIndex1,
+		 Int gridIndex2,
+		 Int leftCornerWhere,
+		 Int leftCornerIndex,
+		 Int rightCornerWhere,
+		 Int rightCornerIndex,
+		 Int bot_leftCornerWhere,
+		 Int bot_leftCornerIndex,
+		 Int bot_rightCornerWhere,
+		 Int bot_rightCornerIndex)
+{
+  Real* leftCornerV;
+  Real* rightCornerV;
+  Real* bot_leftCornerV;
+  Real* bot_rightCornerV;
+
+  if(leftCornerWhere == 1)
+    leftCornerV = topV;
+  else if(leftCornerWhere == 0)
+    leftCornerV = leftChain->getVertex(leftCornerIndex);
+  else
+    leftCornerV = rightChain->getVertex(leftCornerIndex);
+
+  if(rightCornerWhere == 1)
+    rightCornerV = topV;
+  else if(rightCornerWhere == 0)
+    rightCornerV = leftChain->getVertex(rightCornerIndex);
+  else
+    rightCornerV = rightChain->getVertex(rightCornerIndex);
+
+  if(bot_leftCornerWhere == 1)
+    bot_leftCornerV = botV;
+  else if(bot_leftCornerWhere == 0)
+    bot_leftCornerV = leftChain->getVertex(bot_leftCornerIndex);
+  else
+    bot_leftCornerV = rightChain->getVertex(bot_leftCornerIndex);
+
+  if(bot_rightCornerWhere == 1)
+    bot_rightCornerV = botV;
+  else if(bot_rightCornerWhere == 0)
+    bot_rightCornerV = leftChain->getVertex(bot_rightCornerIndex);
+  else
+    bot_rightCornerV = rightChain->getVertex(bot_rightCornerIndex);
+
+  Real topGridV = leftGridChain->get_v_value(gridIndex1);
+  Real topGridU1 = leftGridChain->get_u_value(gridIndex1);
+  Real topGridU2 = rightGridChain->get_u_value(gridIndex1);
+  Real botGridV = leftGridChain->get_v_value(gridIndex2);
+  Real botGridU1 = leftGridChain->get_u_value(gridIndex2);
+  Real botGridU2 = rightGridChain->get_u_value(gridIndex2);
+  
+  glBegin(GL_LINE_STRIP);
+  glVertex2fv(leftCornerV);
+  glVertex2f(topGridU1, topGridV);
+  glEnd();
+
+  glBegin(GL_LINE_STRIP);
+  glVertex2fv(rightCornerV);
+  glVertex2f(topGridU2, topGridV);
+  glEnd();
+
+  glBegin(GL_LINE_STRIP);
+  glVertex2fv(bot_leftCornerV);
+  glVertex2f(botGridU1, botGridV);
+  glEnd();
+
+  glBegin(GL_LINE_STRIP);
+  glVertex2fv(bot_rightCornerV);
+  glVertex2f(botGridU2, botGridV);
+  glEnd();
+
+
+}
+		 
+void toVertexArrays(directedLine* topV, directedLine* botV, vertexArray& leftChain, vertexArray& rightChain)
+{  
+  Int i;
+  directedLine* tempV;
+  for(i=1; i<=topV->get_npoints()-2; i++) { /*the first vertex is the top vertex which doesn't belong to inc_chain*/
+    leftChain.appendVertex(topV->getVertex(i));
+  }
+  for(tempV = topV->getNext(); tempV != botV; tempV = tempV->getNext())
+    {
+      for(i=0; i<=tempV->get_npoints()-2; i++){
+	leftChain.appendVertex(tempV->getVertex(i));
+      }
+    }  
+
+  for(tempV = topV->getPrev(); tempV != botV; tempV = tempV->getPrev())
+    {
+      for(i=tempV->get_npoints()-2; i>=0; i--){
+	rightChain.appendVertex(tempV->getVertex(i));
+      }
+    }
+  for(i=botV->get_npoints()-2; i>=1; i--){ 
+    rightChain.appendVertex(tempV->getVertex(i));
+  }
+}
+
+
+void findTopAndBot(directedLine* polygon, directedLine*& topV, directedLine*& botV)
+{
+  assert(polygon);
+  directedLine* tempV;
+  topV = botV = polygon;
+   for(tempV = polygon->getNext(); tempV != polygon; tempV = tempV->getNext())
+    {
+      if(compV2InY(topV->head(), tempV->head())<0) {
+	topV = tempV;
+      }
+      if(compV2InY(botV->head(), tempV->head())>0) {
+	botV = tempV;
+      }
+    }
+}
+   
+void findGridChains(directedLine* topV, directedLine* botV, 
+		    gridWrap* grid,
+		    gridBoundaryChain*& leftGridChain,
+		    gridBoundaryChain*& rightGridChain)
+{
+  /*find the first(top) and the last (bottom) grid line which intersect the
+   *this polygon
+   */
+  Int firstGridIndex; /*the index in the grid*/
+  Int lastGridIndex;
+
+  firstGridIndex = (Int) ((topV->head()[1] - grid->get_v_min()) / (grid->get_v_max() - grid->get_v_min()) * (grid->get_n_vlines()-1));
+
+  if(botV->head()[1] < grid->get_v_min())
+    lastGridIndex = 0;
+  else
+    lastGridIndex  = (Int) ((botV->head()[1] - grid->get_v_min()) / (grid->get_v_max() - grid->get_v_min()) * (grid->get_n_vlines()-1)) + 1;
+
+  /*find the interval inside  the polygon for each gridline*/
+  Int *leftGridIndices = (Int*) malloc(sizeof(Int) * (firstGridIndex - lastGridIndex +1));
+  assert(leftGridIndices);
+  Int *rightGridIndices = (Int*) malloc(sizeof(Int) * (firstGridIndex - lastGridIndex +1));
+  assert(rightGridIndices);
+  Int *leftGridInnerIndices = (Int*) malloc(sizeof(Int) * (firstGridIndex - lastGridIndex +1));
+  assert(leftGridInnerIndices);
+  Int *rightGridInnerIndices = (Int*) malloc(sizeof(Int) * (firstGridIndex - lastGridIndex +1));
+  assert(rightGridInnerIndices);
+
+  findLeftGridIndices(topV, firstGridIndex, lastGridIndex, grid,  leftGridIndices, leftGridInnerIndices);
+
+  findRightGridIndices(topV, firstGridIndex, lastGridIndex, grid,  rightGridIndices, rightGridInnerIndices);
+
+  leftGridChain =  new gridBoundaryChain(grid, firstGridIndex, firstGridIndex-lastGridIndex+1, leftGridIndices, leftGridInnerIndices);
+
+  rightGridChain = new gridBoundaryChain(grid, firstGridIndex, firstGridIndex-lastGridIndex+1, rightGridIndices, rightGridInnerIndices);
+
+  free(leftGridIndices);
+  free(rightGridIndices);
+  free(leftGridInnerIndices);
+  free(rightGridInnerIndices);
+}
+
+void findDownCorners(Real *botVertex, 
+		   vertexArray *leftChain, Int leftChainStartIndex, Int leftChainEndIndex,
+		   vertexArray *rightChain, Int rightChainStartIndex, Int rightChainEndIndex,
+		   Real v,
+		   Real uleft,
+		   Real uright,
+		   Int& ret_leftCornerWhere, /*0: left chain, 1: topvertex, 2: rightchain*/
+		   Int& ret_leftCornerIndex, /*useful when ret_leftCornerWhere == 0 or 2*/
+		   Int& ret_rightCornerWhere, /*0: left chain, 1: topvertex, 2: rightchain*/
+		   Int& ret_rightCornerIndex /*useful when ret_leftCornerWhere == 0 or 2*/
+		   )
+{
+#ifdef MYDEBUG
+printf("*************enter find donw corner\n");
+printf("finddownCorner: v=%f, uleft=%f, uright=%f\n", v, uleft, uright);
+printf("(%i,%i,%i,%i)\n", leftChainStartIndex, leftChainEndIndex,rightChainStartIndex, rightChainEndIndex); 
+printf("left chain is\n");
+leftChain->print();
+printf("right chain is\n");
+rightChain->print();
+#endif
+
+  assert(v > botVertex[1]);
+  Real leftGridPoint[2];
+  leftGridPoint[0] = uleft;
+  leftGridPoint[1] = v;
+  Real rightGridPoint[2];
+  rightGridPoint[0] = uright;
+  rightGridPoint[1] = v;
+
+  Int i;
+  Int index1, index2;
+
+  index1 = leftChain->findIndexBelowGen(v, leftChainStartIndex, leftChainEndIndex);
+  index2 = rightChain->findIndexBelowGen(v, rightChainStartIndex, rightChainEndIndex);
+
+  if(index2 <= rightChainEndIndex) //index2 was found above
+    index2 = rightChain->skipEqualityFromStart(v, index2, rightChainEndIndex);
+
+  if(index1>leftChainEndIndex && index2 > rightChainEndIndex) /*no point below v on left chain or right chain*/
+    {
+
+      /*the botVertex is the only vertex below v*/
+      ret_leftCornerWhere = 1;
+      ret_rightCornerWhere = 1;
+    }
+  else if(index1>leftChainEndIndex ) /*index2 <= rightChainEndIndex*/
+    {
+
+      ret_rightCornerWhere = 2; /*on right chain*/
+      ret_rightCornerIndex = index2;
+
+
+      Real tempMin = rightChain->getVertex(index2)[0];
+      Int tempI = index2;
+      for(i=index2+1; i<= rightChainEndIndex; i++)
+	if(rightChain->getVertex(i)[0] < tempMin)
+	  {
+	    tempI = i;
+	    tempMin = rightChain->getVertex(i)[0];
+	  }
+
+
+      //we consider whether we can use botVertex as left corner. First check 
+      //if (leftGirdPoint, botVertex) interesects right chian or not.
+     if(DBG_intersectChain(rightChain, rightChainStartIndex,rightChainEndIndex,
+				    leftGridPoint, botVertex))
+       {
+	 ret_leftCornerWhere = 2;//right
+	 ret_leftCornerIndex = index2; //should use tempI???
+       }
+     else if(botVertex[0] < tempMin)
+       ret_leftCornerWhere = 1; //bot
+     else
+       {
+	 ret_leftCornerWhere = 2; //right
+	 ret_leftCornerIndex = tempI;
+       }
+    }
+  else if(index2> rightChainEndIndex) /*index1<=leftChainEndIndex*/
+    {
+      ret_leftCornerWhere = 0; /*left chain*/
+      ret_leftCornerIndex = index1;
+      
+      /*find the vertex on the left chain with the maximum u,
+       *either this vertex or the botvertex can be used as the right corner
+       */
+
+      Int tempI;
+      //skip those points which are equal to v. (avoid degeneratcy)
+      for(tempI = index1; tempI <= leftChainEndIndex; tempI++)
+	if(leftChain->getVertex(tempI)[1] < v) 
+	  break;
+      if(tempI > leftChainEndIndex)
+	ret_rightCornerWhere = 1;
+      else
+	{
+	  Real tempMax = leftChain->getVertex(tempI)[0];
+	  for(i=tempI; i<= leftChainEndIndex; i++)
+	    if(leftChain->getVertex(i)[0] > tempMax)
+	      {
+		tempI = i;
+		tempMax = leftChain->getVertex(i)[0];
+	      }
+
+
+
+	  //we consider whether we can use botVertex as a corner. So first we check 
+	  //whether (rightGridPoint, botVertex) interescts the left chain or not.
+	  if(DBG_intersectChain(leftChain, leftChainStartIndex,leftChainEndIndex,
+				    rightGridPoint, botVertex))
+	    {
+	      ret_rightCornerWhere = 0;
+	      ret_rightCornerIndex = index1; //should use tempI???
+	    }
+	  else if(botVertex[0] > tempMax)
+	    {
+		      
+              ret_rightCornerWhere = 1;
+	    }
+	  else
+	    {
+	      ret_rightCornerWhere = 0;
+	      ret_rightCornerIndex = tempI;
+	    }
+	}
+      
+    }
+  else /*index1<=leftChainEndIndex and index2 <=rightChainEndIndex*/
+    {
+      if(leftChain->getVertex(index1)[1] >= rightChain->getVertex(index2)[1]) /*left point above right point*/
+	{
+	  ret_leftCornerWhere = 0; /*on left chain*/
+	  ret_leftCornerIndex = index1;
+
+	  Real tempMax;
+	  Int tempI;
+
+	  tempI = index1;
+	  tempMax = leftChain->getVertex(index1)[0];
+
+	  /*find the maximum u for all the points on the left above the right point index2*/
+	  for(i=index1+1; i<= leftChainEndIndex; i++)
+	    {
+	      if(leftChain->getVertex(i)[1] < rightChain->getVertex(index2)[1])
+		break;
+
+	      if(leftChain->getVertex(i)[0]>tempMax)
+		{
+		  tempI = i;
+		  tempMax = leftChain->getVertex(i)[0];
+		}
+	    }
+	  //we consider if we can use rightChain(index2) as right corner
+	  //we check if (rightChain(index2), rightGidPoint) intersecs left chain or not.
+	  if(DBG_intersectChain(leftChain, leftChainStartIndex,leftChainEndIndex, rightGridPoint, rightChain->getVertex(index2)))
+	    {
+	      ret_rightCornerWhere = 0;
+	      ret_rightCornerIndex = index1; //should use tempI???
+	    }
+	  else if(tempMax >= rightChain->getVertex(index2)[0] ||
+	     tempMax >= uright
+	     )
+	    {
+
+	      ret_rightCornerWhere = 0; /*on left Chain*/
+	      ret_rightCornerIndex = tempI;
+	    }
+	  else
+	    {
+	      ret_rightCornerWhere = 2; /*on right chain*/
+	      ret_rightCornerIndex = index2;
+	    }
+	}
+      else /*left below right*/
+	{
+	  ret_rightCornerWhere = 2; /*on the right*/
+	  ret_rightCornerIndex = index2;
+	  
+	  Real tempMin;
+	  Int tempI;
+	  
+	  tempI = index2;
+	  tempMin = rightChain->getVertex(index2)[0];
+	  
+	  /*find the minimum u for all the points on the right above the left poitn index1*/
+	  for(i=index2+1; i<= rightChainEndIndex; i++)
+	    {
+	      if( rightChain->getVertex(i)[1] < leftChain->getVertex(index1)[1])
+		break;
+	      if(rightChain->getVertex(i)[0] < tempMin)
+		{
+		  tempI = i;
+		  tempMin = rightChain->getVertex(i)[0];
+		}
+	    }
+
+	  //we consider if we can use leftchain(index1) as left corner. 
+	  //we check if (leftChain(index1) intersects right chian or not
+	  if(DBG_intersectChain(rightChain, rightChainStartIndex, rightChainEndIndex, leftGridPoint, leftChain->getVertex(index1)))
+	    {
+	      ret_leftCornerWhere = 2;
+	      ret_leftCornerIndex = index2; //should use tempI???
+	      }
+	  else if(tempMin <= leftChain->getVertex(index1)[0] ||
+	     tempMin <= uleft)				
+	    {
+	      ret_leftCornerWhere = 2; /* on right chain*/
+	      ret_leftCornerIndex = tempI;
+	    }
+	  else
+	    {
+	      ret_leftCornerWhere = 0; /*on left chain*/
+	      ret_leftCornerIndex = index1;
+	    }
+	}
+    }
+
+}
+
+
+void findUpCorners(Real *topVertex, 
+		   vertexArray *leftChain, Int leftChainStartIndex, Int leftChainEndIndex,
+		   vertexArray *rightChain, Int rightChainStartIndex, Int rightChainEndIndex,
+		   Real v,
+		   Real uleft,
+		   Real uright,
+		   Int& ret_leftCornerWhere, /*0: left chain, 1: topvertex, 2: rightchain*/
+		   Int& ret_leftCornerIndex, /*useful when ret_leftCornerWhere == 0 or 2*/
+		   Int& ret_rightCornerWhere, /*0: left chain, 1: topvertex, 2: rightchain*/
+		   Int& ret_rightCornerIndex /*useful when ret_leftCornerWhere == 0 or 2*/
+		   )
+{
+#ifdef MYDEBUG
+printf("***********enter findUpCorners\n");
+#endif
+
+  assert(v < topVertex[1]);
+  Real leftGridPoint[2];
+  leftGridPoint[0] = uleft;
+  leftGridPoint[1] = v;
+  Real rightGridPoint[2];
+  rightGridPoint[0] = uright;
+  rightGridPoint[1] = v;
+
+  Int i;
+  Int index1, index2;
+
+  index1 = leftChain->findIndexFirstAboveEqualGen(v, leftChainStartIndex, leftChainEndIndex);
+
+
+  index2 = rightChain->findIndexFirstAboveEqualGen(v, rightChainStartIndex, rightChainEndIndex);
+
+  if(index2>= leftChainStartIndex)  //index2 was found above  
+    index2 = rightChain->skipEqualityFromStart(v, index2, rightChainEndIndex);
+
+  if(index1<leftChainStartIndex && index2 <rightChainStartIndex) /*no point above v on left chain or right chain*/
+    {
+      /*the topVertex is the only vertex above v*/
+      ret_leftCornerWhere = 1;
+      ret_rightCornerWhere = 1;
+    }
+  else if(index1<leftChainStartIndex ) /*index2 >= rightChainStartIndex*/
+    {
+      ret_rightCornerWhere = 2; /*on right chain*/
+      ret_rightCornerIndex = index2;
+
+      //find the minimum u on right top, either that, or top, or right[index2] is the left corner
+      Real tempMin = rightChain->getVertex(index2)[0];
+      Int tempI = index2;
+      for(i=index2-1; i>=rightChainStartIndex; i--)
+	if(rightChain->getVertex(i)[0] < tempMin)
+	  {
+	    tempMin = rightChain->getVertex(i)[0];
+	    tempI = i;
+	  }
+      //chech whether (leftGridPoint, top) intersects rightchai,
+      //if yes, use right corner as left corner
+      //if not, use top or right[tempI] as left corner
+      if(DBG_intersectChain(rightChain, rightChainStartIndex, rightChainEndIndex,
+			leftGridPoint, topVertex))
+	{
+	  ret_leftCornerWhere = 2; //rightChain
+	  ret_leftCornerIndex = index2; 
+	}
+      else if(topVertex[0] < tempMin)
+	ret_leftCornerWhere = 1; /*topvertex*/
+      else
+	{
+	  ret_leftCornerWhere = 2; //right chain
+	  ret_leftCornerIndex = tempI;
+	}
+	      
+    }
+  else if(index2< rightChainStartIndex) /*index1>=leftChainStartIndex*/
+    {
+      ret_leftCornerWhere = 0; /*left chain*/
+      ret_leftCornerIndex = index1;
+       
+      //find the maximum u on the left top section. either that or topvertex, or left[index1]  is the right corner
+      Real tempMax = leftChain->getVertex(index1)[0];
+      Int tempI = index1;
+
+      for(i=index1-1; i>=leftChainStartIndex; i--){
+
+	if(leftChain->getVertex(i)[0] > tempMax)
+	  {
+
+	    tempMax = leftChain->getVertex(i)[0];
+	    tempI = i;
+	  }
+      }
+      //check whether (rightGridPoint, top) intersects leftChain or not
+      //if yes, we use leftCorner as the right corner
+      //if not, we use either top or left[tempI] as the right corner
+      if(DBG_intersectChain(leftChain, leftChainStartIndex,leftChainEndIndex,
+			    rightGridPoint, topVertex))
+	 {
+	   ret_rightCornerWhere = 0; //left chan
+	   ret_rightCornerIndex = index1;
+	 }
+      else if(topVertex[0] > tempMax)
+	ret_rightCornerWhere = 1;//topVertex
+      else
+	{
+	  ret_rightCornerWhere = 0;//left chain
+	  ret_rightCornerIndex = tempI;
+	}
+    }
+  else /*index1>=leftChainStartIndex and index2 >=rightChainStartIndex*/
+    {
+      if(leftChain->getVertex(index1)[1] <= rightChain->getVertex(index2)[1]) /*left point below right point*/
+	{
+	  ret_leftCornerWhere = 0; /*on left chain*/
+	  ret_leftCornerIndex = index1;
+
+	  Real tempMax;
+	  Int tempI;
+
+	  tempI = index1;
+	  tempMax = leftChain->getVertex(index1)[0];
+
+	  /*find the maximum u for all the points on the left below the right point index2*/
+	  for(i=index1-1; i>= leftChainStartIndex; i--)
+	    {
+	      if(leftChain->getVertex(i)[1] > rightChain->getVertex(index2)[1])
+		break;
+
+	      if(leftChain->getVertex(i)[0]>tempMax)
+		{
+		  tempI = i;
+		  tempMax = leftChain->getVertex(i)[0];
+		}
+	    }
+	  //chek whether (rightChain(index2), rightGridPoint) intersects leftchian or not
+	  if(DBG_intersectChain(leftChain, leftChainStartIndex, leftChainEndIndex, rightGridPoint, rightChain->getVertex(index2)))
+	     {
+	       ret_rightCornerWhere = 0;
+	       ret_rightCornerIndex = index1;
+	     }
+	  else if(tempMax >= rightChain->getVertex(index2)[0] ||
+	     tempMax >= uright)
+	    {
+	      ret_rightCornerWhere = 0; /*on left Chain*/
+	      ret_rightCornerIndex = tempI;
+	    }
+	  else
+	    {
+	      ret_rightCornerWhere = 2; /*on right chain*/
+	      ret_rightCornerIndex = index2;
+	    }
+	}
+      else /*left above right*/
+	{
+	  ret_rightCornerWhere = 2; /*on the right*/
+	  ret_rightCornerIndex = index2;
+	  
+	  Real tempMin;
+	  Int tempI;
+	  
+	  tempI = index2;
+	  tempMin = rightChain->getVertex(index2)[0];
+	  
+	  /*find the minimum u for all the points on the right below the left poitn index1*/
+	  for(i=index2-1; i>= rightChainStartIndex; i--)
+	    {
+	      if( rightChain->getVertex(i)[1] > leftChain->getVertex(index1)[1])
+		break;
+	      if(rightChain->getVertex(i)[0] < tempMin)
+		{
+		  tempI = i;
+		  tempMin = rightChain->getVertex(i)[0];
+		}
+	    }
+          //check whether (leftGRidPoint,left(index1)) interesect right chain 
+	  if(DBG_intersectChain(rightChain, rightChainStartIndex, rightChainEndIndex,
+				leftGridPoint, leftChain->getVertex(index1)))
+	    {
+	      ret_leftCornerWhere = 2; //right
+	      ret_leftCornerIndex = index2;
+	    }
+	  else if(tempMin <= leftChain->getVertex(index1)[0] ||
+	     tempMin <= uleft)
+	    {
+	      ret_leftCornerWhere = 2; /* on right chain*/
+	      ret_leftCornerIndex = tempI;
+	    }
+	  else
+	    {
+	      ret_leftCornerWhere = 0; /*on left chain*/
+	      ret_leftCornerIndex = index1;
+	    }
+	}
+    }
+#ifdef MYDEBUG
+printf("***********leave findUpCorners\n");
+#endif
+}
+
+//return 1 if neck exists, 0 othewise
+Int findNeckF(vertexArray *leftChain, Int botLeftIndex,
+	      vertexArray *rightChain, Int botRightIndex,
+	      gridBoundaryChain* leftGridChain,
+	      gridBoundaryChain* rightGridChain,
+	      Int gridStartIndex,
+	      Int& neckLeft, 
+	      Int& neckRight)
+{
+/*
+printf("enter findNeckF, botleft, botright=%i,%i,gstartindex=%i\n",botLeftIndex,botRightIndex,gridStartIndex);
+printf("leftChain is\n");
+leftChain->print();
+printf("rightChain is\n");
+rightChain->print();
+*/
+
+  Int lowerGridIndex; //the grid below leftChain and rightChian vertices
+  Int i;
+  Int n_vlines = leftGridChain->get_nVlines();
+  Real v;
+  if(botLeftIndex >= leftChain->getNumElements() ||
+     botRightIndex >= rightChain->getNumElements())
+    return 0; //no neck exists
+     
+  v=min(leftChain->getVertex(botLeftIndex)[1], rightChain->getVertex(botRightIndex)[1]);  
+
+ 
+
+
+  for(i=gridStartIndex; i<n_vlines; i++)
+    if(leftGridChain->get_v_value(i) <= v && 
+       leftGridChain->getUlineIndex(i)<= rightGridChain->getUlineIndex(i))
+      break;
+  
+  lowerGridIndex = i;
+
+  if(lowerGridIndex == n_vlines) //the two trm vertex are higher than all gridlines
+    return 0;
+  else 
+    {
+      Int botLeft2, botRight2;
+/*
+printf("leftGridChain->get_v_)value=%f\n",leftGridChain->get_v_value(lowerGridIndex), botLeftIndex); 
+printf("leftChain->get_vertex(0)=(%f,%f)\n", leftChain->getVertex(0)[0],leftChain->getVertex(0)[1]);
+printf("leftChain->get_vertex(1)=(%f,%f)\n", leftChain->getVertex(1)[0],leftChain->getVertex(1)[1]);
+printf("leftChain->get_vertex(2)=(%f,%f)\n", leftChain->getVertex(2)[0],leftChain->getVertex(2)[1]);
+*/
+      botLeft2 = leftChain->findIndexFirstAboveEqualGen(leftGridChain->get_v_value(lowerGridIndex), botLeftIndex, leftChain->getNumElements()-1) -1 ;
+
+/*
+printf("botLeft2=%i\n", botLeft2);
+printf("leftChain->getNumElements=%i\n", leftChain->getNumElements());
+*/
+
+      botRight2 = rightChain->findIndexFirstAboveEqualGen(leftGridChain->get_v_value(lowerGridIndex), botRightIndex, rightChain->getNumElements()-1) -1;
+      if(botRight2 < botRightIndex) botRight2=botRightIndex;
+
+      if(botLeft2 < botLeftIndex) botLeft2 = botLeftIndex;
+
+      assert(botLeft2 >= botLeftIndex);
+      assert(botRight2 >= botRightIndex);
+      //find nectLeft so that it is th erightmost vertex on letChain
+
+      Int tempI = botLeftIndex;
+      Real temp = leftChain->getVertex(tempI)[0];
+      for(i=botLeftIndex+1; i<= botLeft2; i++)
+	if(leftChain->getVertex(i)[0] > temp)
+	  {
+	    temp = leftChain->getVertex(i)[0];
+	    tempI = i;
+	  }
+      neckLeft = tempI;
+
+      tempI = botRightIndex;
+      temp = rightChain->getVertex(tempI)[0];
+      for(i=botRightIndex+1; i<= botRight2; i++)
+	if(rightChain->getVertex(i)[0] < temp)
+	  {
+	    temp = rightChain->getVertex(i)[0];
+	    tempI = i;
+	  }
+      neckRight = tempI;
+      return 1;
+    }
+}
+							
+  
+	          
+/*find i>=botLeftIndex,j>=botRightIndex so that
+ *(leftChain[i], rightChain[j]) is a neck.
+ */
+void findNeck(vertexArray *leftChain, Int botLeftIndex, 
+	      vertexArray *rightChain, Int botRightIndex, 
+	      Int& leftLastIndex, /*left point of the neck*/
+	      Int& rightLastIndex /*right point of the neck*/
+	      )
+{
+  assert(botLeftIndex < leftChain->getNumElements() &&
+     botRightIndex < rightChain->getNumElements());
+     
+  /*now the neck exists for sure*/
+
+  if(leftChain->getVertex(botLeftIndex)[1] <= rightChain->getVertex(botRightIndex)[1]) //left below right
+    {
+
+      leftLastIndex = botLeftIndex;
+      
+      /*find i so that rightChain[i][1] >= leftchainbotverte[1], and i+1<
+       */
+      rightLastIndex=rightChain->findIndexAboveGen(leftChain->getVertex(botLeftIndex)[1], botRightIndex+1, rightChain->getNumElements()-1);    
+    }
+  else  //left above right
+    {
+
+      rightLastIndex = botRightIndex;
+     
+      leftLastIndex = leftChain->findIndexAboveGen(rightChain->getVertex(botRightIndex)[1], 
+						  botLeftIndex+1,
+						  leftChain->getNumElements()-1);
+    }
+}
+      
+      
+
+void findLeftGridIndices(directedLine* topEdge, Int firstGridIndex, Int lastGridIndex, gridWrap* grid,  Int* ret_indices, Int* ret_innerIndices)
+{
+
+  Int i,k,isHoriz = 0;
+  Int n_ulines = grid->get_n_ulines();
+  Real uMin = grid->get_u_min();
+  Real uMax = grid->get_u_max();
+  /*
+  Real vMin = grid->get_v_min();
+  Real vMax = grid->get_v_max();
+  */
+  Real slop = 0.0, uinterc;
+
+#ifdef SHORTEN_GRID_LINE
+  //uintercBuf stores all the interction u value for each grid line
+  //notice that lastGridIndex<= firstGridIndex
+  Real *uintercBuf = (Real *) malloc (sizeof(Real) * (firstGridIndex-lastGridIndex+1));
+  assert(uintercBuf);
+#endif
+
+  /*initialization to make vtail bigger than grid->...*/
+  directedLine* dLine = topEdge;
+  Real vtail = grid->get_v_value(firstGridIndex) + 1.0; 
+  Real tempMaxU = grid->get_u_min();
+
+
+  /*for each grid line*/
+  for(k=0, i=firstGridIndex; i>=lastGridIndex; i--, k++)
+    {
+
+      Real grid_v_value = grid->get_v_value(i);
+
+      /*check whether this grid line is below the current trim edge.*/
+      if(vtail > grid_v_value)
+	{
+	  /*since the grid line is below the trim edge, we 
+	   *find the trim edge which will contain the trim line
+	   */
+	  while( (vtail=dLine->tail()[1]) > grid_v_value){
+
+	    tempMaxU = max(tempMaxU, dLine->tail()[0]);
+	    dLine = dLine -> getNext();
+	  }
+
+	  if( fabs(dLine->head()[1] - vtail) < ZERO)
+	    isHoriz = 1;
+	  else
+	    {
+	      isHoriz = 0;
+	      slop = (dLine->head()[0] - dLine->tail()[0]) / (dLine->head()[1]-vtail);
+	    }
+	}
+
+      if(isHoriz)
+	{
+	  uinterc = max(dLine->head()[0], dLine->tail()[0]);
+	}
+      else
+	{
+	  uinterc = slop * (grid_v_value - vtail) + dLine->tail()[0];
+	}
+      
+      tempMaxU = max(tempMaxU, uinterc);
+
+      if(uinterc < uMin && uinterc >= uMin - ZERO)
+	uinterc = uMin;
+      if(uinterc > uMax && uinterc <= uMax + ZERO)
+	uinterc = uMax;
+
+#ifdef SHORTEN_GRID_LINE
+      uintercBuf[k] = uinterc;
+#endif
+
+      assert(uinterc >= uMin && uinterc <= uMax);
+       if(uinterc == uMax)
+         ret_indices[k] = n_ulines-1;
+       else
+	 ret_indices[k] = (Int)(((uinterc-uMin)/(uMax - uMin)) * (n_ulines-1)) + 1;
+      if(ret_indices[k] >= n_ulines)
+	ret_indices[k] = n_ulines-1;
+
+
+      ret_innerIndices[k] = (Int)(((tempMaxU-uMin)/(uMax - uMin)) * (n_ulines-1)) + 1;
+
+      /*reinitialize tempMaxU for next grdiLine*/
+      tempMaxU = uinterc;
+    }
+#ifdef SHORTEN_GRID_LINE
+  //for each grid line, compare the left grid point with the 
+  //intersection point. If the two points are too close, then
+  //we should move the grid point one grid to the right
+  //and accordingly we should update the inner index.
+  for(k=0, i=firstGridIndex; i>=lastGridIndex; i--, k++)
+    {
+      //check gridLine i
+      //check ret_indices[k]
+      Real a = grid->get_u_value(ret_indices[k]-1);
+      Real b = grid->get_u_value(ret_indices[k]);
+      assert(uintercBuf[k] >= a && uintercBuf < b);
+      if( (b-uintercBuf[k]) <= 0.2 * (b-a)) //interc is very close to b
+	{
+	  ret_indices[k]++;
+	}
+
+      //check ret_innerIndices[k]
+      if(k>0)
+	{
+	  if(ret_innerIndices[k] < ret_indices[k-1])
+	    ret_innerIndices[k] = ret_indices[k-1];
+	  if(ret_innerIndices[k] < ret_indices[k])
+	    ret_innerIndices[k] = ret_indices[k];
+	}
+    }
+  //clean up
+  free(uintercBuf);
+#endif
+}
+
+void findRightGridIndices(directedLine* topEdge, Int firstGridIndex, Int lastGridIndex, gridWrap* grid,  Int* ret_indices, Int* ret_innerIndices)
+{
+
+  Int i,k;
+  Int n_ulines = grid->get_n_ulines();
+  Real uMin = grid->get_u_min();
+  Real uMax = grid->get_u_max();
+  /*
+  Real vMin = grid->get_v_min();
+  Real vMax = grid->get_v_max();
+  */
+  Real slop = 0.0, uinterc;
+
+#ifdef SHORTEN_GRID_LINE
+  //uintercBuf stores all the interction u value for each grid line
+  //notice that firstGridIndex >= lastGridIndex
+  Real *uintercBuf = (Real *) malloc (sizeof(Real) * (firstGridIndex-lastGridIndex+1));
+  assert(uintercBuf);
+#endif
+
+  /*initialization to make vhead bigger than grid->v_value...*/
+  directedLine* dLine = topEdge->getPrev();
+  Real vhead = dLine->tail()[1];
+  Real tempMinU = grid->get_u_max();
+
+  /*for each grid line*/
+  for(k=0, i=firstGridIndex; i>=lastGridIndex; i--, k++)
+    {
+
+      Real grid_v_value = grid->get_v_value(i);
+
+
+      /*check whether this grid line is below the current trim edge.*/
+      if(vhead >= grid_v_value)
+	{
+	  /*since the grid line is below the tail of the trim edge, we 
+	   *find the trim edge which will contain the trim line
+	   */
+	  while( (vhead=dLine->head()[1]) > grid_v_value){
+	    tempMinU = min(tempMinU, dLine->head()[0]);
+	    dLine = dLine -> getPrev();
+	  }
+
+	  /*skip the equality in the case of degenerat case: horizontal */
+	  while(dLine->head()[1] == grid_v_value)
+	    dLine = dLine->getPrev();
+	    
+	  assert( dLine->tail()[1] != dLine->head()[1]);
+	  slop = (dLine->tail()[0] - dLine->head()[0]) / (dLine->tail()[1]-dLine->head()[1]);
+	  /*
+	   if(dLine->tail()[1] == vhead)
+	     isHoriz = 1;
+	     else
+	    {
+	      isHoriz = 0;
+	      slop = (dLine->tail()[0] - dLine->head()[0]) / (dLine->tail()[1]-vhead);
+	    }
+	    */
+	}
+	uinterc = slop * (grid_v_value - dLine->head()[1]) + dLine->head()[0];
+
+      //in case unterc is outside of the grid due to floating point
+      if(uinterc < uMin)
+	uinterc = uMin;
+      else if(uinterc > uMax)
+	uinterc = uMax;
+
+#ifdef SHORTEN_GRID_LINE
+      uintercBuf[k] = uinterc;
+#endif      
+
+      tempMinU = min(tempMinU, uinterc);
+
+      assert(uinterc >= uMin && uinterc <= uMax);      
+
+      if(uinterc == uMin)
+	ret_indices[k] = 0;
+      else
+	ret_indices[k] = (int)ceil((((uinterc-uMin)/(uMax - uMin)) * (n_ulines-1))) -1;
+/*
+if(ret_indices[k] >= grid->get_n_ulines())
+  {
+  printf("ERROR3\n");
+  exit(0);
+}
+if(ret_indices[k] < 0)    
+  {
+  printf("ERROR4\n");
+  exit(0);
+}
+*/
+      ret_innerIndices[k] = (int)ceil ((((tempMinU-uMin)/(uMax - uMin)) * (n_ulines-1))) -1;
+
+      tempMinU = uinterc;
+    }
+#ifdef SHORTEN_GRID_LINE
+  //for each grid line, compare the left grid point with the 
+  //intersection point. If the two points are too close, then
+  //we should move the grid point one grid to the right
+  //and accordingly we should update the inner index.
+  for(k=0, i=firstGridIndex; i>=lastGridIndex; i--, k++)
+    {
+      //check gridLine i
+      //check ret_indices[k]
+      Real a = grid->get_u_value(ret_indices[k]);
+      Real b = grid->get_u_value(ret_indices[k]+1);
+      assert(uintercBuf[k] > a && uintercBuf <= b);
+      if( (uintercBuf[k]-a) <= 0.2 * (b-a)) //interc is very close to a
+	{
+	  ret_indices[k]--;
+	}
+
+      //check ret_innerIndices[k]
+      if(k>0)
+	{
+	  if(ret_innerIndices[k] > ret_indices[k-1])
+	    ret_innerIndices[k] = ret_indices[k-1];
+	  if(ret_innerIndices[k] > ret_indices[k])
+	    ret_innerIndices[k] = ret_indices[k];
+	}
+    }
+  //clean up
+  free(uintercBuf);
+#endif
+}
+
+
+void sampleMonoPoly(directedLine* polygon, gridWrap* grid, Int ulinear, Int vlinear, primStream* pStream, rectBlockArray* rbArray)
+{
+/*
+{
+grid->print();
+polygon->writeAllPolygons("zloutputFile");
+exit(0);
+}
+*/
+
+if(grid->get_n_ulines() == 2 ||
+   grid->get_n_vlines() == 2)
+{ 
+  if(ulinear && grid->get_n_ulines() == 2)
+    {
+      monoTriangulationFun(polygon, compV2InY, pStream);   
+      return;
+    }
+  else if(DBG_isConvex(polygon) && polygon->numEdges() >=4)
+     {
+       triangulateConvexPoly(polygon, ulinear, vlinear, pStream);
+       return;
+     }
+  else if(vlinear || DBG_is_U_direction(polygon))
+    {
+      Int n_cusps;//num interior cusps
+      Int n_edges = polygon->numEdges();
+      directedLine** cusps = (directedLine**) malloc(sizeof(directedLine*) * n_edges);
+      assert(cusps);
+      findInteriorCuspsX(polygon, n_cusps, cusps);
+
+      if(n_cusps == 0) //u_monotone
+	{
+
+	  monoTriangulationFun(polygon, compV2InX, pStream);
+
+          free(cusps);
+          return;          
+	}
+      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(polygon, compV2InX, pStream);
+	      free(cusps);
+	      return;
+	    }
+
+	  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();	  
+
+          free(cusps);
+          return;
+         }
+     free(cusps);
+     }
+}
+
+  /*find the top and bottom of the polygon. It is supposed to be
+   *a V-monotone polygon
+   */
+
+  directedLine* tempV;
+  directedLine* topV;
+  directedLine* botV;
+  topV = botV = polygon;
+
+  for(tempV = polygon->getNext(); tempV != polygon; tempV = tempV->getNext())
+    {
+      if(compV2InY(topV->head(), tempV->head())<0) {
+
+	topV = tempV;
+      }
+      if(compV2InY(botV->head(), tempV->head())>0) {
+
+	botV = tempV;
+      }
+    }
+  
+  /*find the first(top) and the last (bottom) grid line which intersect the
+   *this polygon
+   */
+  Int firstGridIndex; /*the index in the grid*/
+  Int lastGridIndex;
+  firstGridIndex = (Int) ((topV->head()[1] - grid->get_v_min()) / (grid->get_v_max() - grid->get_v_min()) * (grid->get_n_vlines()-1));
+  lastGridIndex  = (Int) ((botV->head()[1] - grid->get_v_min()) / (grid->get_v_max() - grid->get_v_min()) * (grid->get_n_vlines()-1)) + 1;
+
+
+  /*find the interval inside  the polygon for each gridline*/
+  Int *leftGridIndices = (Int*) malloc(sizeof(Int) * (firstGridIndex - lastGridIndex +1));
+  assert(leftGridIndices);
+  Int *rightGridIndices = (Int*) malloc(sizeof(Int) * (firstGridIndex - lastGridIndex +1));
+  assert(rightGridIndices);
+  Int *leftGridInnerIndices = (Int*) malloc(sizeof(Int) * (firstGridIndex - lastGridIndex +1));
+  assert(leftGridInnerIndices);
+  Int *rightGridInnerIndices = (Int*) malloc(sizeof(Int) * (firstGridIndex - lastGridIndex +1));
+  assert(rightGridInnerIndices);
+
+  findLeftGridIndices(topV, firstGridIndex, lastGridIndex, grid,  leftGridIndices, leftGridInnerIndices);
+
+  findRightGridIndices(topV, firstGridIndex, lastGridIndex, grid,  rightGridIndices, rightGridInnerIndices);
+
+  gridBoundaryChain leftGridChain(grid, firstGridIndex, firstGridIndex-lastGridIndex+1, leftGridIndices, leftGridInnerIndices);
+
+  gridBoundaryChain rightGridChain(grid, firstGridIndex, firstGridIndex-lastGridIndex+1, rightGridIndices, rightGridInnerIndices);
+
+
+
+//  leftGridChain.draw();
+//  leftGridChain.drawInner();
+//  rightGridChain.draw();
+//  rightGridChain.drawInner();
+  /*(1) determine the grid boundaries (left and right).
+   *(2) process polygon  into two monotone chaines: use vertexArray
+   *(3) call sampleMonoPolyRec
+   */
+
+  /*copy the two chains into vertexArray datastructure*/
+  Int i;
+  vertexArray leftChain(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*/
+    leftChain.appendVertex(topV->getVertex(i));
+  }
+  for(tempV = topV->getNext(); tempV != botV; tempV = tempV->getNext())
+    {
+      for(i=0; i<=tempV->get_npoints()-2; i++){
+	leftChain.appendVertex(tempV->getVertex(i));
+      }
+    }
+  
+  vertexArray rightChain(20);
+  for(tempV = topV->getPrev(); tempV != botV; tempV = tempV->getPrev())
+    {
+      for(i=tempV->get_npoints()-2; i>=0; i--){
+	rightChain.appendVertex(tempV->getVertex(i));
+      }
+    }
+  for(i=botV->get_npoints()-2; i>=1; i--){ 
+    rightChain.appendVertex(tempV->getVertex(i));
+  }
+
+  sampleMonoPolyRec(topV->head(),
+		    botV->head(),
+		    &leftChain,
+		    0,
+		    &rightChain,
+		    0,
+		    &leftGridChain,
+		    &rightGridChain,
+		    0,
+		    pStream,
+		    rbArray);
+
+
+  /*cleanup space*/
+  free(leftGridIndices);
+  free(rightGridIndices);
+  free(leftGridInnerIndices);
+  free(rightGridInnerIndices);
+}
+
+void sampleMonoPolyRec(
+		       Real* topVertex,
+		       Real* botVertex,
+		       vertexArray* leftChain, 
+		       Int leftStartIndex,
+		       vertexArray* rightChain,
+		       Int rightStartIndex,
+		       gridBoundaryChain* leftGridChain, 
+		       gridBoundaryChain* rightGridChain, 
+		       Int gridStartIndex,
+		       primStream* pStream,
+		       rectBlockArray* rbArray)
+{
+
+  /*find the first connected component, and the four corners.
+   */
+  Int index1, index2; /*the first and last grid line of the first connected component*/
+
+  if(topVertex[1] <= botVertex[1])
+    return;
+    
+  /*find i so that the grid line is below the top vertex*/
+  Int i=gridStartIndex;
+  while (i < leftGridChain->get_nVlines())
+    {
+      if(leftGridChain->get_v_value(i) < topVertex[1])
+	break;
+      i++;
+    }
+
+  /*find the first connected component starting with i*/
+  /*find index1 so that left_uline_index <= right_uline_index, that is, this
+   *grid line contains at least one inner grid point
+   */
+  index1=i;
+  int num_skipped_grid_lines=0;
+  while(index1 < leftGridChain->get_nVlines())
+    {
+      if(leftGridChain->getUlineIndex(index1) <= rightGridChain->getUlineIndex(index1))
+	break;
+      num_skipped_grid_lines++;
+      index1++;
+    }
+
+
+
+  if(index1 >= leftGridChain->get_nVlines()) /*no grid line exists which has inner point*/
+    {
+      /*stop recursion, ...*/
+      /*monotone triangulate it...*/
+//      printf("no grid line exists\n");      
+/*
+      monoTriangulationRecOpt(topVertex, botVertex, leftChain, leftStartIndex,
+			   rightChain, rightStartIndex, pStream);
+*/
+
+if(num_skipped_grid_lines <2)
+  {
+    monoTriangulationRecGenOpt(topVertex, botVertex, leftChain, leftStartIndex,
+			       leftChain->getNumElements()-1,
+			       rightChain, rightStartIndex, 
+			       rightChain->getNumElements()-1,
+			       pStream);
+  }
+else
+  {
+    //the optimum way to triangulate is top-down since this polygon
+    //is narrow-long.
+    monoTriangulationRec(topVertex, botVertex, leftChain, leftStartIndex,
+			 rightChain, rightStartIndex, pStream);
+  }
+
+/*
+      monoTriangulationRec(topVertex, botVertex, leftChain, leftStartIndex,
+			   rightChain, rightStartIndex, pStream);
+*/
+
+/*      monoTriangulationRecGenTBOpt(topVertex, botVertex, 
+				   leftChain, leftStartIndex, leftChain->getNumElements()-1,
+				   rightChain, rightStartIndex, rightChain->getNumElements()-1, 
+				   pStream);*/
+      
+
+
+    }
+  else
+    {
+
+      /*find index2 so that left_inner_index <= right_inner_index holds until index2*/
+      index2=index1+1;
+      if(index2 < leftGridChain->get_nVlines())
+	while(leftGridChain->getInnerIndex(index2) <= rightGridChain->getInnerIndex(index2))
+	  {
+	    index2++;
+	    if(index2 >= leftGridChain->get_nVlines())
+	      break;
+	  }
+      
+      index2--;
+      
+
+      
+      /*the neck*/
+      Int neckLeftIndex;
+      Int neckRightIndex;
+
+      /*the four corners*/
+      Int up_leftCornerWhere;
+      Int up_leftCornerIndex;
+      Int up_rightCornerWhere;
+      Int up_rightCornerIndex;
+      Int down_leftCornerWhere;
+      Int down_leftCornerIndex;
+      Int down_rightCornerWhere;
+      Int down_rightCornerIndex;
+
+      Real* tempBotVertex; /*the bottom vertex for this component*/
+      Real* nextTopVertex=NULL; /*for the recursion*/
+      Int nextLeftStartIndex=0;
+      Int nextRightStartIndex=0;
+
+      /*find the points below the grid line index2 on both chains*/
+      Int botLeftIndex = leftChain->findIndexStrictBelowGen(
+						      leftGridChain->get_v_value(index2),
+						      leftStartIndex,
+						      leftChain->getNumElements()-1);
+      Int botRightIndex = rightChain->findIndexStrictBelowGen(
+							rightGridChain->get_v_value(index2),
+							rightStartIndex,
+							rightChain->getNumElements()-1);
+      /*if either botLeftIndex>= numelements,
+       *        or botRightIndex >= numelemnet,
+       *then there is no neck exists. the bottom vertex is botVertex, 
+       */
+      if(! findNeckF(leftChain, botLeftIndex, rightChain, botRightIndex,
+		   leftGridChain, rightGridChain, index2, neckLeftIndex, neckRightIndex))
+	 /*
+      if(botLeftIndex == leftChain->getNumElements() ||
+	 botRightIndex == rightChain->getNumElements())
+	 */
+	{
+#ifdef MYDEBUG
+	  printf("neck NOT exists, botRightIndex=%i\n", botRightIndex);
+#endif
+
+	  tempBotVertex =  botVertex;
+	  nextTopVertex = botVertex;
+	  botLeftIndex = leftChain->getNumElements()-1;
+	  botRightIndex = rightChain->getNumElements()-1;
+	}
+      else /*neck exists*/
+	{
+#ifdef MYDEBUG
+	  printf("neck exists\n");
+#endif
+
+          /*
+	  findNeck(leftChain, botLeftIndex,
+		   rightChain, botRightIndex,
+		   neckLeftIndex,
+		   neckRightIndex);
+		   */
+#ifdef MYDEBUG
+printf("neck is found, neckLeftIndex=%i, neckRightIndex=%i\n", neckLeftIndex, neckRightIndex);
+glBegin(GL_LINES);
+glVertex2fv(leftChain->getVertex(neckLeftIndex));
+glVertex2fv(rightChain->getVertex(neckRightIndex));
+glEnd();
+#endif
+
+	  if(leftChain->getVertex(neckLeftIndex)[1] <= rightChain->getVertex(neckRightIndex)[1])
+	    {
+	      tempBotVertex = leftChain->getVertex(neckLeftIndex);
+	      botLeftIndex = neckLeftIndex-1;
+	      botRightIndex = neckRightIndex;
+	      nextTopVertex = rightChain->getVertex(neckRightIndex);
+	      nextLeftStartIndex = neckLeftIndex;
+	      nextRightStartIndex = neckRightIndex+1;
+	    }
+	  else
+	    {
+	      tempBotVertex = rightChain->getVertex(neckRightIndex);
+	      botLeftIndex = neckLeftIndex;
+	      botRightIndex = neckRightIndex-1;		  
+	      nextTopVertex = leftChain->getVertex(neckLeftIndex);
+	      nextLeftStartIndex = neckLeftIndex+1;
+	      nextRightStartIndex = neckRightIndex;
+	    }
+	}
+
+      findUpCorners(topVertex,
+		    leftChain,
+		    leftStartIndex, botLeftIndex,
+		    rightChain,
+		    rightStartIndex, botRightIndex,
+		    leftGridChain->get_v_value(index1),
+		    leftGridChain->get_u_value(index1),
+		    rightGridChain->get_u_value(index1),
+		    up_leftCornerWhere,
+		    up_leftCornerIndex,
+		    up_rightCornerWhere,
+		    up_rightCornerIndex);
+
+      findDownCorners(tempBotVertex,
+		      leftChain,
+		      leftStartIndex, botLeftIndex,
+		      rightChain,
+		      rightStartIndex, botRightIndex,
+		      leftGridChain->get_v_value(index2),
+		      leftGridChain->get_u_value(index2),
+		      rightGridChain->get_u_value(index2),
+		      down_leftCornerWhere,
+		      down_leftCornerIndex,
+		      down_rightCornerWhere,
+		      down_rightCornerIndex);	      
+#ifdef MYDEBUG
+      printf("find corners done, down_leftwhere=%i, down_righwhere=%i,\n",down_leftCornerWhere, down_rightCornerWhere );
+      printf("find corners done, up_leftwhere=%i, up_righwhere=%i,\n",up_leftCornerWhere, up_rightCornerWhere );
+      printf("find corners done, up_leftindex=%i, up_righindex=%i,\n",up_leftCornerIndex, up_rightCornerIndex );
+      printf("find corners done, down_leftindex=%i, down_righindex=%i,\n",down_leftCornerIndex, down_rightCornerIndex );
+#endif
+
+/*
+      drawCorners(topVertex,
+		  tempBotVertex,
+		  leftChain,
+		  rightChain,
+		  leftGridChain,
+		  rightGridChain,
+		  index1,
+		  index2,
+		  up_leftCornerWhere,
+		  up_leftCornerIndex,
+		  up_rightCornerWhere,
+		  up_rightCornerIndex,
+		  down_leftCornerWhere,
+		  down_leftCornerIndex,
+		  down_rightCornerWhere,
+		  down_rightCornerIndex);
+*/
+
+
+      sampleConnectedComp(topVertex, tempBotVertex,
+			  leftChain, 
+			  leftStartIndex, botLeftIndex,
+			  rightChain,
+			  rightStartIndex, botRightIndex,
+			  leftGridChain,
+			  rightGridChain,
+			  index1, index2,
+			  up_leftCornerWhere,
+			  up_leftCornerIndex,
+			  up_rightCornerWhere,
+			  up_rightCornerIndex,
+			  down_leftCornerWhere,
+			  down_leftCornerIndex,
+			  down_rightCornerWhere,
+			  down_rightCornerIndex,
+			  pStream,
+			  rbArray
+			  );
+
+      /*recursion*/
+
+      sampleMonoPolyRec(
+			nextTopVertex,
+			botVertex,
+			leftChain, 
+			nextLeftStartIndex,
+			rightChain,
+			nextRightStartIndex,
+			leftGridChain, 
+			rightGridChain, 
+			index2+1,
+			pStream, rbArray);
+			
+
+    }
+
+}
+
+void sampleLeftStrip(vertexArray* leftChain,
+		     Int topLeftIndex,
+		     Int botLeftIndex,
+		     gridBoundaryChain* leftGridChain,
+		     Int leftGridChainStartIndex,
+		     Int leftGridChainEndIndex,
+		     primStream* pStream
+		     )
+{
+  assert(leftChain->getVertex(topLeftIndex)[1] > leftGridChain->get_v_value(leftGridChainStartIndex));
+  assert(leftChain->getVertex(topLeftIndex+1)[1] <= leftGridChain->get_v_value(leftGridChainStartIndex));
+  assert(leftChain->getVertex(botLeftIndex)[1] <= leftGridChain->get_v_value(leftGridChainEndIndex));
+  assert(leftChain->getVertex(botLeftIndex-1)[1] > leftGridChain->get_v_value(leftGridChainEndIndex));
+
+  /*
+   *(1)find the last grid line which doesn'; pass below
+   * this first edge, sample this region: one trim edge and 
+   * possily multiple grid lines.
+   */
+  Real *upperVert, *lowerVert; /*the end points of the first trim edge*/
+  upperVert = leftChain->getVertex(topLeftIndex);
+  lowerVert = leftChain->getVertex(topLeftIndex+1);
+  
+  Int index = leftGridChainStartIndex;
+  while(leftGridChain->get_v_value(index) >= lowerVert[1]){
+    index++;
+    if(index > leftGridChainEndIndex) 
+      break;
+  }
+  index--;
+  
+  sampleLeftSingleTrimEdgeRegion(upperVert, lowerVert,
+				 leftGridChain,
+				 leftGridChainStartIndex,
+				 index,
+				 pStream);
+  sampleLeftStripRec(leftChain, topLeftIndex+1, botLeftIndex,
+		     leftGridChain, index, leftGridChainEndIndex,
+		     pStream);
+
+}
+
+void sampleLeftStripRec(vertexArray* leftChain,
+		     Int topLeftIndex,
+		     Int botLeftIndex,
+		     gridBoundaryChain* leftGridChain,
+		     Int leftGridChainStartIndex,
+		     Int leftGridChainEndIndex,
+			primStream* pStream
+		     )
+{
+  /*now top left trim vertex is below the top grid line.
+   */
+  /*stop condition: if topLeftIndex >= botLeftIndex, then stop.
+   */
+  if(topLeftIndex >= botLeftIndex) 
+    return;
+
+  /*find the last trim vertex which is above the second top grid line:
+   * index1.
+   *and sampleLeftOneGridStep(leftchain, topLeftIndex, index1, leftGridChain,
+   * leftGridChainStartIndex).
+   * index1 could be equal to topLeftIndex.
+   */
+  Real secondGridChainV = leftGridChain->get_v_value(leftGridChainStartIndex+1);
+  assert(leftGridChainStartIndex < leftGridChainEndIndex);
+  Int index1 = topLeftIndex;
+  while(leftChain->getVertex(index1)[1] > secondGridChainV)
+    index1++;
+  index1--;
+  
+  sampleLeftOneGridStep(leftChain, topLeftIndex, index1, leftGridChain, leftGridChainStartIndex, pStream);
+
+
+  /* 
+   * Let the next trim vertex be nextTrimVertIndex (which should be  
+   *  below the second grid line).
+   * Find the last grid line index2 which is above nextTrimVert.
+   * sampleLeftSingleTrimEdgeRegion(uppervert[2], lowervert[2], 
+   *                      leftGridChain, leftGridChainStartIndex+1, index2).
+   */
+  Real *uppervert, *lowervert;
+  uppervert = leftChain->getVertex(index1);
+  lowervert = leftChain->getVertex(index1+1);
+  Int index2 = leftGridChainStartIndex+1;
+
+  while(leftGridChain->get_v_value(index2) >= lowervert[1])
+    {
+      index2++;
+      if(index2 > leftGridChainEndIndex)
+	break;
+    }
+  index2--;
+  sampleLeftSingleTrimEdgeRegion(uppervert, lowervert, leftGridChain, leftGridChainStartIndex+1, index2,  pStream);
+
+   /* sampleLeftStripRec(leftChain, 
+                        nextTrimVertIndex,
+                        botLeftIndex,
+                        leftGridChain,
+			index2,
+                        leftGridChainEndIndex
+			)
+   *
+   */
+  sampleLeftStripRec(leftChain, index1+1, botLeftIndex, leftGridChain, index2, leftGridChainEndIndex, pStream);
+  
+}
+
+
+/***************begin RecF***********************/
+/* the gridlines from leftGridChainStartIndex to 
+ * leftGridChainEndIndex are assumed to form a
+ * connected component.
+ * the trim vertex of topLeftIndex is assumed to
+ * be below the first gridline, and the tim vertex
+ * of botLeftIndex is assumed to be above the last
+ * grid line.
+ * If botLeftIndex < topLeftIndex, then no connected componeent exists, and this funcion returns without
+ * outputing any triangles.
+ * Otherwise botLeftIndex >= topLeftIndex, there is at least one triangle to output.
+ */
+void sampleLeftStripRecF(vertexArray* leftChain,
+		     Int topLeftIndex,
+		     Int botLeftIndex,
+		     gridBoundaryChain* leftGridChain,
+		     Int leftGridChainStartIndex,
+		     Int leftGridChainEndIndex,
+			primStream* pStream
+		     )
+{
+  /*now top left trim vertex is below the top grid line.
+   */
+  /*stop condition: if topLeftIndex > botLeftIndex, then stop.
+   */
+  if(topLeftIndex > botLeftIndex) 
+    return;
+
+  /*if there is only one grid Line, return.*/
+
+  if(leftGridChainStartIndex>=leftGridChainEndIndex)
+    return;
+
+
+  assert(leftChain->getVertex(topLeftIndex)[1] <= leftGridChain->get_v_value(leftGridChainStartIndex) &&
+	 leftChain->getVertex(botLeftIndex)[1] >= leftGridChain->get_v_value(leftGridChainEndIndex));
+
+  /*firs find the first trim vertex which is below or equal to the second top grid line:
+   * index1.
+   */
+  Real secondGridChainV = leftGridChain->get_v_value(leftGridChainStartIndex+1);
+
+
+  Int index1 = topLeftIndex;
+
+  while(leftChain->getVertex(index1)[1] > secondGridChainV){
+    index1++;
+    if(index1>botLeftIndex)
+      break;
+  }
+
+  /*now leftChain->getVertex(index-1)[1] > secondGridChainV and
+   *    leftChain->getVertex(index)[1] <= secondGridChainV
+   *If equality holds, then we should include the vertex index1, otherwise we include only index1-1, to
+   *perform sampleOneGridStep.
+   */
+  if(index1>botLeftIndex) 
+    index1--;
+  else if(leftChain->getVertex(index1)[1] < secondGridChainV)
+    index1--;
+
+  /*now we have leftChain->getVertex(index1)[1] >= secondGridChainV, and 
+   *  leftChain->getVertex(index1+1)[1] <= secondGridChainV
+   */
+
+
+  sampleLeftOneGridStep(leftChain, topLeftIndex, index1, leftGridChain, leftGridChainStartIndex, pStream);
+
+
+  /*if leftChain->getVertex(index1)[1] == secondGridChainV, then we can recursively do the rest.
+   */
+  if(leftChain->getVertex(index1)[1] == secondGridChainV)
+    {
+
+      sampleLeftStripRecF(leftChain, index1, botLeftIndex,leftGridChain, leftGridChainStartIndex+1, leftGridChainEndIndex, pStream);
+    }
+  else if(index1 < botLeftIndex)
+    {
+
+      /* Otherwise, we have leftChain->getVertex(index1)[1] > secondGridChainV,
+       * let the next trim vertex be nextTrimVertIndex (which should be  strictly
+       *  below the second grid line).
+       * Find the last grid line index2 which is above nextTrimVert.
+       * sampleLeftSingleTrimEdgeRegion(uppervert[2], lowervert[2], 
+       *                      leftGridChain, leftGridChainStartIndex+1, index2).
+       */
+      Real *uppervert, *lowervert;
+      uppervert = leftChain->getVertex(index1);
+      lowervert = leftChain->getVertex(index1+1); //okay since index1<botLeftIndex
+      Int index2 = leftGridChainStartIndex+1;
+
+      
+      while(leftGridChain->get_v_value(index2) >= lowervert[1])
+	{
+	  index2++;
+	  if(index2 > leftGridChainEndIndex)
+	    break;
+	}
+      index2--;
+
+      
+      sampleLeftSingleTrimEdgeRegion(uppervert, lowervert, leftGridChain, leftGridChainStartIndex+1, index2,  pStream);
+      
+      /*recursion*/
+
+      sampleLeftStripRecF(leftChain, index1+1, botLeftIndex, leftGridChain, index2, leftGridChainEndIndex, pStream);
+    }
+  
+}
+
+/***************End RecF***********************/
+
+/*sample the left area in between one trim edge and multiple grid lines.
+ * all the grid lines should be in between the two end poins of the
+ *trim edge.
+ */
+void sampleLeftSingleTrimEdgeRegion(Real upperVert[2], Real lowerVert[2],
+				    gridBoundaryChain* gridChain,
+				    Int beginIndex,
+				    Int endIndex,
+				    primStream* pStream)
+{
+  Int i,j,k;
+
+  vertexArray vArray(endIndex-beginIndex+1);  
+  vArray.appendVertex(gridChain->get_vertex(beginIndex));
+
+  for(k=1, i=beginIndex+1; i<=endIndex; i++, k++)
+    {
+      vArray.appendVertex(gridChain->get_vertex(i));
+
+      /*output the fan of the grid points of the (i)th and (i-1)th grid line.
+       */
+      if(gridChain->getUlineIndex(i) < gridChain->getUlineIndex(i-1))
+	{
+	  pStream->begin();	  
+	  pStream->insert(gridChain->get_vertex(i-1));
+	  for(j=gridChain->getUlineIndex(i); j<= gridChain->getUlineIndex(i-1); j++)
+	    pStream->insert(gridChain->getGrid()->get_u_value(j), gridChain->get_v_value(i));
+	  pStream->end(PRIMITIVE_STREAM_FAN);
+	}
+      else if(gridChain->getUlineIndex(i) > gridChain->getUlineIndex(i-1))
+	{
+	  pStream->begin();
+	  pStream->insert(gridChain->get_vertex(i));
+	  for(j=gridChain->getUlineIndex(i); j>= gridChain->getUlineIndex(i-1); j--)
+	    pStream->insert(gridChain->getGrid()->get_u_value(j), gridChain->get_v_value(i-1));
+	  pStream->end(PRIMITIVE_STREAM_FAN);
+	}
+      /*otherwisem, the two are equal, so there is no fan to outout*/	  
+    }
+  
+  monoTriangulation2(upperVert, lowerVert, &vArray, 0, endIndex-beginIndex, 
+		     0, /*decreasing chain*/
+		     pStream);
+}
+  
+/*return i, such that from begin to i-1 the chain is strictly u-monotone. 
+ */				 
+Int findIncreaseChainFromBegin(vertexArray* chain, Int begin ,Int end)
+{
+  Int i=begin;
+  Real prevU = chain->getVertex(i)[0];
+  Real thisU;
+  for(i=begin+1; i<=end; i++){
+    thisU = chain->getVertex(i)[0];
+
+    if(prevU < thisU){
+      prevU = thisU;
+    }
+    else
+      break;
+  }
+  return i;
+}
+  
+/*check whether there is a vertex whose v value is strictly 
+ *inbetween vup vbelow
+ *if no middle exists return -1, else return the idnex.
+ */
+Int checkMiddle(vertexArray* chain, Int begin, Int end, 
+		Real vup, Real vbelow)
+{
+  Int i;
+  for(i=begin; i<=end; i++)
+    {
+      if(chain->getVertex(i)[1] < vup && chain->getVertex(i)[1]>vbelow)
+	return i;
+    }
+  return -1;
+}
+  
+/*the degenerat case of sampleLeftOneGridStep*/
+void sampleLeftOneGridStepNoMiddle(vertexArray* leftChain,
+				   Int beginLeftIndex,
+				   Int endLeftIndex,
+				   gridBoundaryChain* leftGridChain,
+				   Int leftGridChainStartIndex,
+				   primStream* pStream)
+{
+  /*since there is no middle, there is at most one point which is on the 
+   *second grid line, there could be multiple points on the first (top)
+   *grid line.
+   */
+
+  leftGridChain->leftEndFan(leftGridChainStartIndex+1, pStream);
+
+  monoTriangulation2(leftGridChain->get_vertex(leftGridChainStartIndex),
+		     leftGridChain->get_vertex(leftGridChainStartIndex+1),
+		     leftChain,
+		     beginLeftIndex,
+		     endLeftIndex,
+		     1, //is increase chain.
+		     pStream);
+}
+
+
+
+/*sampling the left area in between two grid lines.
+ */
+void sampleLeftOneGridStep(vertexArray* leftChain,
+		  Int beginLeftIndex,
+		  Int endLeftIndex,
+		  gridBoundaryChain* leftGridChain,
+		  Int leftGridChainStartIndex,
+		  primStream* pStream
+		  )
+{
+  if(checkMiddle(leftChain, beginLeftIndex, endLeftIndex, 
+		 leftGridChain->get_v_value(leftGridChainStartIndex),
+		 leftGridChain->get_v_value(leftGridChainStartIndex+1))<0)
+    
+    {
+      
+      sampleLeftOneGridStepNoMiddle(leftChain, beginLeftIndex, endLeftIndex, leftGridChain, leftGridChainStartIndex, pStream);
+      return;
+    }
+  
+  //copy into a polygon
+  {
+    directedLine* poly = NULL;
+    sampledLine* sline;
+    directedLine* dline;
+    gridWrap* grid = leftGridChain->getGrid();
+    Real vert1[2];
+    Real vert2[2];
+    Int i;
+    
+    Int innerInd = leftGridChain->getInnerIndex(leftGridChainStartIndex+1);
+    Int upperInd = leftGridChain->getUlineIndex(leftGridChainStartIndex);
+    Int lowerInd = leftGridChain->getUlineIndex(leftGridChainStartIndex+1);
+    Real upperV = leftGridChain->get_v_value(leftGridChainStartIndex);
+    Real lowerV = leftGridChain->get_v_value(leftGridChainStartIndex+1);
+
+    //the upper gridline
+    vert1[1] = vert2[1] = upperV;
+    for(i=innerInd;	i>upperInd;	i--)
+      {
+	vert1[0]=grid->get_u_value(i);
+	vert2[0]=grid->get_u_value(i-1);
+	sline = new sampledLine(vert1, vert2);
+	dline = new directedLine(INCREASING, sline);
+	if(poly == NULL)
+	  poly = dline;
+	else
+	  poly->insert(dline);
+      }
+
+    //the edge connecting upper grid with left chain
+    vert1[0] = grid->get_u_value(upperInd);
+    vert1[1] = upperV;
+    sline = new sampledLine(vert1, leftChain->getVertex(beginLeftIndex));
+    dline = new directedLine(INCREASING, sline);
+    if(poly == NULL)
+      poly = dline;
+    else
+      poly->insert(dline);    
+ 
+    //the left chain
+    for(i=beginLeftIndex; i<endLeftIndex; i++)
+      {
+	sline = new sampledLine(leftChain->getVertex(i), leftChain->getVertex(i+1));
+	dline = new directedLine(INCREASING, sline);
+	poly->insert(dline);
+      }
+
+    //the edge connecting left chain with lower gridline
+    vert2[0] = grid->get_u_value(lowerInd);
+    vert2[1] = lowerV;
+    sline = new sampledLine(leftChain->getVertex(endLeftIndex), vert2);
+    dline = new directedLine(INCREASING, sline);
+    poly->insert(dline);
+
+    //the lower grid line
+    vert1[1] = vert2[1] = lowerV;
+    for(i=lowerInd; i<innerInd; i++)
+      {
+	vert1[0] = grid->get_u_value(i);
+	vert2[0] = grid->get_u_value(i+1);
+	sline = new sampledLine(vert1, vert2);
+	dline = new directedLine(INCREASING, sline);
+	poly->insert(dline);       
+      }
+
+    //the vertical grid line segement
+    vert1[0]=vert2[0] = grid->get_u_value(innerInd);
+    vert2[1]=upperV;
+    vert1[1]=lowerV;
+    sline=new sampledLine(vert1, vert2);
+    dline=new directedLine(INCREASING, sline);
+    poly->insert(dline);
+    monoTriangulationOpt(poly, pStream);
+    //cleanup
+    poly->deleteSinglePolygonWithSline();
+    return;
+  }
+ 
+
+
+ 
+
+  Int i;
+  if(1/*leftGridChain->getUlineIndex(leftGridChainStartIndex) >= 
+     leftGridChain->getUlineIndex(leftGridChainStartIndex+1)*/
+     ) /*the second grid line is beyond the first one to the left*/
+    {
+      /*find the maximal U-monotone chain 
+       * of endLeftIndex, endLeftIndex-1, ..., 
+       */
+      i=endLeftIndex;
+      Real prevU = leftChain->getVertex(i)[0];
+      for(i=endLeftIndex-1; i>=beginLeftIndex; i--){
+	Real thisU = leftChain->getVertex(i)[0];
+	if( prevU < thisU){
+	  prevU = thisU;
+	}
+	else 
+	  break;
+      }
+      /*from endLeftIndex to i+1 is strictly U- monotone */
+      /*if i+1==endLeftIndex and the vertex and leftchain is on the second gridline, then
+       *we should use 2 vertices on the leftchain. If we only use one (endLeftIndex), then we
+       *we would output degenerate triangles
+       */
+      if(i+1 == endLeftIndex && leftChain->getVertex(endLeftIndex)[1] == leftGridChain->get_v_value(1+leftGridChainStartIndex))
+	i--;
+
+      Int j = beginLeftIndex/*endLeftIndex*/+1;
+
+
+      if(leftGridChain->getInnerIndex(leftGridChainStartIndex+1) > leftGridChain->getUlineIndex(leftGridChainStartIndex))
+	{
+	  j = findIncreaseChainFromBegin(leftChain, beginLeftIndex, i+1/*endLeftIndex*/);
+
+	  Int temp = beginLeftIndex;
+	  /*now from begin to j-1 is strictly u-monotone*/
+	  /*if j-1 is on the first grid line, then we want to skip to the vertex which is strictly
+	   *below the grid line. This vertexmust exist since there is a 'corner turn' inbetween the two grid lines
+	   */
+	  if(j-1 == beginLeftIndex)
+	    {
+	      while(leftChain->getVertex(j-1)[1] == leftGridChain->get_v_value(leftGridChainStartIndex))
+		j++;	        
+
+	      Real vert[2];
+	      vert[0] = leftGridChain->get_u_value(leftGridChainStartIndex);
+	      vert[1] = leftGridChain->get_v_value(leftGridChainStartIndex);
+
+	      monoTriangulation2(
+				 vert/*leftChain->getVertex(beginLeftIndex)*/,
+				 leftChain->getVertex(j-1),
+				 leftChain,
+				 beginLeftIndex,
+				 j-2,
+				 1,
+				 pStream //increase chain
+				 );
+				 
+	      temp = j-1;
+	    }
+				 
+	  stripOfFanLeft(leftChain, j-1, temp/*beginLeftIndex*/, leftGridChain->getGrid(),
+			 leftGridChain->getVlineIndex(leftGridChainStartIndex),
+			 leftGridChain->getUlineIndex(leftGridChainStartIndex),
+			 leftGridChain->getInnerIndex(leftGridChainStartIndex+1),
+			 pStream,
+			 1 /*the grid line is above the trim line*/
+			 );
+	}
+      
+      stripOfFanLeft(leftChain, endLeftIndex, i+1, leftGridChain->getGrid(), 
+		     leftGridChain->getVlineIndex(leftGridChainStartIndex+1),
+		     leftGridChain->getUlineIndex(leftGridChainStartIndex+1),
+		     leftGridChain->getInnerIndex(leftGridChainStartIndex+1),
+		     pStream,
+		     0 /*the grid line is below the trim lines*/
+		     );
+      
+      /*monotone triangulate the remaining left chain togther with the
+       *two vertices on the two grid v-lines.
+       */
+      Real vert[2][2];
+      vert[0][0]=vert[1][0] = leftGridChain->getInner_u_value(leftGridChainStartIndex+1);
+      vert[0][1] = leftGridChain->get_v_value(leftGridChainStartIndex);      
+      vert[1][1] = leftGridChain->get_v_value(leftGridChainStartIndex+1);
+
+//      vertexArray right(vert, 2);
+
+      monoTriangulation2(
+			 &vert[0][0], /*top vertex */
+			 &vert[1][0], /*bottom vertex*/
+			 leftChain, 
+			 /*beginLeftIndex*/j-1,
+			 i+1,
+			 1, /*an increasing chain*/
+			 pStream);
+    }
+  else /*the second one is shorter than the first one to the left*/
+    {
+      /*find the maximal U-monotone chain of beginLeftIndex, beginLeftIndex+1,...,
+       */
+      i=beginLeftIndex;
+      Real prevU = leftChain->getVertex(i)[0];
+      for(i=beginLeftIndex+1; i<=endLeftIndex; i++){
+	Real thisU = leftChain->getVertex(i)[0];
+
+	if(prevU < thisU){
+	  prevU = thisU;
+	}
+	else
+	  break;
+      }
+      /*from beginLeftIndex to i-1 is strictly U-monotone*/
+
+
+      stripOfFanLeft(leftChain, i-1, beginLeftIndex, leftGridChain->getGrid(),
+			 leftGridChain->getVlineIndex(leftGridChainStartIndex),
+			 leftGridChain->getUlineIndex(leftGridChainStartIndex),
+			 leftGridChain->getUlineIndex(leftGridChainStartIndex+1),
+			 pStream,
+		         1 /*the grid line is above the trim lines*/
+			 );
+      /*monotone triangulate the remaining left chain together with the 
+       *two vertices on the two grid v-lines.
+       */
+      Real vert[2][2];
+      vert[0][0]=vert[1][0] = leftGridChain->get_u_value(leftGridChainStartIndex+1);
+      vert[0][1] = leftGridChain->get_v_value(leftGridChainStartIndex);      
+      vert[1][1] = leftGridChain->get_v_value(leftGridChainStartIndex+1);
+
+      vertexArray right(vert, 2);
+
+      monoTriangulation2(
+			 &vert[0][0], //top vertex 
+			 &vert[1][0], //bottom vertex
+			 leftChain, 
+			 i-1,
+			 endLeftIndex,
+			 1, /*an increase chain*/
+			 pStream);
+
+    }
+}
+  
+/*n_upper>=1
+ *n_lower>=1
+ */
+void triangulateXYMono(Int n_upper, Real upperVerts[][2],
+		       Int n_lower, Real lowerVerts[][2],
+		       primStream* pStream)
+{
+  Int i,j,k,l;
+  Real* leftMostV;
+
+  assert(n_upper>=1 && n_lower>=1);
+  if(upperVerts[0][0] <= lowerVerts[0][0])
+    {
+      i=1;
+      j=0;
+      leftMostV = upperVerts[0];
+    }
+  else
+    {
+      i=0;
+      j=1;
+      leftMostV = lowerVerts[0];
+    }
+  
+  while(1)
+    {
+      if(i >= n_upper) /*case1: no more in upper*/
+	{
+
+	  if(j<n_lower-1) /*at least two vertices in lower*/
+	    {
+	      pStream->begin();
+	      pStream->insert(leftMostV);
+	      while(j<n_lower){
+		pStream->insert(lowerVerts[j]);
+		j++;
+	      }
+	      pStream->end(PRIMITIVE_STREAM_FAN);
+	    }
+
+	  break;	
+	}
+      else if(j>= n_lower) /*case2: no more in lower*/
+	{
+
+	  if(i<n_upper-1) /*at least two vertices in upper*/
+	    {
+	      pStream->begin();
+	      pStream->insert(leftMostV);
+
+	      for(k=n_upper-1; k>=i; k--)
+		pStream->insert(upperVerts[k]);
+
+	      pStream->end(PRIMITIVE_STREAM_FAN);
+	    }
+
+	  break;
+	}
+      else /* case3: neither is empty, plus the leftMostV, there is at least one triangle to output*/
+	{
+
+	  if(upperVerts[i][0] <= lowerVerts[j][0])
+	    {
+	      pStream->begin();
+	      pStream->insert(lowerVerts[j]); /*the origin of this fan*/
+
+	      /*find the last k>=i such that 
+	       *upperverts[k][0] <= lowerverts[j][0]
+	       */
+	      k=i;
+	      while(k<n_upper)
+		{
+		  if(upperVerts[k][0] > lowerVerts[j][0])
+		    break;
+		  k++;
+		}
+	      k--;
+	      for(l=k; l>=i; l--)/*the reverse is for two-face lighting*/
+		{
+		  pStream->insert(upperVerts[l]);
+		}
+	      pStream->insert(leftMostV);
+
+	      pStream->end(PRIMITIVE_STREAM_FAN);
+	      //update i for next loop
+	      i = k+1;
+	      leftMostV = upperVerts[k];
+
+	    }
+	  else /*upperVerts[i][0] > lowerVerts[j][0]*/
+	    {
+	      pStream->begin();
+	      pStream->insert(upperVerts[i]);/*the origion of this fan*/
+	      pStream->insert(leftMostV);
+	      /*find the last k>=j such that
+	       *lowerverts[k][0] < upperverts[i][0]*/
+	      k=j;
+	      while(k< n_lower)
+		{
+		  if(lowerVerts[k][0] >= upperVerts[i][0])
+		    break;
+		  pStream->insert(lowerVerts[k]);
+		  k++;
+		}
+	      pStream->end(PRIMITIVE_STREAM_FAN);
+	      j=k;
+	      leftMostV = lowerVerts[j-1];
+	    }	  
+	}
+    }
+}
+		       
+
+void stripOfFanLeft(vertexArray* leftChain, 
+		    Int largeIndex,
+		    Int smallIndex,
+		    gridWrap* grid,
+		    Int vlineIndex,
+		    Int ulineSmallIndex,
+		    Int ulineLargeIndex,
+		    primStream* pStream,
+		    Int gridLineUp /*1 if the grid line is above the trim lines*/
+		     )
+{
+  assert(largeIndex >= smallIndex);
+
+  Real grid_v_value;
+  grid_v_value = grid->get_v_value(vlineIndex);
+
+  Real2* trimVerts=(Real2*) malloc(sizeof(Real2)* (largeIndex-smallIndex+1));
+  assert(trimVerts);
+
+
+  Real2* gridVerts=(Real2*) malloc(sizeof(Real2)* (ulineLargeIndex-ulineSmallIndex+1));
+  assert(gridVerts);
+
+  Int k,i;
+  if(gridLineUp) /*trim line is below grid line, so trim vertices are going right when index increases*/
+    for(k=0, i=smallIndex; i<=largeIndex; i++, k++)
+      {
+      trimVerts[k][0] = leftChain->getVertex(i)[0];
+      trimVerts[k][1] = leftChain->getVertex(i)[1];
+    }
+  else
+    for(k=0, i=largeIndex; i>=smallIndex; i--, k++)
+      {
+	trimVerts[k][0] = leftChain->getVertex(i)[0];
+	trimVerts[k][1] = leftChain->getVertex(i)[1];
+      }
+
+  for(k=0, i=ulineSmallIndex; i<= ulineLargeIndex; i++, k++)
+    {
+      gridVerts[k][0] = grid->get_u_value(i);
+      gridVerts[k][1] = grid_v_value;
+    }
+
+  if(gridLineUp)
+    triangulateXYMono(
+		      ulineLargeIndex-ulineSmallIndex+1, gridVerts,
+		      largeIndex-smallIndex+1, trimVerts,
+		      pStream);
+  else
+    triangulateXYMono(largeIndex-smallIndex+1, trimVerts,
+		      ulineLargeIndex-ulineSmallIndex+1, gridVerts,
+		      pStream);
+  free(trimVerts);
+  free(gridVerts);
+}
+
+  
+
+
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleMonoPoly.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleMonoPoly.h
new file mode 100644
index 000000000..3a5fa6c91
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampleMonoPoly.h
@@ -0,0 +1,184 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _SAMPLEMONOPOLY_H
+#define _SAMPLEMONOPOLY_H
+
+#include "monoTriangulation.h"
+#include "gridWrap.h"
+#include "rectBlock.h"
+
+
+void  triangulateXYMono(Int n_upper, Real upperVerts[][2],
+		       Int n_lower, Real lowerVerts[][2],
+		       primStream* pStream);
+
+void stripOfFanLeft(vertexArray* leftChain, 
+		     Int largeIndex,
+		     Int smallIndex,
+		     gridWrap* grid,
+		     Int vlineIndex,
+		     Int ulineSmallIndex,
+		     Int ulineLargeIndex,
+		     primStream* pStream,
+		    Int gridLineUp
+		     );
+void sampleLeftOneGridStep(vertexArray* leftChain,
+		  Int beginLeftIndex,
+		  Int endLeftIndex,
+		  gridBoundaryChain* leftGridChain,
+		  Int leftGridChainStartIndex,
+		  primStream* pStream
+		  );
+
+void sampleLeftSingleTrimEdgeRegion(Real upperVert[2], Real lowerVert[2],
+				    gridBoundaryChain* gridChain,
+				    Int beginIndex,
+				    Int endIndex,
+				    primStream* pStream);
+
+void sampleLeftStripRec(vertexArray* leftChain,
+		     Int topLeftIndex,
+		     Int botLeftIndex,
+		     gridBoundaryChain* leftGridChain,
+		     Int leftGridChainStartIndex,
+		     Int leftGridChainEndIndex,
+			primStream* pStream
+		     );
+
+void sampleLeftStrip(vertexArray* leftChain,
+		     Int topLeftIndex,
+		     Int botLeftIndex,
+		     gridBoundaryChain* leftGridChain,
+		     Int leftGridChainStartIndex,
+		     Int leftGridChainEndIndex,
+		     primStream* pStream
+		     );
+
+void findLeftGridIndices(directedLine* topEdge, Int firstGridIndex, Int lastGridIndex, gridWrap* grid,  Int* ret_indices, Int* ret_inner);
+
+void findRightGridIndices(directedLine* topEdge, Int firstGridIndex, Int lastGridIndex, gridWrap* grid,  Int* ret_indices, Int* ret_inner);
+
+void sampleMonoPoly(directedLine* polygon, gridWrap* grid, Int ulinear, Int vlinear, primStream *pStream, rectBlockArray* rbArray);
+
+void sampleMonoPolyRec(
+		       Real* topVertex,
+		       Real* botVertex,
+		       vertexArray* leftChain, 
+		       Int leftStartIndex,
+		       vertexArray* rightChain,
+		       Int rightStartIndex,
+		       gridBoundaryChain* leftGridChain, 
+		       gridBoundaryChain* rightGridChain, 
+		       Int gridStartIndex,
+		       primStream* pStream,
+		       rectBlockArray* rbArray
+		       );
+
+void sampleLeftStripRecF(vertexArray* leftChain,
+		     Int topLeftIndex,
+		     Int botLeftIndex,
+		     gridBoundaryChain* leftGridChain,
+		     Int leftGridChainStartIndex,
+		     Int leftGridChainEndIndex,
+			primStream* pStream
+		     );
+
+void findUpCorners(Real *topVertex, 
+		   vertexArray *leftChain, 
+		   Int leftChainStartIndex, Int leftChainEndIndex,
+		   vertexArray *rightChain, 
+		   Int rightChainStartIndex, Int rightChainEndIndex,
+		   Real v,
+		   Real uleft,
+		   Real uright,
+		   Int& ret_leftCornerWhere, 
+		   Int& ret_leftCornerIndex,
+		   Int& ret_rightCornerWhere,
+		   Int& ret_rightCornerIndex
+		   );
+void findDownCorners(Real *botVertex, 
+		   vertexArray *leftChain, Int leftChainStartIndex, Int leftChainEndIndex,
+		   vertexArray *rightChain, Int rightChainStartIndex, Int rightChainEndIndex,
+		   Real v,
+		   Real uleft,
+		   Real uright,
+		   Int& ret_leftCornerWhere,
+		   Int& ret_leftCornerIndex,
+		   Int& ret_rightCornerWhere,
+		   Int& ret_rightCornerIndex
+		   );
+void findNeck(vertexArray *leftChain, Int botLeftIndex, 
+	      vertexArray *rightChain, Int botRightIndex, 
+	      Int& leftLastIndex, /*left point of the neck*/
+	      Int& rightLastIndex /*right point of the neck*/
+	      );
+
+Int findNeckF(vertexArray *leftChain, Int botLeftIndex,
+	       vertexArray *rightChain, Int botRightIndex,
+	       gridBoundaryChain* leftGridChain,
+	       gridBoundaryChain* rightGridChain,
+	       Int gridStartIndex,
+	       Int& neckLeft, 
+	       Int& neckRight);
+
+void findTopAndBot(directedLine* polygon, 
+		   directedLine*& topV, 
+		   directedLine*& botV);
+void findGridChains(directedLine* top, directedLine* bot, 
+		    gridWrap* grid,
+		    gridBoundaryChain*& leftGridChain,
+		    gridBoundaryChain*& rightGridChain);
+void toVertexArrays(directedLine* topV, directedLine* botV, vertexArray& leftChain, vertexArray& rightChain);
+
+void drawCorners(
+		 Real* topV, Real* botV,		 
+		 vertexArray* leftChain,
+		 vertexArray* rightChain,
+		 gridBoundaryChain* leftGridChain,
+		 gridBoundaryChain* rightGridChain,
+		 Int gridIndex1,
+		 Int gridIndex2,
+		 Int leftCornerWhere,
+		 Int leftCornerIndex,
+		 Int rightCornerWhere,
+		 Int rightCornerIndex,
+		 Int bot_leftCornerWhere,
+		 Int bot_leftCornerIndex,
+		 Int bot_rightCornerWhere,
+		 Int bot_rightCornerIndex);
+
+Int checkMiddle(vertexArray* chain, Int begin, Int end, 
+		Real vup, Real vbelow);
+
+#endif
+
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampledLine.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampledLine.cc
new file mode 100644
index 000000000..6253a7c09
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampledLine.cc
@@ -0,0 +1,179 @@
+/*
+** 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 <math.h> //for fabs()
+#include "glimports.h"
+#include "zlassert.h"
+#include "sampledLine.h"
+
+void sampledLine::setPoint(Int i, Real p[2]) 
+{
+  points[i][0]=p[0];  
+  points[i][1]=p[1];
+}
+
+
+/*insert this single line in front of the oldList*/
+sampledLine* sampledLine::insert(sampledLine *oldList)
+{
+  next = oldList;
+  return this;
+}
+
+void sampledLine::deleteList()
+{
+  sampledLine *temp, *tempNext;
+  for(temp = this; temp != NULL; temp = tempNext)
+    {
+      tempNext = temp->next;
+      delete temp;
+    }
+}
+ 
+
+/*space of points[][2] is allocated*/
+sampledLine::sampledLine(Int n_points)
+{
+  npoints = n_points;
+  points = (Real2*) malloc(sizeof(Real2) * n_points);
+  assert(points);
+  next = NULL;
+}
+
+/*space of points[][2] is allocated and 
+ *points are copied
+ */
+sampledLine::sampledLine(Int n_points, Real2 pts[])
+{
+  int i;
+  npoints = n_points;
+  points = (Real2*) malloc(sizeof(Real2) * n_points);
+  assert(points);
+  for(i=0; i<npoints; i++) {
+    points[i][0] = pts[i][0];
+    points[i][1] = pts[i][1];
+  }
+  next = NULL;
+}
+
+sampledLine::sampledLine(Real pt1[2], Real pt2[2])
+{
+  npoints = 2;
+  points = (Real2*) malloc(sizeof(Real2) * 2);
+  assert(points);
+  points[0][0] = pt1[0];
+  points[0][1] = pt1[1];
+  points[1][0] = pt2[0];
+  points[1][1] = pt2[1];
+  next = NULL;
+}
+
+//needs tp call init to setup
+sampledLine::sampledLine()
+{
+}
+
+//warning: ONLY pointer is copies!!!
+void sampledLine::init(Int n_points, Real2 *pts)
+{
+  npoints = n_points;
+  points = pts;
+}
+
+/*points[] is dealocated
+ */
+sampledLine::~sampledLine()
+{
+  free(points);
+}
+
+void sampledLine::print()
+{
+  int i;
+  printf("npoints=%i\n", npoints);
+
+  for(i=0; i<npoints; i++){
+    printf("(%f,%f)\n", points[i][0], points[i][1]);
+  }
+
+}
+
+void sampledLine::tessellate(Real u_reso, Real v_reso)
+{
+  int i;
+
+  Int nu, nv, n;
+  nu = 1+(Int) (fabs((points[npoints-1][0] - points[0][0])) * u_reso);
+  nv = 1+(Int) (fabs((points[npoints-1][1] - points[0][1])) * v_reso);
+
+  if(nu > nv) n = nu;
+  else 
+    n = nv;
+  if(n<1)
+    n = 1;
+  //du dv could be negative  
+  Real du = (points[npoints-1][0] - points[0][0])/n;
+  Real dv = (points[npoints-1][1] - points[0][1])/n;
+  Real2 *temp = (Real2*) malloc(sizeof(Real2) * (n+1));
+  assert(temp);
+
+  Real u,v;
+  for(i=0, u=points[0][0], v=points[0][1]; i<n; i++, u+=du, v+=dv)
+    {
+      temp[i][0] = u;
+      temp[i][1] = v;
+    }
+  temp[n][0] = points[npoints-1][0];
+  temp[n][1] = points[npoints-1][1];
+
+  free(points);
+
+  npoints = n+1;
+  points = temp;
+
+}
+
+void sampledLine::tessellateAll(Real u_reso, Real v_reso)
+{
+  sampledLine* temp;
+  for(temp = this; temp != NULL; temp = temp->next)
+    {
+      temp->tessellate(u_reso, v_reso);
+    }
+}
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/sampledLine.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampledLine.h
new file mode 100644
index 000000000..2cc726948
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/sampledLine.h
@@ -0,0 +1,71 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _SAMPLEDLINE_H
+#define _SAMPLEDLINE_H
+
+#include "definitions.h"
+
+class sampledLine{
+  Int npoints;
+  Real2 *points;
+
+public:
+  sampledLine(Int n_points);
+  sampledLine(Int n_points, Real  pts[][2]);
+  sampledLine(Real pt1[2], Real pt2[2]);
+  sampledLine(); //special, careful about memory
+  ~sampledLine();
+
+  void init(Int n_points, Real2 *pts);//special, careful about memory
+
+  void setPoint(Int i, Real p[2]) ;
+
+  sampledLine* insert(sampledLine *nline);
+  void deleteList();
+
+  Int get_npoints() {return npoints;}
+  Real2* get_points() {return points;}
+
+  //u_reso is number of segments (may not be integer) per unit u
+  void tessellate(Real u_reso, Real v_reso);//n segments
+  void tessellateAll(Real u_reso, Real v_reso);
+
+  void print();
+  
+  sampledLine* next;
+};
+
+
+
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/searchTree.cc b/mesalib/src/glu/sgi/libnurbs/nurbtess/searchTree.cc
new file mode 100644
index 000000000..1865755a4
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/searchTree.cc
@@ -0,0 +1,282 @@
+/*
+** 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 "zlassert.h"
+
+#include "searchTree.h"
+
+#define max(a,b) ((a>b)? a:b)
+
+treeNode* TreeNodeMake(void *key)
+{
+  treeNode *ret = (treeNode*) malloc(sizeof(treeNode));
+  assert(ret);
+  ret->key = key;
+  ret->parent = NULL;
+  ret->left = NULL;
+  ret->right = NULL;
+  return ret;
+}
+
+void TreeNodeDeleteSingleNode(treeNode* node)
+{
+  free(node);
+}
+
+void TreeNodeDeleteWholeTree(treeNode* node)
+{
+  if(node == NULL) return;
+  TreeNodeDeleteWholeTree(node->left);
+  TreeNodeDeleteWholeTree(node->right);
+  TreeNodeDeleteSingleNode(node);
+}
+
+void TreeNodePrint(treeNode* node, 
+		   void (*keyPrint) (void*))
+{
+  if(node ==NULL) return;
+  TreeNodePrint(node->left, keyPrint);
+  keyPrint(node->key);
+  TreeNodePrint(node->right, keyPrint);  
+}
+
+int TreeNodeDepth(treeNode* root)
+{
+  if(root == NULL) return 0;
+  else{
+    int leftdepth = TreeNodeDepth(root->left);
+    int rightdepth = TreeNodeDepth(root->right);  
+    return 1 + max(leftdepth, rightdepth);
+  }
+}
+
+/*return the node with the key.
+ *NULL is returned if not found
+ */
+treeNode* TreeNodeFind(treeNode* tree, void* key,
+		       int (*compkey) (void*, void*)) 	       
+{
+  if(tree == NULL) 
+    return NULL;
+  if(key == tree->key)
+    return tree;
+  else if(compkey(key, tree->key) < 0)
+    return TreeNodeFind(tree->left, key, compkey);
+  else 
+    return TreeNodeFind(tree->right, key, compkey);    
+}
+
+
+treeNode* TreeNodeInsert(treeNode* root, treeNode* newnode,
+		    int (*compkey) (void *, void *))
+{
+  treeNode *y = NULL;
+  treeNode *x = root;
+  /*going down the tree from the root.
+   *x traces the path, y is the parent of x.
+   */
+  while (x != NULL){
+    y = x;
+    if(compkey(newnode->key,x->key) < 0) /*if newnode < x*/
+      x = x->left;
+    else 
+      x = x->right;
+  }
+
+  /*now y has the property that 
+   * if newnode < y, then y->left is NULL
+   * if newnode > y, then y->right is NULL.
+   *So we want to isnert newnode to be the child of y
+   */
+  newnode->parent = y;
+  if(y == NULL) 
+    return newnode;
+  else if( compkey(newnode->key, y->key) <0)
+    {
+      y->left = newnode;
+    }
+  else
+    {
+      y->right = newnode;
+    }
+
+  return root;
+}
+    
+treeNode* TreeNodeDeleteSingleNode(treeNode* tree, treeNode* node)
+{
+  treeNode* y;
+  treeNode* x;
+  treeNode* ret;
+  if(node==NULL) return tree;
+
+  if(node->left == NULL || node->right == NULL) {
+
+    y = node;
+    if(y->left != NULL) 
+      x = y->left;
+    else
+      x = y->right;
+
+    if( x != NULL)
+      x->parent = y->parent;
+
+    if(y->parent == NULL) /*y is the root which has at most one child x*/
+      ret = x;
+    else /*y is not the root*/
+      {
+	if(y == y->parent->left) 
+	  y->parent->left = x;
+	else
+	  y->parent->right = x;
+	ret =  tree;
+      }
+  }
+  else { /*node has two children*/
+
+     y = TreeNodeSuccessor(node);
+     assert(y->left == NULL);
+
+     if(y == node->right) /*y is the right child if node*/
+       {
+	 y->parent = node->parent;
+	 y->left = node->left;
+	 node->left->parent = y;
+	 
+       }
+     else  /*y != node->right*/
+       {
+	 x = y->right;
+	 if(x!= NULL)
+	   x->parent = y->parent;
+
+	 assert(y->parent != NULL);
+	 if(y == y->parent->left) 
+	   y->parent->left = x;
+	 else
+	   y->parent->right = x;
+	 /*move y to the position of node*/
+	 y->parent = node->parent;
+	 y->left = node->left;
+	 y->right = node->right;
+	 node->left->parent = y;
+	 node->right->parent = y;
+       }
+    if(node->parent != NULL) {
+      if(node->parent->left == node)
+	node->parent->left = y;
+      else
+	node->parent->right = y;
+      ret = tree; /*the root if the tree doesn't change*/
+    }
+    else /*node->parent is NULL: node is the root*/
+      ret = y;    
+  }
+
+  /*finally free the node, and return the new root*/
+  TreeNodeDeleteSingleNode(node);
+  return ret;
+}
+     
+
+/*the minimum node in the tree rooted by node
+ */
+treeNode* TreeNodeMinimum(treeNode* node)
+{
+  treeNode* temp = node;
+  if(temp == NULL) return NULL;
+  while(temp->left != NULL) {
+    temp = temp->left;
+  }
+  return temp;
+}
+
+/*the maximum node in the tree rooted by node
+ */
+treeNode* TreeNodeMaximum(treeNode* node)
+{
+  treeNode* temp = node;
+  if(temp == NULL) return NULL;
+  while(temp->right != NULL) {
+    temp = temp->right;
+  }
+  return temp;
+}
+
+/*return the first node (in sorted order) which is to the right of this node
+ */
+treeNode* TreeNodeSuccessor(treeNode* node)
+{
+  if(node == NULL) return NULL;
+  if(node->right != NULL)
+    return TreeNodeMinimum(node->right);
+  else{ /*node->right is NULL*/
+
+    /*find the first right-ancestor*/
+    treeNode *y = node->parent;
+    treeNode* x = node;
+    while(y != NULL && x == y->right) /*if y is a left parent of x*/
+      {
+
+	x = y;
+	y = y->parent;
+      }
+    return y;
+  }
+}
+
+/*return the first node (in sorted order) which is to the left of this node
+ */
+treeNode* TreeNodePredecessor(treeNode* node)
+{
+  if(node == NULL) return NULL;
+  if(node->left != NULL)
+    return TreeNodeMaximum(node->left);
+  else{ /*node->left is NULL*/
+    /*find the first left-ancestor*/
+    treeNode *y = node->parent;
+    treeNode *x = node;
+    while(y != NULL && x == y->left) /*if y is a right parent of x*/
+      {
+	x = y;
+	y = y->parent;
+      }
+    return y;
+  }
+}
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/searchTree.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/searchTree.h
new file mode 100644
index 000000000..d5e33314b
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/searchTree.h
@@ -0,0 +1,61 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+#ifndef _SEARCHTREE_H
+#define _SEARCHTREE_H
+
+typedef struct treeNode{
+  void *key;
+  struct treeNode* parent;
+  struct treeNode* left; /*children*/
+  struct treeNode* right; 
+} treeNode;
+
+treeNode* TreeNodeMake(void *key);
+void TreeNodeDeleteSingleNode(treeNode* node);
+void TreeNodeDeleteWholeTree(treeNode* node);
+void TreeNodePrint(treeNode* node, 
+		   void (*keyPrint) (void*));
+int TreeNodeDepth(treeNode* root);
+treeNode* TreeNodeMinimum(treeNode* node);
+treeNode* TreeNodeMaximum(treeNode* node);
+treeNode* TreeNodePredecessor(treeNode* node);
+treeNode* TreeNodeSuccessor(treeNode* node);
+treeNode* TreeNodeFind(treeNode* tree, void* key,
+		       int (*compkey) (void*, void*));
+
+treeNode* TreeNodeInsert(treeNode* root, treeNode* newnode,
+		    int (*comp) (void *, void *));
+treeNode* TreeNodeDeleteSingleNode(treeNode* tree, treeNode* node);
+
+
+#endif
diff --git a/mesalib/src/glu/sgi/libnurbs/nurbtess/zlassert.h b/mesalib/src/glu/sgi/libnurbs/nurbtess/zlassert.h
new file mode 100644
index 000000000..b9c073257
--- /dev/null
+++ b/mesalib/src/glu/sgi/libnurbs/nurbtess/zlassert.h
@@ -0,0 +1,34 @@
+/*
+ * SGI FREE SOFTWARE LICENSE B (Version 2.0, Sept. 18, 2008)
+ * Copyright (C) 1991-2000 Silicon Graphics, Inc. All Rights Reserved.
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice including the dates of first publication and
+ * either this permission notice or a reference to
+ * http://oss.sgi.com/projects/FreeB/
+ * shall be included in all copies or substantial portions of the Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
+ * OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
+ * SILICON GRAPHICS, INC. BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
+ * WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF
+ * OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ *
+ * Except as contained in this notice, the name of Silicon Graphics, Inc.
+ * shall not be used in advertising or otherwise to promote the sale, use or
+ * other dealings in this Software without prior written authorization from
+ * Silicon Graphics, Inc.
+ */
+/*
+*/
+
+/*XXXblythe this file should be deleted*/
+#include <assert.h>