Imported nx-X11-3.1.0-1.tar.gznx-X11/3.1.0-1

Summary: Imported nx-X11-3.1.0-1.tar.gz
Keywords:

Imported nx-X11-3.1.0-1.tar.gz
into Git repository

1 files changed, 2023 insertions, 0 deletions

diff --git a/nx-X11/extras/ogl-sample/main/gfx/lib/glu/libnurbs/interface/insurfeval.cc b/nx-X11/extras/ogl-sample/main/gfx/lib/glu/libnurbs/interface/insurfeval.cc
new file mode 100644
index 000000000..7908d60a0
--- /dev/null
+++ b/nx-X11/extras/ogl-sample/main/gfx/lib/glu/libnurbs/interface/insurfeval.cc
@@ -0,0 +1,2023 @@
+/*
+** License Applicability. Except to the extent portions of this file are
+** made subject to an alternative license as permitted in the SGI Free
+** Software License B, Version 1.1 (the "License"), the contents of this
+** file are subject only to the provisions of the License. You may not use
+** this file except in compliance with the License. You may obtain a copy
+** of the License at Silicon Graphics, Inc., attn: Legal Services, 1600
+** Amphitheatre Parkway, Mountain View, CA 94043-1351, or at:
+** 
+** http://oss.sgi.com/projects/FreeB
+** 
+** Note that, as provided in the License, the Software is distributed on an
+** "AS IS" basis, with ALL EXPRESS AND IMPLIED WARRANTIES AND CONDITIONS
+** DISCLAIMED, INCLUDING, WITHOUT LIMITATION, ANY IMPLIED WARRANTIES AND
+** CONDITIONS OF MERCHANTABILITY, SATISFACTORY QUALITY, FITNESS FOR A
+** PARTICULAR PURPOSE, AND NON-INFRINGEMENT.
+** 
+** Original Code. The Original Code is: OpenGL Sample Implementation,
+** Version 1.2.1, released January 26, 2000, developed by Silicon Graphics,
+** Inc. The Original Code is Copyright (c) 1991-2000 Silicon Graphics, Inc.
+** Copyright in any portions created by third parties is as indicated
+** elsewhere herein. All Rights Reserved.
+** 
+** Additional Notice Provisions: The application programming interfaces
+** established by SGI in conjunction with the Original Code are The
+** OpenGL(R) Graphics System: A Specification (Version 1.2.1), released
+** April 1, 1999; The OpenGL(R) Graphics System Utility Library (Version
+** 1.3), released November 4, 1998; and OpenGL(R) Graphics with the X
+** Window System(R) (Version 1.3), released October 19, 1998. This software
+** was created using the OpenGL(R) version 1.2.1 Sample Implementation
+** published by SGI, but has not been independently verified as being
+** compliant with the OpenGL(R) version 1.2.1 Specification.
+**
+** $Date: 2004/04/23 18:42:55 $ $Revision: 1.2 $
+*/
+/*
+** $Header: /cvs/xorg/xc/extras/ogl-sample/main/gfx/lib/glu/libnurbs/interface/insurfeval.cc,v 1.2 2004/04/23 18:42:55 eich Exp $
+*/
+/* $XFree86: xc/extras/ogl-sample/main/gfx/lib/glu/libnurbs/interface/insurfeval.cc,v 1.2tsi Exp $ */
+
+#include "gluos.h"
+#include <stdlib.h>
+#include <stdio.h>
+#include <GL/gl.h>
+#include <math.h>
+#include <assert.h>
+
+#include "glsurfeval.h"
+
+//extern int surfcount;
+
+//#define CRACK_TEST
+
+#define AVOID_ZERO_NORMAL
+
+#ifdef AVOID_ZERO_NORMAL
+#define myabs(x)  ((x>0)? x: (-x))
+#define MYZERO 0.000001
+#define MYDELTA 0.001
+#endif
+
+//#define USE_LOD
+#ifdef USE_LOD
+//#define LOD_EVAL_COORD(u,v) inDoEvalCoord2EM(u,v)
+#define LOD_EVAL_COORD(u,v) glEvalCoord2f(u,v)
+
+static void LOD_interpolate(REAL A[2], REAL B[2], REAL C[2], int j, int k, int pow2_level,
+			    REAL& u, REAL& v)
+{
+  REAL a,a1,b,b1;
+
+  a = ((REAL) j) / ((REAL) pow2_level);
+  a1 = 1-a;
+
+  if(j != 0)
+    {
+      b = ((REAL) k) / ((REAL)j);
+      b1 = 1-b;
+    }
+  REAL x,y,z;
+  x = a1;
+  if(j==0)
+    {
+      y=0; z=0;
+    }
+  else{
+    y = b1*a;
+    z = b *a;
+  }
+
+  u = x*A[0] + y*B[0] + z*C[0];
+  v = x*A[1] + y*B[1] + z*C[1];
+}
+
+void OpenGLSurfaceEvaluator::LOD_triangle(REAL A[2], REAL B[2], REAL C[2], 
+			 int level)     
+{
+  int k,j;
+  int pow2_level;
+  /*compute 2^level*/
+  pow2_level = 1;
+
+  for(j=0; j<level; j++)
+    pow2_level *= 2;
+  for(j=0; j<=pow2_level-1; j++)
+    {
+      REAL u,v;
+
+/*      beginCallBack(GL_TRIANGLE_STRIP);*/
+glBegin(GL_TRIANGLE_STRIP);
+      LOD_interpolate(A,B,C, j+1, j+1, pow2_level, u,v);
+#ifdef USE_LOD
+      LOD_EVAL_COORD(u,v);
+//      glEvalCoord2f(u,v);
+#else
+      inDoEvalCoord2EM(u,v);
+#endif
+
+      for(k=0; k<=j; k++)
+	{
+	  LOD_interpolate(A,B,C,j,j-k,pow2_level, u,v);
+#ifdef USE_LOD
+          LOD_EVAL_COORD(u,v);
+//	  glEvalCoord2f(u,v);
+#else
+	  inDoEvalCoord2EM(u,v);
+#endif
+
+	  LOD_interpolate(A,B,C,j+1,j-k,pow2_level, u,v);
+
+#ifdef USE_LOD
+	  LOD_EVAL_COORD(u,v);
+//	  glEvalCoord2f(u,v);
+#else
+	  inDoEvalCoord2EM(u,v);
+#endif
+	}
+//      endCallBack();	
+glEnd();
+    }
+}
+
+void OpenGLSurfaceEvaluator::LOD_eval(int num_vert, REAL* verts, int type,
+		     int level
+		     )
+{
+  int i,k;
+  switch(type){
+  case GL_TRIANGLE_STRIP:
+  case GL_QUAD_STRIP:
+    for(i=2, k=4; i<=num_vert-2; i+=2, k+=4)
+      {
+	LOD_triangle(verts+k-4, verts+k-2, verts+k,
+		     level
+		     );
+	LOD_triangle(verts+k-2, verts+k+2, verts+k,
+		     level
+		     );
+      }
+    if(num_vert % 2 ==1) 
+      {
+	LOD_triangle(verts+2*(num_vert-3), verts+2*(num_vert-2), verts+2*(num_vert-1),
+		     level
+		     );
+      }
+    break;      
+  case GL_TRIANGLE_FAN:
+    for(i=1, k=2; i<=num_vert-2; i++, k+=2)
+      {
+	LOD_triangle(verts,verts+k, verts+k+2,
+		     level
+		     );
+      }
+    break;
+  
+  default:
+    fprintf(stderr, "typy not supported in LOD_\n");
+  }
+}
+	
+
+#endif //USE_LOD
+
+//#define  GENERIC_TEST
+#ifdef GENERIC_TEST
+extern float xmin, xmax, ymin, ymax, zmin, zmax; /*bounding box*/
+extern int temp_signal;
+
+static void gTessVertexSphere(float u, float v, float temp_normal[3], float temp_vertex[3])
+{
+  float r=2.0;
+  float Ox = 0.5*(xmin+xmax);
+  float Oy = 0.5*(ymin+ymax);
+  float Oz = 0.5*(zmin+zmax);
+  float nx = cos(v) * sin(u);
+  float ny = sin(v) * sin(u);
+  float nz = cos(u);
+  float x= Ox+r * nx;
+  float y= Oy+r * ny;
+  float z= Oz+r * nz;
+
+  temp_normal[0] = nx;
+  temp_normal[1] = ny;
+  temp_normal[2] =  nz;
+  temp_vertex[0] = x;
+  temp_vertex[1] = y;
+  temp_vertex[2] = z;
+
+//  glNormal3f(nx,ny,nz);
+//  glVertex3f(x,y,z);
+}
+
+static void gTessVertexCyl(float u, float v, float temp_normal[3], float temp_vertex[3])
+{
+   float r=2.0;
+  float Ox = 0.5*(xmin+xmax);
+  float Oy = 0.5*(ymin+ymax);
+  float Oz = 0.5*(zmin+zmax);
+  float nx = cos(v);
+  float ny = sin(v);
+  float nz = 0;
+  float x= Ox+r * nx;
+  float y= Oy+r * ny;
+  float z= Oz - 2*u;
+
+  temp_normal[0] = nx;
+  temp_normal[1] = ny;
+  temp_normal[2] =  nz;
+  temp_vertex[0] = x;
+  temp_vertex[1] = y;
+  temp_vertex[2] = z;
+
+/*  
+  glNormal3f(nx,ny,nz);
+  glVertex3f(x,y,z);
+*/
+}
+
+#endif //GENERIC_TEST
+
+void OpenGLSurfaceEvaluator::inBPMListEval(bezierPatchMesh* list)
+{
+  bezierPatchMesh* temp;
+  for(temp = list; temp != NULL; temp = temp->next)
+    {
+      inBPMEval(temp);
+    }
+}
+
+void OpenGLSurfaceEvaluator::inBPMEval(bezierPatchMesh* bpm)
+{
+  int i,j,k,l;
+  float u,v;
+
+  int ustride = bpm->bpatch->dimension * bpm->bpatch->vorder;
+  int vstride = bpm->bpatch->dimension;
+  inMap2f( 
+	  (bpm->bpatch->dimension == 3)? GL_MAP2_VERTEX_3 : GL_MAP2_VERTEX_4,
+	  bpm->bpatch->umin,
+	  bpm->bpatch->umax,
+	  ustride,
+	  bpm->bpatch->uorder,
+	  bpm->bpatch->vmin,
+	  bpm->bpatch->vmax,
+	  vstride,
+	  bpm->bpatch->vorder,
+	  bpm->bpatch->ctlpoints);
+  
+  bpm->vertex_array = (float*) malloc(sizeof(float)* (bpm->index_UVarray/2) * 3+1); /*in case the origional dimenion is 4, then we need 4 space to pass to evaluator.*/
+  assert(bpm->vertex_array);
+  bpm->normal_array = (float*) malloc(sizeof(float)* (bpm->index_UVarray/2) * 3);
+  assert(bpm->normal_array);
+#ifdef CRACK_TEST
+if(  global_ev_u1 ==2 &&   global_ev_u2 == 3
+  && global_ev_v1 ==2 &&   global_ev_v2 == 3)
+{
+REAL vertex[4];
+REAL normal[4];
+#ifdef DEBUG
+printf("***number 1\n");
+#endif
+
+beginCallBack(GL_QUAD_STRIP, NULL);
+inEvalCoord2f(3.0, 3.0);
+inEvalCoord2f(2.0, 3.0);
+inEvalCoord2f(3.0, 2.7);
+inEvalCoord2f(2.0, 2.7);
+inEvalCoord2f(3.0, 2.0);
+inEvalCoord2f(2.0, 2.0);
+endCallBack(NULL);
+
+
+beginCallBack(GL_TRIANGLE_STRIP, NULL);
+inEvalCoord2f(2.0, 3.0);
+inEvalCoord2f(2.0, 2.0);
+inEvalCoord2f(2.0, 2.7);
+endCallBack(NULL);
+
+}
+
+/*
+if(  global_ev_u1 ==2 &&   global_ev_u2 == 3
+  && global_ev_v1 ==1 &&   global_ev_v2 == 2)
+{
+#ifdef DEBUG
+printf("***number 2\n");
+#endif
+beginCallBack(GL_QUAD_STRIP);
+inEvalCoord2f(2.0, 2.0);
+inEvalCoord2f(2.0, 1.0);
+inEvalCoord2f(3.0, 2.0);
+inEvalCoord2f(3.0, 1.0);
+endCallBack();
+}
+*/
+if(  global_ev_u1 ==1 &&   global_ev_u2 == 2
+  && global_ev_v1 ==2 &&   global_ev_v2 == 3)
+{
+#ifdef DEBUG
+printf("***number 3\n");
+#endif
+beginCallBack(GL_QUAD_STRIP, NULL);
+inEvalCoord2f(2.0, 3.0);
+inEvalCoord2f(1.0, 3.0);
+inEvalCoord2f(2.0, 2.3);
+inEvalCoord2f(1.0, 2.3);
+inEvalCoord2f(2.0, 2.0);
+inEvalCoord2f(1.0, 2.0);
+endCallBack(NULL);
+
+beginCallBack(GL_TRIANGLE_STRIP, NULL);
+inEvalCoord2f(2.0, 2.3);
+inEvalCoord2f(2.0, 2.0);
+inEvalCoord2f(2.0, 3.0);
+endCallBack(NULL);
+
+}
+return;
+#endif
+
+  k=0;
+  l=0;
+
+  for(i=0; i<bpm->index_length_array; i++)
+    {
+      beginCallBack(bpm->type_array[i], userData);
+      for(j=0; j<bpm->length_array[i]; j++)
+	{
+	  u = bpm->UVarray[k];
+	  v = bpm->UVarray[k+1];
+	  inDoEvalCoord2NOGE(u,v,
+			     bpm->vertex_array+l,
+			     bpm->normal_array+l);
+
+	  normalCallBack(bpm->normal_array+l, userData);
+	  vertexCallBack(bpm->vertex_array+l, userData);
+
+	  k += 2;
+	  l += 3;
+	}
+      endCallBack(userData);
+    }
+}
+
+void OpenGLSurfaceEvaluator::inEvalPoint2(int i, int j)
+{
+  REAL du, dv;
+  REAL point[4];
+  REAL normal[3];
+  REAL u,v;
+  du = (global_grid_u1 - global_grid_u0) / (REAL)global_grid_nu;
+  dv = (global_grid_v1 - global_grid_v0) / (REAL)global_grid_nv;
+  u = (i==global_grid_nu)? global_grid_u1:(global_grid_u0 + i*du);
+  v = (j == global_grid_nv)? global_grid_v1: (global_grid_v0 +j*dv);
+  inDoEvalCoord2(u,v,point,normal);
+}
+
+void OpenGLSurfaceEvaluator::inEvalCoord2f(REAL u, REAL v)
+{
+
+  REAL point[4];
+  REAL normal[3];
+  inDoEvalCoord2(u,v,point, normal);
+}
+
+
+
+/*define a grid. store the values into the global variabls:
+ * global_grid_*
+ *These values will be used later by evaluating functions
+ */
+void OpenGLSurfaceEvaluator::inMapGrid2f(int nu, REAL u0, REAL u1,
+		 int nv, REAL v0, REAL v1)
+{
+ global_grid_u0 = u0;
+ global_grid_u1 = u1;
+ global_grid_nu = nu;
+ global_grid_v0 = v0;
+ global_grid_v1 = v1;
+ global_grid_nv = nv;
+}
+
+void OpenGLSurfaceEvaluator::inEvalMesh2(int lowU, int lowV, int highU, int highV)
+{
+  REAL du, dv;
+  int i,j;
+  REAL point[4];
+  REAL normal[3];
+  if(global_grid_nu == 0 || global_grid_nv == 0)
+    return; /*no points need to be output*/
+  du = (global_grid_u1 - global_grid_u0) / (REAL)global_grid_nu;
+  dv = (global_grid_v1 - global_grid_v0) / (REAL)global_grid_nv;  
+  
+  if(global_grid_nu >= global_grid_nv){
+    for(i=lowU; i<highU; i++){
+      REAL u1 = (i==global_grid_nu)? global_grid_u1:(global_grid_u0 + i*du);
+      REAL u2 = ((i+1) == global_grid_nu)? global_grid_u1: (global_grid_u0+(i+1)*du);
+      
+      bgnqstrip();
+      for(j=highV; j>=lowV; j--){
+	REAL v1 = (j == global_grid_nv)? global_grid_v1: (global_grid_v0 +j*dv);
+	
+	inDoEvalCoord2(u1, v1, point, normal);
+	inDoEvalCoord2(u2, v1, point, normal);
+      }
+      endqstrip();
+    }
+  }
+  
+  else{
+    for(i=lowV; i<highV; i++){
+      REAL v1 = (i==global_grid_nv)? global_grid_v1:(global_grid_v0 + i*dv);
+      REAL v2 = ((i+1) == global_grid_nv)? global_grid_v1: (global_grid_v0+(i+1)*dv);
+      
+      bgnqstrip();
+      for(j=highU; j>=lowU; j--){
+	REAL u1 = (j == global_grid_nu)? global_grid_u1: (global_grid_u0 +j*du);	
+	inDoEvalCoord2(u1, v2, point, normal);
+	inDoEvalCoord2(u1, v1, point, normal);
+      }
+      endqstrip();
+    }
+  }
+}
+
+void OpenGLSurfaceEvaluator::inMap2f(int k,
+	     REAL ulower,
+	     REAL uupper,
+	     int ustride,
+	     int uorder,
+	     REAL vlower,
+	     REAL vupper,
+	     int vstride,
+	     int vorder,
+	     REAL *ctlPoints)
+{
+  int i,j,x;
+  REAL *data = global_ev_ctlPoints;
+  
+
+
+  if(k == GL_MAP2_VERTEX_3) k=3;
+  else if (k==GL_MAP2_VERTEX_4) k =4;
+  else {
+    printf("error in inMap2f, maptype=%i is wrong, k,map is not updated\n", k);
+    return;
+  }
+  
+  global_ev_k = k;
+  global_ev_u1 = ulower;
+  global_ev_u2 = uupper;
+  global_ev_ustride = ustride;
+  global_ev_uorder = uorder;
+  global_ev_v1 = vlower;
+  global_ev_v2 = vupper;
+  global_ev_vstride = vstride;
+  global_ev_vorder = vorder;
+
+  /*copy the contrl points from ctlPoints to global_ev_ctlPoints*/
+  for (i=0; i<uorder; i++) {
+    for (j=0; j<vorder; j++) {
+      for (x=0; x<k; x++) {
+	data[x] = ctlPoints[x];
+      }
+      ctlPoints += vstride;
+      data += k;
+    }
+    ctlPoints += ustride - vstride * vorder;
+  }
+
+}
+
+
+/*
+ *given a point p with homegeneous coordiante (x,y,z,w), 
+ *let pu(x,y,z,w) be its partial derivative vector with
+ *respect to u
+ *and pv(x,y,z,w) be its partial derivative vector with repect to v.
+ *This function returns the partial derivative vectors of the
+ *inhomegensous coordinates, i.e., 
+ * (x/w, y/w, z/w) with respect to u and v.
+ */
+void OpenGLSurfaceEvaluator::inComputeFirstPartials(REAL *p, REAL *pu, REAL *pv)
+{
+    pu[0] = pu[0]*p[3] - pu[3]*p[0];
+    pu[1] = pu[1]*p[3] - pu[3]*p[1];
+    pu[2] = pu[2]*p[3] - pu[3]*p[2];
+
+    pv[0] = pv[0]*p[3] - pv[3]*p[0];
+    pv[1] = pv[1]*p[3] - pv[3]*p[1];
+    pv[2] = pv[2]*p[3] - pv[3]*p[2];
+}
+
+/*compute the cross product of pu and pv and normalize.
+ *the normal is returned in retNormal
+ * pu: dimension 3
+ * pv: dimension 3
+ * n: return normal, of dimension 3
+ */
+void OpenGLSurfaceEvaluator::inComputeNormal2(REAL *pu, REAL *pv, REAL *n)
+{
+  REAL mag; 
+
+  n[0] = pu[1]*pv[2] - pu[2]*pv[1];
+  n[1] = pu[2]*pv[0] - pu[0]*pv[2];
+  n[2] = pu[0]*pv[1] - pu[1]*pv[0];  
+
+  mag = sqrt(n[0]*n[0] + n[1]*n[1] + n[2]*n[2]);
+
+  assert(mag > 0.0); /*better be some threshold*/
+  n[0] /= mag; 
+  n[1] /= mag;
+  n[2] /= mag;
+
+}
+ 
+
+
+/*Compute point and normal
+ *see the head of inDoDomain2WithDerivs
+ *for the meaning of the arguments
+ */
+void OpenGLSurfaceEvaluator::inDoEvalCoord2(REAL u, REAL v,
+			   REAL *retPoint, REAL *retNormal)
+{
+
+  REAL du[4];
+  REAL dv[4];
+
+  assert(global_ev_k>=3 && global_ev_k <= 4);
+  /*compute homegeneous point and partial derivatives*/
+  inDoDomain2WithDerivs(global_ev_k, u, v, global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, retPoint, du, dv);
+
+#ifdef AVOID_ZERO_NORMAL
+
+  if(myabs(dv[0]) <= MYZERO && myabs(dv[1]) <= MYZERO && myabs(dv[2]) <= MYZERO)
+    {
+
+      REAL tempdu[4];
+      REAL tempdata[4];
+      REAL u1 = global_ev_u1;
+      REAL u2 = global_ev_u2;
+      if(u-MYDELTA*(u2-u1) < u1)
+	u = u+ MYDELTA*(u2-u1);
+      else
+	u = u-MYDELTA*(u2-u1);
+      inDoDomain2WithDerivs(global_ev_k, u,v,global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, tempdata, tempdu, dv);
+    }
+  if(myabs(du[0]) <= MYZERO && myabs(du[1]) <= MYZERO && myabs(du[2]) <= MYZERO)
+    {
+      REAL tempdv[4];
+      REAL tempdata[4];
+      REAL v1 = global_ev_v1;
+      REAL v2 = global_ev_v2;
+      if(v-MYDELTA*(v2-v1) < v1)
+	v = v+ MYDELTA*(v2-v1);
+      else
+	v = v-MYDELTA*(v2-v1);
+      inDoDomain2WithDerivs(global_ev_k, u,v,global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, tempdata, du, tempdv);
+    }
+#endif
+
+
+  /*compute normal*/
+  switch(global_ev_k){
+  case 3:
+    inComputeNormal2(du, dv, retNormal);
+
+    break;
+  case 4:
+    inComputeFirstPartials(retPoint, du, dv);
+    inComputeNormal2(du, dv, retNormal);
+    /*transform the homegeneous coordinate of retPoint into inhomogenous one*/
+    retPoint[0] /= retPoint[3];
+    retPoint[1] /= retPoint[3];
+    retPoint[2] /= retPoint[3];
+    break;
+  }
+  /*output this vertex*/
+/*  inMeshStreamInsert(global_ms, retPoint, retNormal);*/
+
+
+
+  glNormal3fv(retNormal);
+  glVertex3fv(retPoint);
+
+
+
+
+#ifdef DEBUG
+  printf("vertex(%f,%f,%f)\n", retPoint[0],retPoint[1],retPoint[2]);
+#endif
+}
+
+/*Compute point and normal
+ *see the head of inDoDomain2WithDerivs
+ *for the meaning of the arguments
+ */
+void OpenGLSurfaceEvaluator::inDoEvalCoord2NOGE_BU(REAL u, REAL v,
+			   REAL *retPoint, REAL *retNormal)
+{
+
+  REAL du[4];
+  REAL dv[4];
+
+  assert(global_ev_k>=3 && global_ev_k <= 4);
+  /*compute homegeneous point and partial derivatives*/
+//   inPreEvaluateBU(global_ev_k, global_ev_uorder, global_ev_vorder, (u-global_ev_u1)/(global_ev_u2-global_ev_u1), global_ev_ctlPoints);
+  inDoDomain2WithDerivsBU(global_ev_k, u, v, global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, retPoint, du, dv);
+
+
+#ifdef AVOID_ZERO_NORMAL
+
+  if(myabs(dv[0]) <= MYZERO && myabs(dv[1]) <= MYZERO && myabs(dv[2]) <= MYZERO)
+    {
+
+      REAL tempdu[4];
+      REAL tempdata[4];
+      REAL u1 = global_ev_u1;
+      REAL u2 = global_ev_u2;
+      if(u-MYDELTA*(u2-u1) < u1)
+	u = u+ MYDELTA*(u2-u1);
+      else
+	u = u-MYDELTA*(u2-u1);
+      inDoDomain2WithDerivs(global_ev_k, u,v,global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, tempdata, tempdu, dv);
+    }
+  if(myabs(du[0]) <= MYZERO && myabs(du[1]) <= MYZERO && myabs(du[2]) <= MYZERO)
+    {
+      REAL tempdv[4];
+      REAL tempdata[4];
+      REAL v1 = global_ev_v1;
+      REAL v2 = global_ev_v2;
+      if(v-MYDELTA*(v2-v1) < v1)
+	v = v+ MYDELTA*(v2-v1);
+      else
+	v = v-MYDELTA*(v2-v1);
+      inDoDomain2WithDerivs(global_ev_k, u,v,global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, tempdata, du, tempdv);
+    }
+#endif
+
+  /*compute normal*/
+  switch(global_ev_k){
+  case 3:
+    inComputeNormal2(du, dv, retNormal);
+    break;
+  case 4:
+    inComputeFirstPartials(retPoint, du, dv);
+    inComputeNormal2(du, dv, retNormal);
+    /*transform the homegeneous coordinate of retPoint into inhomogenous one*/
+    retPoint[0] /= retPoint[3];
+    retPoint[1] /= retPoint[3];
+    retPoint[2] /= retPoint[3];
+    break;
+  }
+}
+
+/*Compute point and normal
+ *see the head of inDoDomain2WithDerivs
+ *for the meaning of the arguments
+ */
+void OpenGLSurfaceEvaluator::inDoEvalCoord2NOGE_BV(REAL u, REAL v,
+			   REAL *retPoint, REAL *retNormal)
+{
+
+  REAL du[4];
+  REAL dv[4];
+
+  assert(global_ev_k>=3 && global_ev_k <= 4);
+  /*compute homegeneous point and partial derivatives*/
+//   inPreEvaluateBV(global_ev_k, global_ev_uorder, global_ev_vorder, (v-global_ev_v1)/(global_ev_v2-global_ev_v1), global_ev_ctlPoints);
+
+  inDoDomain2WithDerivsBV(global_ev_k, u, v, global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, retPoint, du, dv);
+
+
+#ifdef AVOID_ZERO_NORMAL
+
+  if(myabs(dv[0]) <= MYZERO && myabs(dv[1]) <= MYZERO && myabs(dv[2]) <= MYZERO)
+    {
+
+      REAL tempdu[4];
+      REAL tempdata[4];
+      REAL u1 = global_ev_u1;
+      REAL u2 = global_ev_u2;
+      if(u-MYDELTA*(u2-u1) < u1)
+	u = u+ MYDELTA*(u2-u1);
+      else
+	u = u-MYDELTA*(u2-u1);
+      inDoDomain2WithDerivs(global_ev_k, u,v,global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, tempdata, tempdu, dv);
+    }
+  if(myabs(du[0]) <= MYZERO && myabs(du[1]) <= MYZERO && myabs(du[2]) <= MYZERO)
+    {
+      REAL tempdv[4];
+      REAL tempdata[4];
+      REAL v1 = global_ev_v1;
+      REAL v2 = global_ev_v2;
+      if(v-MYDELTA*(v2-v1) < v1)
+	v = v+ MYDELTA*(v2-v1);
+      else
+	v = v-MYDELTA*(v2-v1);
+      inDoDomain2WithDerivs(global_ev_k, u,v,global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, tempdata, du, tempdv);
+    }
+#endif
+
+  /*compute normal*/
+  switch(global_ev_k){
+  case 3:
+    inComputeNormal2(du, dv, retNormal);
+    break;
+  case 4:
+    inComputeFirstPartials(retPoint, du, dv);
+    inComputeNormal2(du, dv, retNormal);
+    /*transform the homegeneous coordinate of retPoint into inhomogenous one*/
+    retPoint[0] /= retPoint[3];
+    retPoint[1] /= retPoint[3];
+    retPoint[2] /= retPoint[3];
+    break;
+  }
+}
+ 
+
+/*Compute point and normal
+ *see the head of inDoDomain2WithDerivs
+ *for the meaning of the arguments
+ */
+void OpenGLSurfaceEvaluator::inDoEvalCoord2NOGE(REAL u, REAL v,
+			   REAL *retPoint, REAL *retNormal)
+{
+
+  REAL du[4];
+  REAL dv[4];
+
+  assert(global_ev_k>=3 && global_ev_k <= 4);
+  /*compute homegeneous point and partial derivatives*/
+  inDoDomain2WithDerivs(global_ev_k, u, v, global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, retPoint, du, dv);
+
+
+#ifdef AVOID_ZERO_NORMAL
+
+  if(myabs(dv[0]) <= MYZERO && myabs(dv[1]) <= MYZERO && myabs(dv[2]) <= MYZERO)
+    {
+
+      REAL tempdu[4];
+      REAL tempdata[4];
+      REAL u1 = global_ev_u1;
+      REAL u2 = global_ev_u2;
+      if(u-MYDELTA*(u2-u1) < u1)
+	u = u+ MYDELTA*(u2-u1);
+      else
+	u = u-MYDELTA*(u2-u1);
+      inDoDomain2WithDerivs(global_ev_k, u,v,global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, tempdata, tempdu, dv);
+    }
+  if(myabs(du[0]) <= MYZERO && myabs(du[1]) <= MYZERO && myabs(du[2]) <= MYZERO)
+    {
+      REAL tempdv[4];
+      REAL tempdata[4];
+      REAL v1 = global_ev_v1;
+      REAL v2 = global_ev_v2;
+      if(v-MYDELTA*(v2-v1) < v1)
+	v = v+ MYDELTA*(v2-v1);
+      else
+	v = v-MYDELTA*(v2-v1);
+      inDoDomain2WithDerivs(global_ev_k, u,v,global_ev_u1, global_ev_u2, global_ev_uorder, global_ev_v1, global_ev_v2, global_ev_vorder, global_ev_ctlPoints, tempdata, du, tempdv);
+    }
+#endif
+
+  /*compute normal*/
+  switch(global_ev_k){
+  case 3:
+    inComputeNormal2(du, dv, retNormal);
+    break;
+  case 4:
+    inComputeFirstPartials(retPoint, du, dv);
+    inComputeNormal2(du, dv, retNormal);
+    /*transform the homegeneous coordinate of retPoint into inhomogenous one*/
+    retPoint[0] /= retPoint[3];
+    retPoint[1] /= retPoint[3];
+    retPoint[2] /= retPoint[3];
+    break;
+  }
+//  glNormal3fv(retNormal);
+//  glVertex3fv(retPoint);
+}
+ 
+void OpenGLSurfaceEvaluator::inPreEvaluateBV(int k, int uorder, int vorder, REAL vprime, REAL *baseData)
+{
+  int j,row,col;
+  REAL p, pdv;
+  REAL *data;
+
+  if(global_vprime != vprime || global_vorder != vorder) {      
+    inPreEvaluateWithDeriv(vorder, vprime, global_vcoeff, global_vcoeffDeriv);
+    global_vprime = vprime;
+    global_vorder = vorder;
+  }
+
+  for(j=0; j<k; j++){
+    data = baseData+j;
+    for(row=0; row<uorder; row++){
+      p = global_vcoeff[0] * (*data);
+      pdv = global_vcoeffDeriv[0] * (*data);
+      data += k;
+      for(col = 1; col < vorder; col++){
+	p += global_vcoeff[col] *  (*data);
+	pdv += global_vcoeffDeriv[col] * (*data);
+	data += k;
+      }
+      global_BV[row][j]  = p;
+      global_PBV[row][j]  = pdv;
+    }
+  }
+}
+
+void OpenGLSurfaceEvaluator::inPreEvaluateBU(int k, int uorder, int vorder, REAL uprime, REAL *baseData)
+{
+  int j,row,col;
+  REAL p, pdu;
+  REAL *data;
+
+  if(global_uprime != uprime || global_uorder != uorder) {      
+    inPreEvaluateWithDeriv(uorder, uprime, global_ucoeff, global_ucoeffDeriv);
+    global_uprime = uprime;
+    global_uorder = uorder;
+  }
+
+  for(j=0; j<k; j++){
+    data = baseData+j;
+    for(col=0; col<vorder; col++){
+      data = baseData+j + k*col;
+      p = global_ucoeff[0] * (*data);
+      pdu = global_ucoeffDeriv[0] * (*data);
+      data += k*uorder;
+      for(row = 1; row < uorder; row++){
+	p += global_ucoeff[row] *  (*data);
+	pdu += global_ucoeffDeriv[row] * (*data);
+	data += k * uorder;
+      }
+      global_BU[col][j]  = p;
+      global_PBU[col][j]  = pdu;
+    }
+  }
+}
+ 
+void OpenGLSurfaceEvaluator::inDoDomain2WithDerivsBU(int k, REAL u, REAL v,
+						      REAL u1, REAL u2, int uorder,
+						      REAL v1, REAL v2, int vorder,
+						      REAL *baseData,
+						      REAL *retPoint, REAL* retdu, REAL *retdv)
+{
+  int j, col;
+
+  REAL vprime;
+
+
+  if((u2 == u1) || (v2 == v1))
+    return;
+
+  vprime = (v - v1) / (v2 - v1);
+
+
+  if(global_vprime != vprime || global_vorder != vorder) {
+    inPreEvaluateWithDeriv(vorder, vprime, global_vcoeff, global_vcoeffDeriv);
+    global_vprime = vprime;
+    global_vorder = vorder;
+  }
+
+
+  for(j=0; j<k; j++)
+    {
+      retPoint[j] = retdu[j] = retdv[j] = 0.0;
+      for (col = 0; col < vorder; col++)  {
+	retPoint[j] += global_BU[col][j] * global_vcoeff[col];
+	retdu[j] += global_PBU[col][j] * global_vcoeff[col];
+	retdv[j] += global_BU[col][j] * global_vcoeffDeriv[col];
+      }
+    }
+}    
+   
+void OpenGLSurfaceEvaluator::inDoDomain2WithDerivsBV(int k, REAL u, REAL v,
+						      REAL u1, REAL u2, int uorder,
+						      REAL v1, REAL v2, int vorder,
+						      REAL *baseData,
+						      REAL *retPoint, REAL* retdu, REAL *retdv)
+{
+  int j, row;
+  REAL uprime;
+
+
+  if((u2 == u1) || (v2 == v1))
+    return;
+  uprime = (u - u1) / (u2 - u1);
+
+
+  if(global_uprime != uprime || global_uorder != uorder) {
+    inPreEvaluateWithDeriv(uorder, uprime, global_ucoeff, global_ucoeffDeriv);
+    global_uprime = uprime;
+    global_uorder = uorder;
+  }
+
+
+  for(j=0; j<k; j++)
+    {
+      retPoint[j] = retdu[j] = retdv[j] = 0.0;
+      for (row = 0; row < uorder; row++)  {
+	retPoint[j] += global_BV[row][j] * global_ucoeff[row];
+	retdu[j] += global_BV[row][j] * global_ucoeffDeriv[row];
+	retdv[j] += global_PBV[row][j] * global_ucoeff[row];
+      }
+    }
+}
+  
+
+/*
+ *given a Bezier surface, and parameter (u,v), compute the point in the object space,
+ *and the normal
+ *k: the dimension of the object space: usually 2,3,or 4.
+ *u,v: the paramter pair.
+ *u1,u2,uorder: the Bezier polynomial of u coord is defined on [u1,u2] with order uorder.
+ *v1,v2,vorder: the Bezier polynomial of v coord is defined on [v1,v2] with order vorder.
+ *baseData: contrl points. arranged as: (u,v,k).
+ *retPoint:  the computed point (one point) with dimension k.
+ *retdu: the computed partial derivative with respect to u.
+ *retdv: the computed partial derivative with respect to v.
+ */
+void OpenGLSurfaceEvaluator::inDoDomain2WithDerivs(int k, REAL u, REAL v, 
+				REAL u1, REAL u2, int uorder, 
+				REAL v1,  REAL v2, int vorder, 
+				REAL *baseData,
+				REAL *retPoint, REAL *retdu, REAL *retdv)
+{
+    int j, row, col;
+    REAL uprime;
+    REAL vprime;
+    REAL p;
+    REAL pdv;
+    REAL *data;
+
+    if((u2 == u1) || (v2 == v1))
+	return;
+    uprime = (u - u1) / (u2 - u1);
+    vprime = (v - v1) / (v2 - v1);
+    
+    /* Compute coefficients for values and derivs */
+
+    /* Use already cached values if possible */
+    if(global_uprime != uprime || global_uorder != uorder) {
+        inPreEvaluateWithDeriv(uorder, uprime, global_ucoeff, global_ucoeffDeriv);
+	global_uorder = uorder;
+	global_uprime = uprime;
+    }
+    if (global_vprime != vprime || 
+	  global_vorder != vorder) {
+	inPreEvaluateWithDeriv(vorder, vprime, global_vcoeff, global_vcoeffDeriv);
+	global_vorder = vorder;
+	global_vprime = vprime;
+    }
+
+    for (j = 0; j < k; j++) {
+	data=baseData+j;
+	retPoint[j] = retdu[j] = retdv[j] = 0.0;
+	for (row = 0; row < uorder; row++)  {
+	    /* 
+	    ** Minor optimization.
+	    ** The col == 0 part of the loop is extracted so we don't
+	    ** have to initialize p and pdv to 0.
+	    */
+	    p = global_vcoeff[0] * (*data);
+	    pdv = global_vcoeffDeriv[0] * (*data);
+	    data += k;
+	    for (col = 1; col < vorder; col++) {
+		/* Incrementally build up p, pdv value */
+		p += global_vcoeff[col] * (*data);
+		pdv += global_vcoeffDeriv[col] * (*data);
+		data += k;
+	    }
+	    /* Use p, pdv value to incrementally add up r, du, dv */
+	    retPoint[j] += global_ucoeff[row] * p;
+	    retdu[j] += global_ucoeffDeriv[row] * p;
+	    retdv[j] += global_ucoeff[row] * pdv;
+	}
+    }  
+}
+
+
+/*
+ *compute the Bezier polynomials C[n,j](v) for all j at v with 
+ *return values stored in coeff[], where 
+ *  C[n,j](v) = (n,j) * v^j * (1-v)^(n-j),
+ *  j=0,1,2,...,n.
+ *order : n+1
+ *vprime: v
+ *coeff : coeff[j]=C[n,j](v), this array store the returned values.
+ *The algorithm is a recursive scheme:
+ *   C[0,0]=1;
+ *   C[n,j](v) = (1-v)*C[n-1,j](v) + v*C[n-1,j-1](v), n>=1
+ *This code is copied from opengl/soft/so_eval.c:PreEvaluate
+ */
+void OpenGLSurfaceEvaluator::inPreEvaluate(int order, REAL vprime, REAL *coeff)
+{
+  int i, j;
+  REAL oldval, temp;
+  REAL oneMinusvprime;
+  
+  /*
+   * Minor optimization
+   * Compute orders 1 and 2 outright, and set coeff[0], coeff[1] to
+     * their i==1 loop values to avoid the initialization and the i==1 loop.
+     */
+  if (order == 1) {
+    coeff[0] = 1.0;
+    return;
+  }
+  
+  oneMinusvprime = 1-vprime;
+  coeff[0] = oneMinusvprime;
+  coeff[1] = vprime;
+  if (order == 2) return;
+  
+  for (i = 2; i < order; i++) {
+    oldval = coeff[0] * vprime;
+    coeff[0] = oneMinusvprime * coeff[0];
+    for (j = 1; j < i; j++) {
+      temp = oldval;
+      oldval = coeff[j] * vprime;
+	    coeff[j] = temp + oneMinusvprime * coeff[j];
+    }
+    coeff[j] = oldval;
+  }
+}
+
+/*
+ *compute the Bezier polynomials C[n,j](v) and derivatives for all j at v with 
+ *return values stored in coeff[] and coeffDeriv[].
+ *see the head of function inPreEvaluate for the definition of C[n,j](v)
+ *and how to compute the values. 
+ *The algorithm to compute the derivative is:
+ *   dC[0,0](v) = 0.
+ *   dC[n,j](v) = n*(dC[n-1,j-1](v) - dC[n-1,j](v)).
+ *
+ *This code is copied from opengl/soft/so_eval.c:PreEvaluateWidthDeriv
+ */
+void OpenGLSurfaceEvaluator::inPreEvaluateWithDeriv(int order, REAL vprime, 
+    REAL *coeff, REAL *coeffDeriv)
+{
+  int i, j;
+  REAL oldval, temp;
+  REAL oneMinusvprime;
+  
+  oneMinusvprime = 1-vprime;
+  /*
+   * Minor optimization
+   * Compute orders 1 and 2 outright, and set coeff[0], coeff[1] to 
+   * their i==1 loop values to avoid the initialization and the i==1 loop.
+   */
+  if (order == 1) {
+    coeff[0] = 1.0;
+    coeffDeriv[0] = 0.0;
+    return;
+  } else if (order == 2) {
+    coeffDeriv[0] = -1.0;
+    coeffDeriv[1] = 1.0;
+    coeff[0] = oneMinusvprime;
+    coeff[1] = vprime;
+    return;
+  }
+  coeff[0] = oneMinusvprime;
+  coeff[1] = vprime;
+  for (i = 2; i < order - 1; i++) {
+    oldval = coeff[0] * vprime;
+    coeff[0] = oneMinusvprime * coeff[0];
+    for (j = 1; j < i; j++) {
+      temp = oldval;
+      oldval = coeff[j] * vprime;
+      coeff[j] = temp + oneMinusvprime * coeff[j];
+    }
+    coeff[j] = oldval;
+  }
+  coeffDeriv[0] = -coeff[0];
+  /*
+   ** Minor optimization:
+   ** Would make this a "for (j=1; j<order-1; j++)" loop, but it is always
+   ** executed at least once, so this is more efficient.
+   */
+  j=1;
+  do {
+    coeffDeriv[j] = coeff[j-1] - coeff[j];
+    j++;
+  } while (j < order - 1);
+  coeffDeriv[j] = coeff[j-1];
+  
+  oldval = coeff[0] * vprime;
+  coeff[0] = oneMinusvprime * coeff[0];
+  for (j = 1; j < i; j++) {
+    temp = oldval;
+    oldval = coeff[j] * vprime;
+    coeff[j] = temp + oneMinusvprime * coeff[j];
+  }
+  coeff[j] = oldval;
+}
+
+void OpenGLSurfaceEvaluator::inEvalULine(int n_points, REAL v, REAL* u_vals, 
+	int stride, REAL ret_points[][3], REAL ret_normals[][3])
+{
+  int i,k;
+  REAL temp[4];
+inPreEvaluateBV_intfac(v);
+
+  for(i=0,k=0; i<n_points; i++, k += stride)
+    {
+      inDoEvalCoord2NOGE_BV(u_vals[k],v,temp, ret_normals[i]);
+
+      ret_points[i][0] = temp[0];
+      ret_points[i][1] = temp[1];
+      ret_points[i][2] = temp[2];
+
+    }
+
+}
+
+void OpenGLSurfaceEvaluator::inEvalVLine(int n_points, REAL u, REAL* v_vals, 
+	int stride, REAL ret_points[][3], REAL ret_normals[][3])
+{
+  int i,k;
+  REAL temp[4];
+inPreEvaluateBU_intfac(u);
+  for(i=0,k=0; i<n_points; i++, k += stride)
+    {
+      inDoEvalCoord2NOGE_BU(u, v_vals[k], temp, ret_normals[i]);
+      ret_points[i][0] = temp[0];
+      ret_points[i][1] = temp[1];
+      ret_points[i][2] = temp[2];
+    }
+}
+      
+
+/*triangulate a strip bounded by two lines which are parallel  to U-axis
+ *upperVerts: the verteces on the upper line
+ *lowerVertx: the verteces on the lower line
+ *n_upper >=1
+ *n_lower >=1
+ */
+void OpenGLSurfaceEvaluator::inEvalUStrip(int n_upper, REAL v_upper, REAL* upper_val, int n_lower, REAL v_lower, REAL* lower_val)
+{
+  int i,j,k,l;
+ typedef REAL REAL3[3];
+
+  REAL3* upperXYZ = (REAL3*) malloc(sizeof(REAL3)*n_upper);
+  assert(upperXYZ);
+  REAL3* upperNormal = (REAL3*) malloc(sizeof(REAL3) * n_upper);
+  assert(upperNormal);
+  REAL3* lowerXYZ = (REAL3*) malloc(sizeof(REAL3)*n_lower);
+  assert(lowerXYZ);
+  REAL3* lowerNormal = (REAL3*) malloc(sizeof(REAL3) * n_lower);
+  assert(lowerNormal);
+  
+  inEvalULine(n_upper, v_upper, upper_val,  1, upperXYZ, upperNormal);
+  inEvalULine(n_lower, v_lower, lower_val,  1, lowerXYZ, lowerNormal);
+
+
+
+  REAL* leftMostXYZ;
+  REAL* leftMostNormal;
+
+  /*
+   *the algorithm works by scanning from left to right.
+   */
+
+  if(upper_val[0] <= lower_val[0])
+    {
+      i=1;
+      j=0;
+
+      leftMostXYZ = upperXYZ[0];
+      leftMostNormal = upperNormal[0];
+    }
+  else
+    {
+      i=0;
+      j=1;
+
+      leftMostXYZ = lowerXYZ[0];
+      leftMostNormal = lowerNormal[0];
+    }
+  
+  /*the main loop.
+   */
+  while(1)
+    {
+      if(i >= n_upper) /*case1: no more in upper*/
+        {
+          if(j<n_lower-1) /*at least two vertices in lower*/
+            {
+              bgntfan();
+	      glNormal3fv(leftMostNormal);
+              glVertex3fv(leftMostXYZ);
+
+              while(j<n_lower){
+		glNormal3fv(lowerNormal[j]);
+		glVertex3fv(lowerXYZ[j]);
+		j++;
+
+              }
+              endtfan();
+            }
+          break; /*exit the main loop*/
+        }
+      else if(j>= n_lower) /*case2: no more in lower*/
+        {
+          if(i<n_upper-1) /*at least two vertices in upper*/
+            {
+              bgntfan();
+	      glNormal3fv(leftMostNormal);
+	      glVertex3fv(leftMostXYZ);
+	      
+              for(k=n_upper-1; k>=i; k--) /*reverse order for two-side lighting*/
+		{
+		  glNormal3fv(upperNormal[k]);
+		  glVertex3fv(upperXYZ[k]);
+		}
+
+              endtfan();
+            }
+          break; /*exit the main loop*/
+        }
+      else /* case3: neither is empty, there is at least one triangle to output*/
+        {
+          if(upper_val[i] <= lower_val[j])
+            {
+	      bgntfan();
+
+	      glNormal3fv(lowerNormal[j]);
+	      glVertex3fv(lowerXYZ[j]);
+
+              /*find the last k>=i such that 
+               *upperverts[k][0] <= lowerverts[j][0]
+               */
+              k=i;
+
+              while(k<n_upper)
+                {
+                  if(upper_val[k] > lower_val[j])
+                    break;
+                  k++;
+
+                }
+              k--;
+
+
+              for(l=k; l>=i; l--)/*the reverse is for two-side lighting*/
+                {
+		  glNormal3fv(upperNormal[l]);
+		  glVertex3fv(upperXYZ[l]);
+
+                }
+	      glNormal3fv(leftMostNormal);
+	      glVertex3fv(leftMostXYZ);
+
+              endtfan();
+
+              /*update i for next loop
+               */
+              i = k+1;
+
+	      leftMostNormal = upperNormal[k];
+	      leftMostXYZ = upperXYZ[k];
+            }
+          else /*upperVerts[i][0] > lowerVerts[j][0]*/
+            {
+	      bgntfan();
+	      glNormal3fv(upperNormal[i]);
+	      glVertex3fv(upperXYZ[i]);
+	      
+              glNormal3fv(leftMostNormal);
+	      glVertex3fv(leftMostXYZ);
+	      
+
+              /*find the last k>=j such that
+               *lowerverts[k][0] < upperverts[i][0]
+               */
+              k=j;
+              while(k< n_lower)
+                {
+                  if(lower_val[k] >= upper_val[i])
+                    break;
+		  glNormal3fv(lowerNormal[k]);
+		  glVertex3fv(lowerXYZ[k]);
+
+                  k++;
+                }
+              endtfan();
+
+              /*update j for next loop
+               */
+              j=k;
+
+	      leftMostNormal = lowerNormal[j-1];
+	      leftMostXYZ = lowerXYZ[j-1];
+            }     
+        }
+    }
+  //clean up 
+  free(upperXYZ);
+  free(lowerXYZ);
+  free(upperNormal);
+  free(lowerNormal);
+}
+
+/*triangulate a strip bounded by two lines which are parallel  to V-axis
+ *leftVerts: the verteces on the left line
+ *rightVertx: the verteces on the right line
+ *n_left >=1
+ *n_right >=1
+ */
+void OpenGLSurfaceEvaluator::inEvalVStrip(int n_left, REAL u_left, REAL* left_val, int n_right, REAL u_right, REAL* right_val)
+{
+  int i,j,k,l;
+  typedef REAL REAL3[3];
+
+  REAL3* leftXYZ = (REAL3*) malloc(sizeof(REAL3)*n_left);
+  assert(leftXYZ);
+  REAL3* leftNormal = (REAL3*) malloc(sizeof(REAL3) * n_left);
+  assert(leftNormal);
+  REAL3* rightXYZ = (REAL3*) malloc(sizeof(REAL3)*n_right);
+  assert(rightXYZ);
+  REAL3* rightNormal = (REAL3*) malloc(sizeof(REAL3) * n_right);
+  assert(rightNormal);
+  
+  inEvalVLine(n_left, u_left, left_val,  1, leftXYZ, leftNormal);
+  inEvalVLine(n_right, u_right, right_val,  1, rightXYZ, rightNormal);
+
+
+
+  REAL* botMostXYZ;
+  REAL* botMostNormal;
+
+  /*
+   *the algorithm works by scanning from bot to top.
+   */
+
+  if(left_val[0] <= right_val[0])
+    {
+      i=1;
+      j=0;
+
+      botMostXYZ = leftXYZ[0];
+      botMostNormal = leftNormal[0];
+    }
+  else
+    {
+      i=0;
+      j=1;
+
+      botMostXYZ = rightXYZ[0];
+      botMostNormal = rightNormal[0];
+    }
+  
+  /*the main loop.
+   */
+  while(1)
+    {
+      if(i >= n_left) /*case1: no more in left*/
+        {
+          if(j<n_right-1) /*at least two vertices in right*/
+            {
+              bgntfan();
+	      glNormal3fv(botMostNormal);
+              glVertex3fv(botMostXYZ);
+
+              while(j<n_right){
+		glNormal3fv(rightNormal[j]);
+		glVertex3fv(rightXYZ[j]);
+		j++;
+
+              }
+              endtfan();
+            }
+          break; /*exit the main loop*/
+        }
+      else if(j>= n_right) /*case2: no more in right*/
+        {
+          if(i<n_left-1) /*at least two vertices in left*/
+            {
+              bgntfan();
+	      glNormal3fv(botMostNormal);
+	      glVertex3fv(botMostXYZ);
+	      
+              for(k=n_left-1; k>=i; k--) /*reverse order for two-side lighting*/
+		{
+		  glNormal3fv(leftNormal[k]);
+		  glVertex3fv(leftXYZ[k]);
+		}
+
+              endtfan();
+            }
+          break; /*exit the main loop*/
+        }
+      else /* case3: neither is empty, there is at least one triangle to output*/
+        {
+          if(left_val[i] <= right_val[j])
+            {
+	      bgntfan();
+
+	      glNormal3fv(rightNormal[j]);
+	      glVertex3fv(rightXYZ[j]);
+
+              /*find the last k>=i such that 
+               *leftverts[k][0] <= rightverts[j][0]
+               */
+              k=i;
+
+              while(k<n_left)
+                {
+                  if(left_val[k] > right_val[j])
+                    break;
+                  k++;
+
+                }
+              k--;
+
+
+              for(l=k; l>=i; l--)/*the reverse is for two-side lighting*/
+                {
+		  glNormal3fv(leftNormal[l]);
+		  glVertex3fv(leftXYZ[l]);
+
+                }
+	      glNormal3fv(botMostNormal);
+	      glVertex3fv(botMostXYZ);
+
+              endtfan();
+
+              /*update i for next loop
+               */
+              i = k+1;
+
+	      botMostNormal = leftNormal[k];
+	      botMostXYZ = leftXYZ[k];
+            }
+          else /*left_val[i] > right_val[j])*/
+            {
+	      bgntfan();
+	      glNormal3fv(leftNormal[i]);
+	      glVertex3fv(leftXYZ[i]);
+	      
+              glNormal3fv(botMostNormal);
+	      glVertex3fv(botMostXYZ);
+	      
+
+              /*find the last k>=j such that
+               *rightverts[k][0] < leftverts[i][0]
+               */
+              k=j;
+              while(k< n_right)
+                {
+                  if(right_val[k] >= left_val[i])
+                    break;
+		  glNormal3fv(rightNormal[k]);
+		  glVertex3fv(rightXYZ[k]);
+
+                  k++;
+                }
+              endtfan();
+
+              /*update j for next loop
+               */
+              j=k;
+
+	      botMostNormal = rightNormal[j-1];
+	      botMostXYZ = rightXYZ[j-1];
+            }     
+        }
+    }
+  //clean up 
+  free(leftXYZ);
+  free(leftXYZ);
+  free(rightNormal);
+  free(rightNormal);
+}
+
+/*-----------------------begin evalMachine-------------------*/
+void OpenGLSurfaceEvaluator::inMap2fEM(int which, int k,
+	     REAL ulower,
+	     REAL uupper,
+	     int ustride,
+	     int uorder,
+	     REAL vlower,
+	     REAL vupper,
+	     int vstride,
+	     int vorder,
+	     REAL *ctlPoints)
+{
+  int i,j,x;
+  surfEvalMachine *temp_em;
+  switch(which){
+  case 0: //vertex
+    vertex_flag = 1;
+    temp_em = &em_vertex;
+    break;
+  case 1: //normal
+    normal_flag = 1;
+    temp_em = &em_normal;
+    break;
+  case 2: //color
+    color_flag = 1;
+    temp_em = &em_color;
+    break;
+  default:
+    texcoord_flag = 1;
+    temp_em = &em_texcoord;
+    break;
+  }
+
+  REAL *data = temp_em->ctlPoints;
+  
+  temp_em->uprime = -1;//initilized
+  temp_em->vprime = -1;
+
+  temp_em->k = k;
+  temp_em->u1 = ulower;
+  temp_em->u2 = uupper;
+  temp_em->ustride = ustride;
+  temp_em->uorder = uorder;
+  temp_em->v1 = vlower;
+  temp_em->v2 = vupper;
+  temp_em->vstride = vstride;
+  temp_em->vorder = vorder;
+
+  /*copy the contrl points from ctlPoints to global_ev_ctlPoints*/
+  for (i=0; i<uorder; i++) {
+    for (j=0; j<vorder; j++) {
+      for (x=0; x<k; x++) {
+	data[x] = ctlPoints[x];
+      }
+      ctlPoints += vstride;
+      data += k;
+    }
+    ctlPoints += ustride - vstride * vorder;
+  }
+}
+
+void OpenGLSurfaceEvaluator::inDoDomain2WithDerivsEM(surfEvalMachine *em, REAL u, REAL v, 
+				REAL *retPoint, REAL *retdu, REAL *retdv)
+{
+    int j, row, col;
+    REAL the_uprime;
+    REAL the_vprime;
+    REAL p;
+    REAL pdv;
+    REAL *data;
+
+    if((em->u2 == em->u1) || (em->v2 == em->v1))
+	return;
+    the_uprime = (u - em->u1) / (em->u2 - em->u1);
+    the_vprime = (v - em->v1) / (em->v2 - em->v1);
+    
+    /* Compute coefficients for values and derivs */
+
+    /* Use already cached values if possible */
+    if(em->uprime != the_uprime) {
+        inPreEvaluateWithDeriv(em->uorder, the_uprime, em->ucoeff, em->ucoeffDeriv);
+	em->uprime = the_uprime;
+    }
+    if (em->vprime != the_vprime) {
+	inPreEvaluateWithDeriv(em->vorder, the_vprime, em->vcoeff, em->vcoeffDeriv);
+	em->vprime = the_vprime;
+    }
+
+    for (j = 0; j < em->k; j++) {
+	data=em->ctlPoints+j;
+	retPoint[j] = retdu[j] = retdv[j] = 0.0;
+	for (row = 0; row < em->uorder; row++)  {
+	    /* 
+	    ** Minor optimization.
+	    ** The col == 0 part of the loop is extracted so we don't
+	    ** have to initialize p and pdv to 0.
+	    */
+	    p = em->vcoeff[0] * (*data);
+	    pdv = em->vcoeffDeriv[0] * (*data);
+	    data += em->k;
+	    for (col = 1; col < em->vorder; col++) {
+		/* Incrementally build up p, pdv value */
+		p += em->vcoeff[col] * (*data);
+		pdv += em->vcoeffDeriv[col] * (*data);
+		data += em->k;
+	    }
+	    /* Use p, pdv value to incrementally add up r, du, dv */
+	    retPoint[j] += em->ucoeff[row] * p;
+	    retdu[j] += em->ucoeffDeriv[row] * p;
+	    retdv[j] += em->ucoeff[row] * pdv;
+	}
+    }  
+}  
+
+void OpenGLSurfaceEvaluator::inDoDomain2EM(surfEvalMachine *em, REAL u, REAL v, 
+				REAL *retPoint)
+{
+    int j, row, col;
+    REAL the_uprime;
+    REAL the_vprime;
+    REAL p;
+    REAL *data;
+
+    if((em->u2 == em->u1) || (em->v2 == em->v1))
+	return;
+    the_uprime = (u - em->u1) / (em->u2 - em->u1);
+    the_vprime = (v - em->v1) / (em->v2 - em->v1);
+    
+    /* Compute coefficients for values and derivs */
+
+    /* Use already cached values if possible */
+    if(em->uprime != the_uprime) {
+        inPreEvaluate(em->uorder, the_uprime, em->ucoeff);
+	em->uprime = the_uprime;
+    }
+    if (em->vprime != the_vprime) {
+	inPreEvaluate(em->vorder, the_vprime, em->vcoeff);
+	em->vprime = the_vprime;
+    }
+
+    for (j = 0; j < em->k; j++) {
+	data=em->ctlPoints+j;
+	retPoint[j] = 0.0;
+	for (row = 0; row < em->uorder; row++)  {
+	    /* 
+	    ** Minor optimization.
+	    ** The col == 0 part of the loop is extracted so we don't
+	    ** have to initialize p and pdv to 0.
+	    */
+	    p = em->vcoeff[0] * (*data);
+	    data += em->k;
+	    for (col = 1; col < em->vorder; col++) {
+		/* Incrementally build up p, pdv value */
+		p += em->vcoeff[col] * (*data);
+		data += em->k;
+	    }
+	    /* Use p, pdv value to incrementally add up r, du, dv */
+	    retPoint[j] += em->ucoeff[row] * p;
+	}
+    }  
+}  
+
+
+void OpenGLSurfaceEvaluator::inDoEvalCoord2EM(REAL u, REAL v)
+{
+  REAL temp_vertex[5];
+  REAL temp_normal[3];
+  REAL temp_color[4];
+  REAL temp_texcoord[4];
+
+  if(texcoord_flag)
+    {
+      inDoDomain2EM(&em_texcoord, u,v, temp_texcoord);
+      texcoordCallBack(temp_texcoord, userData);
+    }
+  if(color_flag)
+    {
+      inDoDomain2EM(&em_color, u,v, temp_color);
+      colorCallBack(temp_color, userData);
+    }
+
+  if(normal_flag) //there is a normla map
+    {
+      inDoDomain2EM(&em_normal, u,v, temp_normal);
+      normalCallBack(temp_normal, userData);
+    
+      if(vertex_flag)
+	{
+	  inDoDomain2EM(&em_vertex, u,v,temp_vertex);
+	  if(em_vertex.k == 4)
+	    {
+	      temp_vertex[0] /= temp_vertex[3];
+	      temp_vertex[1] /= temp_vertex[3];
+	      temp_vertex[2] /= temp_vertex[3];	      
+	    }
+          temp_vertex[3]=u;
+          temp_vertex[4]=v;	  
+	  vertexCallBack(temp_vertex, userData);
+	}
+    }
+  else if(auto_normal_flag) //no normal map but there is a normal callbackfunctin
+    {
+      REAL du[4];
+      REAL dv[4];
+      
+      /*compute homegeneous point and partial derivatives*/
+      inDoDomain2WithDerivsEM(&em_vertex, u,v,temp_vertex,du,dv);
+
+      if(em_vertex.k ==4)
+	inComputeFirstPartials(temp_vertex, du, dv);
+
+#ifdef AVOID_ZERO_NORMAL
+      if(myabs(dv[0]) <= MYZERO && myabs(dv[1]) <= MYZERO && myabs(dv[2]) <= MYZERO)
+	{
+	  
+	  REAL tempdu[4];
+	  REAL tempdata[4];
+	  REAL u1 = em_vertex.u1;
+	  REAL u2 = em_vertex.u2;
+	  if(u-MYDELTA*(u2-u1) < u1)
+	    u = u+ MYDELTA*(u2-u1);
+	  else
+	    u = u-MYDELTA*(u2-u1);
+	  inDoDomain2WithDerivsEM(&em_vertex,u,v, tempdata, tempdu, dv);
+
+	  if(em_vertex.k ==4)
+	    inComputeFirstPartials(temp_vertex, du, dv);	  
+	}
+      else if(myabs(du[0]) <= MYZERO && myabs(du[1]) <= MYZERO && myabs(du[2]) <= MYZERO)
+	{
+	  REAL tempdv[4];
+	  REAL tempdata[4];
+	  REAL v1 = em_vertex.v1;
+	  REAL v2 = em_vertex.v2;
+	  if(v-MYDELTA*(v2-v1) < v1)
+	    v = v+ MYDELTA*(v2-v1);
+	  else
+	    v = v-MYDELTA*(v2-v1);
+	  inDoDomain2WithDerivsEM(&em_vertex,u,v, tempdata, du, tempdv);
+
+	  if(em_vertex.k ==4)
+	    inComputeFirstPartials(temp_vertex, du, dv);
+	}
+#endif
+
+      /*compute normal*/
+      switch(em_vertex.k){
+      case 3:
+
+	inComputeNormal2(du, dv, temp_normal);
+	break;
+      case 4:
+
+//	inComputeFirstPartials(temp_vertex, du, dv);
+	inComputeNormal2(du, dv, temp_normal);
+
+	/*transform the homegeneous coordinate of retPoint into inhomogenous one*/
+	temp_vertex[0] /= temp_vertex[3];
+	temp_vertex[1] /= temp_vertex[3];
+	temp_vertex[2] /= temp_vertex[3];
+	break;
+      }
+      normalCallBack(temp_normal, userData);
+      temp_vertex[3] = u;
+      temp_vertex[4] = v;
+      vertexCallBack(temp_vertex, userData);
+    }/*end if auto_normal*/
+  else //no normal map, and no normal callback function
+    {
+      if(vertex_flag)
+	{
+	  inDoDomain2EM(&em_vertex, u,v,temp_vertex);
+	  if(em_vertex.k == 4)
+	    {
+	      temp_vertex[0] /= temp_vertex[3];
+	      temp_vertex[1] /= temp_vertex[3];
+	      temp_vertex[2] /= temp_vertex[3];	      
+	    }
+          temp_vertex[3] = u;
+          temp_vertex[4] = v;
+	  vertexCallBack(temp_vertex, userData);
+	}
+    }
+}
+
+
+void OpenGLSurfaceEvaluator::inBPMEvalEM(bezierPatchMesh* bpm)
+{
+  int i,j,k;
+  float u,v;
+
+  int ustride;
+  int vstride;
+
+#ifdef USE_LOD
+  if(bpm->bpatch != NULL)
+    {
+      bezierPatch* p=bpm->bpatch;
+      ustride = p->dimension * p->vorder;
+      vstride = p->dimension;
+
+      glMap2f( (p->dimension == 3)? GL_MAP2_VERTEX_3 : GL_MAP2_VERTEX_4,
+	      p->umin,
+	      p->umax,
+	      ustride,
+	      p->uorder,
+	      p->vmin,
+	      p->vmax,
+	      vstride,
+	      p->vorder,
+	      p->ctlpoints);
+
+
+/*
+    inMap2fEM(0, p->dimension,
+	  p->umin,
+	  p->umax,
+	  ustride,
+	  p->uorder,
+	  p->vmin,
+	  p->vmax,
+	  vstride,
+	  p->vorder,
+	  p->ctlpoints);
+*/
+    }
+#else
+
+  if(bpm->bpatch != NULL){
+    bezierPatch* p = bpm->bpatch;
+    ustride = p->dimension * p->vorder;
+    vstride = p->dimension;
+    inMap2fEM(0, p->dimension,
+	  p->umin,
+	  p->umax,
+	  ustride,
+	  p->uorder,
+	  p->vmin,
+	  p->vmax,
+	  vstride,
+	  p->vorder,
+	  p->ctlpoints);
+  }
+  if(bpm->bpatch_normal != NULL){
+    bezierPatch* p = bpm->bpatch_normal;
+    ustride = p->dimension * p->vorder;
+    vstride = p->dimension;
+    inMap2fEM(1, p->dimension,
+	  p->umin,
+	  p->umax,
+	  ustride,
+	  p->uorder,
+	  p->vmin,
+	  p->vmax,
+	  vstride,
+	  p->vorder,
+	  p->ctlpoints);
+  }
+  if(bpm->bpatch_color != NULL){
+    bezierPatch* p = bpm->bpatch_color;
+    ustride = p->dimension * p->vorder;
+    vstride = p->dimension;
+    inMap2fEM(2, p->dimension,
+	  p->umin,
+	  p->umax,
+	  ustride,
+	  p->uorder,
+	  p->vmin,
+	  p->vmax,
+	  vstride,
+	  p->vorder,
+	  p->ctlpoints);
+  }
+  if(bpm->bpatch_texcoord != NULL){
+    bezierPatch* p = bpm->bpatch_texcoord;
+    ustride = p->dimension * p->vorder;
+    vstride = p->dimension;
+    inMap2fEM(3, p->dimension,
+	  p->umin,
+	  p->umax,
+	  ustride,
+	  p->uorder,
+	  p->vmin,
+	  p->vmax,
+	  vstride,
+	  p->vorder,
+	  p->ctlpoints);
+  }
+#endif
+
+
+  k=0;
+  for(i=0; i<bpm->index_length_array; i++)
+    {
+#ifdef USE_LOD
+      if(bpm->type_array[i] == GL_POLYGON) //a mesh
+	{
+	  GLfloat *temp = bpm->UVarray+k;
+	  GLfloat u0 = temp[0];
+	  GLfloat v0 = temp[1];
+	  GLfloat u1 = temp[2];
+	  GLfloat v1 = temp[3];
+	  GLint nu = (GLint) ( temp[4]);
+	  GLint nv = (GLint) ( temp[5]);
+	  GLint umin = (GLint) ( temp[6]);
+	  GLint vmin = (GLint) ( temp[7]);
+	  GLint umax = (GLint) ( temp[8]);
+	  GLint vmax = (GLint) ( temp[9]);
+
+	  glMapGrid2f(LOD_eval_level*nu, u0, u1, LOD_eval_level*nv, v0, v1);
+	  glEvalMesh2(GL_FILL, LOD_eval_level*umin, LOD_eval_level*umax, LOD_eval_level*vmin, LOD_eval_level*vmax);
+	}
+      else
+	{
+	  LOD_eval(bpm->length_array[i], bpm->UVarray+k, bpm->type_array[i],
+		   0
+		   );
+	}
+	  k+= 2*bpm->length_array[i];       
+    
+#else //undef  USE_LOD
+
+#ifdef CRACK_TEST
+if(  bpm->bpatch->umin == 2 &&   bpm->bpatch->umax == 3
+  && bpm->bpatch->vmin ==2 &&    bpm->bpatch->vmax == 3)
+{
+REAL vertex[4];
+REAL normal[4];
+#ifdef DEBUG
+printf("***number ****1\n");
+#endif
+
+beginCallBack(GL_QUAD_STRIP, NULL);
+inDoEvalCoord2EM(3.0, 3.0);
+inDoEvalCoord2EM(2.0, 3.0);
+inDoEvalCoord2EM(3.0, 2.7);
+inDoEvalCoord2EM(2.0, 2.7);
+inDoEvalCoord2EM(3.0, 2.0);
+inDoEvalCoord2EM(2.0, 2.0);
+endCallBack(NULL);
+
+beginCallBack(GL_TRIANGLE_STRIP, NULL);
+inDoEvalCoord2EM(2.0, 3.0);
+inDoEvalCoord2EM(2.0, 2.0);
+inDoEvalCoord2EM(2.0, 2.7);
+endCallBack(NULL);
+
+}
+if(  bpm->bpatch->umin == 1 &&   bpm->bpatch->umax == 2
+  && bpm->bpatch->vmin ==2 &&    bpm->bpatch->vmax == 3)
+{
+#ifdef DEBUG
+printf("***number 3\n");
+#endif
+beginCallBack(GL_QUAD_STRIP, NULL);
+inDoEvalCoord2EM(2.0, 3.0);
+inDoEvalCoord2EM(1.0, 3.0);
+inDoEvalCoord2EM(2.0, 2.3);
+inDoEvalCoord2EM(1.0, 2.3);
+inDoEvalCoord2EM(2.0, 2.0);
+inDoEvalCoord2EM(1.0, 2.0);
+endCallBack(NULL);
+
+beginCallBack(GL_TRIANGLE_STRIP, NULL);
+inDoEvalCoord2EM(2.0, 2.3);
+inDoEvalCoord2EM(2.0, 2.0);
+inDoEvalCoord2EM(2.0, 3.0);
+endCallBack(NULL);
+
+}
+return;
+#endif //CRACK_TEST
+
+      beginCallBack(bpm->type_array[i], userData);
+
+      for(j=0; j<bpm->length_array[i]; j++)
+	{
+	  u = bpm->UVarray[k];
+	  v = bpm->UVarray[k+1];
+#ifdef USE_LOD
+          LOD_EVAL_COORD(u,v);
+//	  glEvalCoord2f(u,v);
+#else
+
+#ifdef  GENERIC_TEST
+          float temp_normal[3];
+          float temp_vertex[3];
+          if(temp_signal == 0)
+	    {
+	      gTessVertexSphere(u,v, temp_normal, temp_vertex);
+//printf("normal=(%f,%f,%f)\n", temp_normal[0], temp_normal[1], temp_normal[2])//printf("veretx=(%f,%f,%f)\n", temp_vertex[0], temp_vertex[1], temp_vertex[2]);
+              normalCallBack(temp_normal, userData);
+	      vertexCallBack(temp_vertex, userData);
+	    }
+          else if(temp_signal == 1)
+	    {
+	      gTessVertexCyl(u,v, temp_normal, temp_vertex);
+//printf("normal=(%f,%f,%f)\n", temp_normal[0], temp_normal[1], temp_normal[2])//printf("veretx=(%f,%f,%f)\n", temp_vertex[0], temp_vertex[1], temp_vertex[2]);
+              normalCallBack(temp_normal, userData);
+	      vertexCallBack(temp_vertex, userData);
+	    }
+	  else
+#endif //GENERIC_TEST
+
+	    inDoEvalCoord2EM(u,v);
+     
+#endif //USE_LOD
+
+	  k += 2;
+	}
+      endCallBack(userData);
+
+#endif //USE_LOD
+    }
+}
+
+void OpenGLSurfaceEvaluator::inBPMListEvalEM(bezierPatchMesh* list)
+{
+  bezierPatchMesh* temp;
+  for(temp = list; temp != NULL; temp = temp->next)
+    {
+      inBPMEvalEM(temp);
+    }
+}
+