/*
 ** 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: 2004/05/12 15:29:36 $ $Revision: 1.3 $
 */
/*
 ** $Header: /home/krh/git/sync/mesa-cvs-repo/Mesa/src/glu/sgi/libnurbs/interface/insurfeval.cc,v 1.3 2004/05/12 15:29:36 brianp Exp $
 */

#include "gluos.h"
#include <stdlib.h>
#include <stdio.h>
#include <GL/gl.h>
#include <math.h>
#include <assert.h>
#include "glsurfeval.h"
#include "cgl_prototypes.h"

#undef glNormal3fv
#undef glVertex3fv

#define glVertex3fv(v) 	\
	cgl_GLVertex4f(m_Self,(v)[0], (v)[1], (v)[2], 1.0f)
#define glNormal3fv(v)	\
	cgl_GLNormal3f(m_Self,(v)[0], (v)[1], (v)[2])

//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);*/
		cgl_GLglBegin(m_Self,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();	
		cgl_GLEnd(m_Self);
	}
}

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]);

	if (mag > 0.0) {
		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;
	default:
		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;

	/*
	 * note: leftMostV has been optimized away
	
	 *the algorithm works by scanning from left to right.
	 *leftMostV: the left most of the remaining verteces (on both upper and lower).
	 *           it could an element of upperVerts or lowerVerts.
	 *i: upperVerts[i] is the first vertex to the right of leftMostV on upper line   *j: lowerVerts[j] is the first vertex to the right of leftMostV on lower line   */

	/*initialize i,j,and leftMostV
	 */
	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.
	 *the invariance is that: 
	 *at the beginning of each loop, the meaning of i,j,and leftMostV are 
	 *maintained
	 */
	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, plus the leftMostV, 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 and leftMostV 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 and leftMostV 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;

	/*
	 * note: botMostV has been optimized away
	
	 *the algorithm works by scanning from bot to top.
	 *botMostV: the bot most of the remaining verteces (on both left and right).
	 *           it could an element of leftVerts or rightVerts.
	 *i: leftVerts[i] is the first vertex to the top of botMostV on left line   
	 *j: rightVerts[j] is the first vertex to the top of botMostV on rightline   */

	/*initialize i,j,and botMostV
	 */
	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.
	 *the invariance is that: 
	 *at the beginning of each loop, the meaning of i,j,and botMostV are 
	 *maintained
	 */
	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, plus the botMostV, 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 and botMostV 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 and botMostV 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;

		cgl_GLMap2f(m_Self, (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]);

			cgl_GLMapGrid2f(m_Self,LOD_eval_level*nu, u0, u1, LOD_eval_level*nv, v0, v1);
			cgl_GLEvalMesh2(m_Self,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);
	}
}