#ifndef _mynurbs_h
#ifndef _MYNURBS_H
#include "gl\gl.h"
#include "math.h"
//*-*-*-*-*-*-*-*-*-*-*-*-*-*-* B样条基函数计算部分 *-*-*-*-*-*-*-*-*-*-*-*-*-*
//确定参数u所在的节点区间下标
//n=m-p-1
//m为节点矢量U[]的最大下标
//p为B样条函数次数
int FindSource(int n,int p,float u,float U[])
{
int low,high,mid;
if(u==U[n+1])//特殊情况
return n;
//进行二分搜索
low=p;
high=n+1;
mid=(int)(low+high)/2;
while(u<U[mid]||u>U[mid])
{
if(u<U[mid])
high=mid;
else
low=mid;
mid=(int)(low+high)/2;
if(u>=U[mid]&&u<U[mid+1])//找到u所在的节点区间的下标
break; //退出二分搜索
}
return mid; //返回区间下标
}
//计算所有非零B样条基函数并返回其值
//i为参数u所在的节点区间下标
void BasisFunction(int i,int p,float u,float U[],float N[])
{
int j,di,dp,k;
float tul,tur,left,right;
float tmpN[50][50];
for(k=0;k<=p;k++)
{
dp=0;
for(di=i+p-k;di>=i-k;di--)
{
if(u>=U[di]&&u<U[di+1])
tmpN[di][0]=1;
else
tmpN[di][0]=0;
dp+=1;
for(j=1;j<dp;j++)
{
tul=U[di+j]-U[di];
tur=U[di+j+1]-U[di+1];
if(tul!=0)
left=(u-U[di])/tul;
else
left=0;
if(tur!=0)
right=(U[di+j+1]-u)/tur;
else
right=0;
tmpN[di][j]=left*tmpN[di][j-1]+right*tmpN[di+1][j-1];
}
}
N[i-k]=tmpN[i-k][p];
}
}
//-----------------------------------------------------------------------
//计算基函数的1阶导数并保存在NP[]中
//i为参数u所在的节点区间下标
//p为B样条函数次数P>2
void DerBasisFunc(int i,int p,float u,float U[],float NP[])
{
int j,di,dp,k;
float tul,tur,left,right,saved,dl,dr;
float tmpN[50][50];
for(k=0;k<=p;k++)
{
dp=0;
for(di=i+p-k;di>=i-k;di--)
{
if(u>=U[di]&&u<U[di+1])
tmpN[di][0]=1;
else
tmpN[di][0]=0;
dp+=1;
for(j=1;j<dp;j++)
{
tul=U[di+j]-U[di];
tur=U[di+j+1]-U[di+1];
if(tul!=0)
left=(u-U[di])/tul,dl=1/tul;
else
left=0,dl=0;
if(tur!=0)
right=(U[di+j+1]-u)/tur,dr=1/tur;
else
right=0,dr=0;
tmpN[di][j]=(left*tmpN[di][j-1]+right*tmpN[di+1][j-1]);
saved=p*(dl*tmpN[di][j-1]-dr*tmpN[di+1][j-1])/(p+p-1);
}
}
NP[i-k]=saved;
}
}
//*-*-*-*-*-*-*-*-*-*-*-*-*-* Bezier曲线曲面部分 *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
//计算参数u的p次基函数值并存在BC[]中
void BernsteinFunc(int p,double t,float BC[])
{
for(int i=0;i<=p;i++)
{
if(i==0)
BC[0]=(float)pow(1-t,p);
if(i==p)
BC[p]=(float)pow(t,p);
if(i>0&&i<p)
BC[i]=p*(float)pow(t,i)*(float)pow(1-t,p-i);
}
}
//获取p次Bezier曲线上的lines个点的值
void BezierPoint(int p,float px[],float py[],float pz[],int lines,float tmp[][3])
{
float BC[20];
int i,j;
for(j=0;j<=lines;j++)
{
double t=j/(float)lines;
BernsteinFunc(p,t,BC);
tmp[j][0]=tmp[j][1]=tmp[j][2]=0;
for(i=0;i<p+1;i++)
{
tmp[j][0]+=BC[i]*px[i];
tmp[j][1]+=BC[i]*py[i];
tmp[j][2]+=BC[i]*pz[i];
}
}
}
//获取p次有理Bezier曲线上的lines个点的值
void NBezierPoint(int p,float px[],float py[],float pz[],float pw[],int lines,float tmp[][4])
{
float x,y,z,w,BC[20];
int i,j;
for(j=0;j<=lines;j++)
{
double t=j/(float)lines;
BernsteinFunc(p,t,BC);
x=y=z=w=0;
for(i=0;i<p+1;i++)
{
x+=BC[i]*px[i]*pw[i];
y+=BC[i]*py[i]*pw[i];
z+=BC[i]*pz[i]*pw[i];
w+=BC[i]*pw[i];
}
tmp[j][0]=x/w;
tmp[j][1]=y/w;
tmp[j][2]=z/w;
tmp[j][3]=w;
}
}
//-----------------------------------------------------------------------------------
//绘制p次的Bezier曲线
void Bezier(int p,float px[],float py[],float pz[],int lines)
{
float pt[100][3];
int j;
BezierPoint(p,px,py,pz,lines,pt);
for(j=1;j<=lines;j++)
{
glBegin(GL_LINES);
glVertex3f(pt[j-1][0],pt[j-1][1],pt[j-1][2]);
glVertex3f(pt[j][0],pt[j][1],pt[j][2]);
glEnd();
}
}
//------------------------------------------------------------------------------
//绘制p次的有理Bezier曲线
void NBezier(int p,float px[],float py[],float pz[],float w[],int lines)
{
float pt[100][4];
int j;
NBezierPoint(p,px,py,pz,w,lines,pt);
for(j=1;j<=lines;j++)
{
glBegin(GL_LINES);
glVertex3f(pt[j-1][0],pt[j-1][1],pt[j-1][2]);
glVertex3f(pt[j][0],pt[j][1],pt[j][2]);
glEnd();
}
}
//---------------------------------------------------------------------------------
//计算双p次Bezier曲面上所有的点并保存在Pt[][][]中
//u和v分别为曲面(u,v)方向上的网格数
void BezierFacePoint(int p,int u,int v,float px[][4],float py[][4],float pz[][4],float pt[161][161][3])
{
float urx[11][161],ury[11][161],urz[11][161];
float tx[11],ty[11],tz[11],tmp[161][3];
int i,j,k;
for(j=0;j<p+1;j++)
{
for(i=0;i<p+1;i++)
{
tx[i]=px[i][j];
ty[i]=py[i][j];
tz[i]=pz[i][j];
}
BezierPoint(p,tx,ty,tz,v,tmp);
for(k=0;k<=v;k++)
{
urx[j][k]=tmp[k][0];
ury[j][k]=tmp[k][1];
urz[j][k]=tmp[k][2];
}
}
for(i=0;i<=v;i++)
{
for(k=0;k<p+1;k++)
{
tx[k]=urx[k][i];
ty[k]=ury[k][i];
tz[k]=urz[k][i];
}
BezierPoint(p,tx,ty,tz,u,tmp);
for(j=0;j<=u;j++)
{
pt[i][j][0]=tmp[j][0];
pt[i][j][1]=tmp[j][1];
pt[i][j][2]=tmp[j][2];
}
}
}
//--------------------------------------------------------------------------------
//计算双p次有理Bezier曲面上所有的点并保存在Pt[][][]中
//u和v分别为曲面(u,v)方向上的网格数
void NuBezierFacePoint(int p,int u,int v,float px[][4],float py[][4],float pz[][4],float w[][4],float pt[161][161][3])
{
float urx[11][161],ury[11][161],urz[11][161],urw[11][161];
float tx[11],ty[11],tz[11],tw[11],tmp[161][4];
int i,j,k;
for(j=0;j<p+1;j++)
{
for(i=0;i<p+1;i++)
{
tx[i]=px[i][j];
ty[i]=py[i][j];
tz[i]=pz[i][j];
tw[i]=w[i][j];
}
NBezierPoint(p,tx,ty,tz,tw,v,tmp);
for(k=0;k<=v;k++)
{
urx[j][k]=tmp[k][0];
ury[j][k]=tmp[k][1];
urz[j][k]=tmp[k][2];
urw[j][k]=tmp[k][3];
}
}
for(i=0;i<=v;i++)
{
for(k=0;k<p+1;k++)
{
tx[k]=urx[k][i];
ty[k]=ury[k][i];
tz[k]=urz[k][i];
tw[k]=urw[k][i];
}
NBezierPoint(p,tx,ty,tz,tw,u,tmp);
for(j=0;j<=u;j++)
{
pt[i][j][0]=tmp[j][0];
pt[i][j][1]=tmp[j][1];
pt[i][j][2]=tmp[j][2];
}
}
}
//-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* B样条曲线曲面部分 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-
//计算样条曲线的1阶导矢（u所对应的所有点）保存在Der[]中
//n=m-p-1
//p为曲线的次数
void BSplineDer(int n,int p,float U[],float P[],float Der[])
{
float N[100],tmp;
int i,j;
for(i=p+1;i<=n;i++)
{
DerBasisFunc(i,p,U[i],U,N);
tmp=0;
for(j=i;j>=i-p;j--)
tmp+=N[j]*P[j];
Der[i-p]=tmp;
}
}
//计算曲线上的点（u所对应的所有点）保存在Poi[]中
//n=m-p-1
//p为曲线的次数
void BSplinePoint(int n,int p,float U[],float P[],float Poi[])
{
float N[100],tmp;
int i,j;
for(i=p+1;i<=n;i++)
{
BasisFunction(i,p,U[i],U,N);
tmp=0;
for(j=i;j>=i-p;j--)
tmp+=N[j]*P[j];
Poi[i-p]=tmp;
}
}
//计算3次样条曲线上的所有控制多边形保存在CP[]中
//m为节点矢量U[]的最大下标
void B3SplineControlPoint(int m,float U[],float P[],float CP[])
{
int n,k,i,cp,p;
float Poi[100],Der[100],add;
p=3;
n=m-p-1;
BSplinePoint(n,p,U,P,Poi);
BSplineDer(n,p,U,P,Der);
cp=(n-p)*3+p;
for(i=0;i<2;i++)
{
CP[i]=P[i];
CP[cp-i]=P[n-i];
}
for(i=3;i<cp-1;i+=3)
{
k=(int)i/3;
add=Der[k]/p;
CP[i]=Poi[k];
CP[i-1]=CP[i]-add;
CP[i+1]=CP[i]+add;
}
}
//计算2次样条曲线上的所有控制多边形保存在CP[]中
//m为节点矢量U[]的最大下标
void B2SplineControlPoint(int m,float U[],float P[],float CP[])
{
int n,k,tm,i,cp,p;
float Poi[100];
p=2;
n=m-p-1;
BSplinePoint(n,p,U,P,Poi);
cp=(n-p)*2+p;
for(i=0;i<2;i++)
CP[i]=P[i];
CP[cp]=P[n];
tm=2;
for(i=2;i<cp-1;i+=2)
{
k=(int)i/2;
CP[i]=Poi[k];
CP[i+1]=P[tm];
tm++;
}
}
//绘制3次B样条曲线
//m为节点矢量U[]的最大下标
void BSpline3L(int m,float U[],float px[],float py[],float pz[])
{
float pcx[100],pcy[100],pcz[100],drx[4],dry[4],drz[4];
int i,j,tmcp;
B3SplineControlPoint(m,U,px,pcx);
B3SplineControlPoint(m,U,py,pcy);
B3SplineControlPoint(m,U,pz,pcz);
/*
glColor3f(0.0f,0.0f,0.0f);
for(i=1;i<3*m-17;i++)
{
glBegin(GL_LINES);
glVertex3f(pcx[i-1],pcy[i-1],pcz[i-1]);
glVertex3f(pcx[i],pcy[i],pcz[i]);
glEnd();
}
glColor3f(1.0f,0.0f,0.0f);*/
tmcp=m-7;
for(i=0;i<=tmcp;i++)
{
for(j=i*3;j<i*3+4;j++)
{
drx[j-i*3]=pcx[j];
dry[j-i*3]=pcy[j];
drz[j-i*3]=pcz[j];
}
Bezier(3,drx,dry,drz,20);
}
}
//绘制2次B样条曲线
//m为节点矢量U[]的最大下标
void BSpline2L(int m,float U[],float px[],float py[],float pz[])
{
float pcx[100],pcy[100],pcz[100],drx[3],dry[3],drz[3];
int i,j,tmcp;
B2SplineControlPoint(m,U,px,pcx);
B2SplineControlPoint(m,U,py,pcy);
B2SplineControlPoint(m,U,pz,pcz);
tmcp=m-5;
for(i=0;i<=tmcp;i++)
{
for(j=i*2;j<i*2+3;j++)
{
drx[j-i*2]=pcx[j];
dry[j-i*2]=pcy[j];
drz[j-i*2]=pcz[j];
}
Bezier(2,drx,dry,drz,20);
}
}
//计算双三次（3x3）B样条曲面所有控制多边形顶点，并保存在pt[][][]中
//mu,mv分别为节点矢量U[],V[]的最大下标值
void BS3FaceControlPoint(int mu,float U[],int mv,float V[],float px[],float py[],float pz[],float pt[100][100][3])
{
int i,j,k,dp;
float tmx[50],tmy[50],tmz[50];
float tmpx[50][100],tmpy[50][100],tmpz[50][100];
float uvx[100][100],uvy[100][100],uvz[100][100];
for(i=0;i<mv-3;i++)
{
dp=i*(mu-3);
for(j=dp;j<mu-3+dp;j++)
{
tmx[j-dp]=px[j];
tmy[j-dp]=py[j];
tmz[j-dp]=pz[j];
}
B3SplineControlPoint(mu,U,tmx,tmpx[i]);
B3SplineControlPoint(mu,U,tmy,tmpy[i]);
B3SplineControlPoint(mu,U,tmz,tmpz[i]);
}
for(i=0;i<3*mu-17;i++)
{
for(j=0;j<mv-3;j++)
{
tmx[j]=tmpx[j][i];
tmy[j]=tmpy[j][i];
tmz[j]=tmpz[j][i];
}
B3SplineControlPoint(mv,V,tmx,uvx[i]);
B3SplineControlPoint(mv,V,tmy,uvy[i]);
B3SplineControlPoint(mv,V,tmz,uvz[i]);
for(k=0;k<3*mv-17;k++)
{
pt[i][k][0]=uvx[i][k];
pt[i][k][1]=uvy[i][k];
pt[i][k][2]=uvz[i][k];
}
}
}
//计算双二次（2x2）B样条曲面所有控制多边形顶点，并保存在pt[][][]中
//mu,mv分别为节点矢量U[],V[]的最大下标值
void BS2FaceControlPoint(int mu,float U[],int mv,float V[],float px[],float py[],float pz[],float pt[100][100][3])
{
int i,j,k,dp;
float tmx[50],tmy[50],tmz[50];
float tmpx[50][100],tmpy[50][100],tmpz[50][100];
float uvx[100][100],uvy[100][100],uvz[100][100];
for(i=0;i<mv-2;i++)
{
dp=i*(mu-2);
for(j=dp;j<mu-2+dp;j++)
{
tmx[j-dp]=px[j];
tmy[j-dp]=py[j];
tmz[j-dp]=pz[j];
}
B2SplineControlPoint(mu,U,tmx,tmpx[i]);
B2SplineControlPoint(mu,U,tmy,tmpy[i]);
B2SplineControlPoint(mu,U,tmz,tmpz[i]);
}
for(i=0;i<2*mu-7;i++)
{
for(j=0;j<mv-2;j++)
{
tmx[j]=tmpx[j][i];
tmy[j]=tmpy[j][i];
tmz[j]=tmpz[j][i];
}
B2SplineControlPoint(mv,V,tmx,uvx[i]);
B2SplineControlPoint(mv,V,tmy,uvy[i]);
B2SplineControlPoint(mv,V,tmz,uvz[i]);
for(k=0;k<2*mv-7;k++)
{
pt[i][k][0]=uvx[i][k];
pt[i][k][1]=uvy[i][k];
pt[i][k][2]=uvz[i][k];
}
}
}
//-------------------------------------------------------------------------------
//设置网格数
void SetGridCount(int dt,int tu,int tmk[])
{
int i,tm;
tm=tu%dt;
for(i=0;i<dt-1;i++)
tmk[i]=(tu-tm)/dt;
tmk[dt-1]=tmk[0]+tm;
}
//------------------------------------------------------------------------------
//计算双三次(3x3次)或双二次(2x2次)B样条曲面上所有的点并保存在bs[][][]中
//nu,mv分别为节点矢量U[],V[]的最大下标
//uk,vk分别为B样条曲面(u,v)方向上的网格数
//p为曲面的次数
void BSplineFace(int p,int nu,float U[],int uk,int mv,float V[],int vk,
float px[],float py[],float pz[],float bs[161][161][3])
{
int udk[20],vdk[20],i,j,k,l,hu,sv,du,dv;
float tp[100][100][3],td[161][161][3];
float tmx[4][4],tmy[4][4],tmz[4][4];
du=nu-2*p;
dv=mv-2*p;
SetGridCount(du,uk,udk);
SetGridCount(dv,vk,vdk);
if(p==3)
BS3FaceControlPoint(nu,U,mv,V,px,py,pz,tp);
if(p==2)
BS2FaceControlPoint(nu,U,mv,V,px,py,pz,tp);
for(i=0;i<dv;i++)
{
for(k=0;k<du;k++)
{
for(j=i*p;j<p+1+i*p;j++)
for(l=k*p;l<p+1+k*p;l++)
{
tmx[j-i*p][l-k*p]=tp[l][j][0];
tmy[j-i*p][l-k*p]=tp[l][j][1];
tmz[j-i*p][l-k*p]=tp[l][j][2];
}
BezierFacePoint(p,udk[k],vdk[i],tmx,tmy,tmz,td);
for(sv=i*vdk[0];sv<=vdk[i]+i*vdk[0];sv++)
for(hu=k*udk[0];hu<=udk[k]+k*udk[0];hu++)
{
bs[sv][hu][0]=td[sv-i*vdk[0]][hu-k*udk[0]][0];
bs[sv][hu][1]=td[sv-i*vdk[0]][hu-k*udk[0]][1];
bs[sv][hu][2]=td[sv-i*vdk[0]][hu-k*udk[0]][2];
}
}
}
}
//-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-* Nurbs 样条曲线曲面部分 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-
//计算Nurbs曲线上的点（u所对应的所有点）保存在Poi[]中
//n=m-p-1
//p为曲线的次数
void NurbsPoint(int n,int p,float U[],float P[],float W[],float Poi[])
{
float N[100],tmp,tmw;
int i,j;
for(i=p+1;i<=n;i++)
{
BasisFunction(i,p,U[i],U,N);
tmp=0;tmw=0;
for(j=i;j>=i-p;j--)
{
tmp+=N[j]*P[j]*W[j];
tmw+=N[j]*W[j];
}
Poi[i-p]=tmp/tmw;
}
}
//计算Nurbs曲线的1阶导矢（u所对应的所有点）保存在Der[]中
//n=m-p-1
//p为曲线的次数
void NurbsDer(int n,int p,float U[],float P[],float W[],float Der[])
{
float N[100],CP[100],NW[100],tmp,tw;
int i,j;
NurbsPoint(n,p,U,P,W,CP);
BSplinePoint(n,p,U,W,NW);
for(i=p+1;i<=n;i++)
{
DerBasisFunc(i,p,U[i],U,N);
tmp=0;tw=0;
for(j=i;j>=i-p;j--)
{
tmp+=N[j]*P[j]*W[j];
tw+=N[j]*W[j];
}
Der[i-p]=(tmp-tw*CP[i-p])/NW[i-p];
}
}
//计算3次Nurbs曲线上的所有控制多边形保存在CP[]中
//m为节点矢量U[]的最大下标
void Nurbs3ControlPoint(int m,float U[],float P[],float W[],float CP[])
{
int n,k,i,cp,p;
float Poi[100],Der[100],add;
p=3;
n=m-p-1;
NurbsPoint(n,p,U,P,W,Poi);
NurbsDer(n,p,U,P,W,Der);
cp=(n-p)*3+p;
for(i=0;i<2;i++)
{
CP[i]=P[i];
CP[cp-i]=P[n-i];
}
for(i=3;i<cp-1;i+=3)
{
k=(int)i/3;
add=Der[k]/p;
CP[i]=Poi[k];
CP[i-1]=CP[i]-add;
CP[i+1]=CP[i]+add;
}
}
//计算2次Nurbs曲线上的所有控制多边形保存在CP[]中
//m为节点矢量U[]的最大下标
void Nurbs2ControlPoint(int m,float U[],float P[],float W[],float CP[])
{
int n,k,tm,i,cp,p;
float Poi[100];
p=2;
n=m-p-1;
NurbsPoint(n,p,U,P,W,Poi);
cp=(n-p)*2+p;
for(i=0;i<2;i++)
CP[i]=P[i];
CP[cp]=P[n];
tm=2;
for(i=2;i<cp-1;i+=2)
{
k=(int)i/2;
CP[i]=Poi[k];
CP[i+1]=P[tm];
tm++;
}
}
//绘制3次Nurbs样条曲线
//m为节点矢量U[]的最大下标
void Nurbs3L(int m,float U[],float px[],float py[],float pz[],float W[])
{
float pcx[100],pcy[100],pcz[100],drx[4],dry[4],drz[4];
float pcw[100],drw[4];
int i,j,tmcp;
Nurbs3ControlPoint(m,U,px,W,pcx);
Nurbs3ControlPoint(m,U,py,W,pcy);
Nurbs3ControlPoint(m,U,pz,W,pcz);
B3SplineControlPoint(m,U,W,pcw);
tmcp=m-7;
for(i=0;i<=tmcp;i++)
{
for(j=i*3;j<i*3+4;j++)
{
drx[j-i*3]=pcx[j];
dry[j-i*3]=pcy[j];
drz[j-i*3]=pcz[j];
drw[j-i*3]=pcw[j];
}
NBezier(3,drx,dry,drz,drw,20);
}
}
//绘制2次Nurbs样条曲线
//m为节点矢量U[]的最大下标
void Nurbs2L(int m,float U[],float px[],float py[],float pz[],float W[])
{
float pcx[100],pcy[100],pcz[100],drx[3],dry[3],drz[3];
float pcw[100],drw[3];
int i,j,tmcp;
Nurbs2ControlPoint(m,U,px,W,pcx);
Nurbs2ControlPoint(m,U,py,W,pcy);
Nurbs2ControlPoint(m,U,pz,W,pcz);
B2SplineControlPoint(m,U,W,pcw);
tmcp=m-5;
for(i=0;i<=tmcp;i++)
{
for(j=i*2;j<i*2+3;j++)
{
drx[j-i*2]=pcx[j];
dry[j-i*2]=pcy[j];
drz[j-i*2]=pcz[j];
drw[j-i*2]=pcw[j];
}
NBezier(2,drx,dry,drz,drw,20);
}
}
//计算双三次（3x3）Nurbs样条曲面所有控制多边形顶点，并保存在pt[][][]中
//mu,mv分别为节点矢量U[],V[]的最大下标值
void Nurbs3FControlPoint(int mu,float U[],int mv,float V[],float px[],float py[],float pz[],float W[],float pt[100][100][4])
{
int i,j,k,dp;
float tmx[50],tmy[50],tmz[50],tmw[50];
float tmpx[50][100],tmpy[50][100],tmpz[50][100],tmpw[50][100];
float uvx[100][100],uvy[100][100],uvz[100][100],uvw[100][100];
for(i=0;i<mv-3;i++)
{
dp=i*(mu-3);
for(j=dp;j<mu-3+dp;j++)
{
tmx[j-dp]=px[j];
tmy[j-dp]=py[j];
tmz[j-dp]=pz[j];
tmw[j-dp]=W[j];
}
Nurbs3ControlPoint(mu,U,tmx,tmw,tmpx[i]);
Nurbs3ControlPoint(mu,U,tmy,tmw,tmpy[i]);
Nurbs3ControlPoint(mu,U,tmz,tmw,tmpz[i]);
B3SplineControlPoint(mu,U,tmw,tmpw[i]);
}
for(i=0;i<3*mu-17;i++)
{
for(j=0;j<mv-3;j++)
{
tmx[j]=tmpx[j][i];
tmy[j]=tmpy[j][i];
tmz[j]=tmpz[j][i];
tmw[j]=tmpw[j][i];
}
Nurbs3ControlPoint(mv,V,tmx,tmw,uvx[i]);
Nurbs3ControlPoint(mv,V,tmy,tmw,uvy[i]);
Nurbs3ControlPoint(mv,V,tmz,tmw,uvz[i]);
B3SplineControlPoint(mv,V,tmw,uvw[i]);
for(k=0;k<3*mv-17;k++)
{
pt[i][k][0]=uvx[i][k];
pt[i][k][1]=uvy[i][k];
pt[i][k][2]=uvz[i][k];
pt[i][k][3]=uvw[i][k];
}
}
}
//计算双二次（2x2）Nurbs样条曲面所有控制多边形顶点，并保存在pt[][][]中
//mu,mv分别为节点矢量U[],V[]的最大下标值
void Nurbs2FControlPoint(int mu,float U[],int mv,float V[],float px[],float py[],float pz[],float W[],float pt[100][100][4])
{
int i,j,k,dp;
float tmx[50],tmy[50],tmz[50],tmw[50];
float tmpx[50][100],tmpy[50][100],tmpz[50][100],tmpw[50][100];
float uvx[100][100],uvy[100][100],uvz[100][100],uvw[100][100];
for(i=0;i<mv-2;i++)
{
dp=i*(mu-2);
for(j=dp;j<mu-2+dp;j++)
{
tmx[j-dp]=px[j];
tmy[j-dp]=py[j];
tmz[j-dp]=pz[j];
tmw[j-dp]=W[j];
}
Nurbs2ControlPoint(mu,U,tmx,tmw,tmpx[i]);
Nurbs2ControlPoint(mu,U,tmy,tmw,tmpy[i]);
Nurbs2ControlPoint(mu,U,tmz,tmw,tmpz[i]);
B2SplineControlPoint(mu,U,tmw,tmpw[i]);
}
for(i=0;i<2*mu-7;i++)
{
for(j=0;j<mv-2;j++)
{
tmx[j]=tmpx[j][i];
tmy[j]=tmpy[j][i];
tmz[j]=tmpz[j][i];
tmw[j]=tmpw[j][i];
}
Nurbs2ControlPoint(mv,V,tmx,tmw,uvx[i]);
Nurbs2ControlPoint(mv,V,tmy,tmw,uvy[i]);
Nurbs2ControlPoint(mv,V,tmz,tmw,uvz[i]);
B2SplineControlPoint(mv,V,tmw,uvw[i]);
for(k=0;k<2*mv-7;k++)
{
pt[i][k][0]=uvx[i][k];
pt[i][k][1]=uvy[i][k];
pt[i][k][2]=uvz[i][k];
pt[i][k][3]=uvw[i][k];
}
}
}
//------------------------------------------------------------------------------
//计算双三次(3x3次)或双二次(2x2次)Nurbs样条曲面上所有的点并保存在bs[][][]中
//nu,mv分别为节点矢量U[],V[]的最大下标
//uk,vk分别为B样条曲面(u,v)方向上的网格数
//p为曲面的次数
void NurbsFace(int p,int nu,float U[],int uk,int mv,float V[],int vk,
float px[],float py[],float pz[],float w[],float bs[161][161][3])
{
int udk[20],vdk[20],i,j,k,l,hu,sv,du,dv;
float tp[100][100][4],td[161][161][3];
float tmx[4][4],tmy[4][4],tmz[4][4],tmw[4][4];
du=nu-2*p;
dv=mv-2*p;
SetGridCount(du,uk,udk);
SetGridCount(dv,vk,vdk);
if(p==3)
Nurbs3FControlPoint(nu,U,mv,V,px,py,pz,w,tp);
if(p==2)
Nurbs2FControlPoint(nu,U,mv,V,px,py,pz,w,tp);
for(i=0;i<dv;i++)
{
for(k=0;k<du;k++)
{
for(j=i*p;j<p+1+i*p;j++)
for(l=k*p;l<p+1+k*p;l++)
{
tmx[j-i*p][l-k*p]=tp[l][j][0];
tmy[j-i*p][l-k*p]=tp[l][j][1];
tmz[j-i*p][l-k*p]=tp[l][j][2];
tmw[j-i*p][l-k*p]=tp[l][j][3];
}
NuBezierFacePoint(p,udk[k],vdk[i],tmx,tmy,tmz,tmw,td);
for(sv=i*vdk[0];sv<=vdk[i]+i*vdk[0];sv++)
for(hu=k*udk[0];hu<=udk[k]+k*udk[0];hu++)
{
bs[sv][hu][0]=td[sv-i*vdk[0]][hu-k*udk[0]][0];
bs[sv][hu][1]=td[sv-i*vdk[0]][hu-k*udk[0]][1];
bs[sv][hu][2]=td[sv-i*vdk[0]][hu-k*udk[0]][2];
}
}
}
}
//*-*-*-*-*-*-*-*-*-*-*-*-*-*-* 绘制曲面部分 *-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*
//计算多边形的外法线返回值tmN[]
void getN(float x[3],float y[3],float z[3],float tmN[3])
{
float p1,p2,p3,q1,q2,q3;
float nx,ny,nz;
p1=x[1]-x[0];
p2=y[1]-y[0];
p3=z[1]-z[0];
q1=x[2]-x[1];
q2=y[2]-y[1];
q3=z[2]-z[1];
nx=p2*q3-q2*p3;
ny=q1*p3-p1*q3;
nz=p1*q2-p2*q1;
tmN[0]=nx;
tmN[1]=ny;
tmN[2]=nz;
}
//-----------------------------------------------------------------------------------
//显示B样条曲面
//fill取值为0或1
void ShowSurface(int u,int v,float bs[161][161][3],int fill)
{
int i,j;
float x[3],y[3],z[3],tmn[3];
for(i=0;i<=v;i++)
for(j=0;j<=u;j++)
{
if(fill!=0)
{
x[0]=bs[i][j][0];
x[1]=bs[i+1][j][0];
x[2]=bs[i+1][j+1][0];
y[0]=bs[i][j][1];
y[1]=bs[i+1][j][1];
y[2]=bs[i+1][j+1][1];
z[0]=bs[i][j][2];
z[1]=bs[i+1][j][2];
z[2]=bs[i+1][j+1][2];
getN(x,y,z,tmn);
glEnable(GL_NORMALIZE);
glBegin(GL_QUADS);
glNormal3f(tmn[0],tmn[1],tmn[2]);
if(j<u)
{
glVertex3f(bs[i][j][0],bs[i][j][1],bs[i][j][2]);
glVertex3f(bs[i][j+1][0],bs[i][j+1][1],bs[i][j+1][2]);
}
if(i<v)
{
glVertex3f(bs[i+1][j+1][0],bs[i+1][j+1][1],bs[i+1][j+1][2]);
glVertex3f(bs[i+1][j][0],bs[i+1][j][1],bs[i+1][j][2]);
}
glEnd();
glDisable(GL_NORMALIZE);
}
else{
glBegin(GL_LINES);
if(j<u)
{
glVertex3f(bs[i][j][0],bs[i][j][1],bs[i][j][2]);
glVertex3f(bs[i][j+1][0],bs[i][j+1][1],bs[i][j+1][2]);
}
if(i<v)
{
glVertex3f(bs[i][j][0],bs[i][j][1],bs[i][j][2]);
glVertex3f(bs[i+1][j][0],bs[i+1][j][1],bs[i+1][j][2]);
}
glEnd();
}
}
}
#endif
#endif
建立库文件“myNurbs.h”保存在include目录下，在文件开始处写上#include "myNurbs.h"即可用各函数的功能。
例如：
#include "windows.h"
#include "glut.h"
#include "myNurbs.h"
float x[]={17,17,-17,-17,-17,17,17,
10,10,-10,-10,-10,10,10,
15,15,-15,-15,-15,15,15,
30,30,-30,-30,-30,30,30,
20,20,-20,-20,-20,20,20,
10,10,-10,-10,-10,10,10,
0,0,0,0,0,0,0};
float y[]={100,100,100,100,100,100,100,
90,90,90,90,90,90,90,
60,60,60,60,60,60,60,
30,30,30,30,30,30,30,
10,10,10,10,10,10,10,
0,0,0,0,0,0,0,
0,0,0,0,0,0,0};
float z[]={60,77,77,60,43,43,60,
60,70,70,60,50,50,60,
60,75,75,60,45,45,60,
60,90,90,60,30,30,60,
60,80,80,60,40,40,60,
60,70,70,60,50,50,60,
60,60,60,60,60,60,60};
float w[]={1,0.5,0.5,1,0.5,0.5,1,
1,0.5,0.5,1,0.5,0.5,1,
1,0.5,0.5,1,0.5,0.5,1,
1,0.5,0.5,1,0.5,0.5,1,
1,0.5,0.5,1,0.5,0.5,1,
1,0.5,0.5,1,0.5,0.5,1,
1,0.5,0.5,1,0.5,0.5,1};
float u[]={0,0,0,0.25,0.5,0.5,0.75,1,1,1};
float v[]={0,0,0,0.1,0.4,0.6,0.95,1,1,1};
float suv[161][161][3];
float r=0.0f;
float dx=1.0f;
float mx=0.0f;
void lightm()
{
GLfloat lamb[4]={0.35f,0.35f,0.35f,1.0f};
GLfloat ldif[4]={0.35f,0.35f,0.35f,1.0f};
GLfloat lspe[4]={0.55f,0.55f,0.55f,1.0f};
GLfloat lpos[4]={200.0f,200.0f,60.0f,1.0f};
GLfloat mamb[4]={0.5f,0.5f,0.5f,1.0f};
GLfloat mdif[4]={0.5f,0.5f,0.5f,1.0f};
GLfloat mspe[4]={0.7f,0.7f,0.7f,1.0f};
GLfloat memi[4]={0.0f,0.0f,0.0f,1.0f};
GLfloat mshininess=128.0f;
glLightfv(GL_LIGHT1,GL_AMBIENT,lamb);
glLightfv(GL_LIGHT1,GL_DIFFUSE,ldif);
glLightfv(GL_LIGHT1,GL_SPECULAR,lspe);
glLightfv(GL_LIGHT1,GL_POSITION,lpos);
glMaterialfv(GL_FRONT_AND_BACK,GL_AMBIENT,mamb);
glMaterialfv(GL_FRONT_AND_BACK,GL_DIFFUSE,mdif);
glMaterialfv(GL_FRONT_AND_BACK,GL_SPECULAR,mspe);
glMaterialfv(GL_FRONT_AND_BACK,GL_EMISSION,memi);
glMaterialf(GL_FRONT_AND_BACK,GL_SHININESS,mshininess);
}
void TimerFunction(int value)
{
if(r<360.f)
r+=1.0f;
else
r=0.0f;
mx+=dx;
if(mx>50)
dx=-dx;
if(mx<-100)
dx=-dx;
glutPostRedisplay();
glutTimerFunc(33,TimerFunction,1);
}
void RenderScene()
{
glClear(GL_COLOR_BUFFER_BIT|GL_DEPTH_BUFFER_BIT);
glPushMatrix();
glColor3f(1.0f,1.0f,1.0f);
glTranslatef(0,-60,0);
glRotatef(-30,1.0,0.0,0.0);
glRotatef(-2*r,0.0,1.0,0.0);
glRotatef(-r,1.0,1.0,1.0);
//NurbsFace(2,9,u,40,9,v,40,x,y,z,w,suv);
//ShowSurface(40,40,suv,0);
NurbsFace(2,9,u,160,9,v,160,x,y,z,w,suv);
ShowSurface(160,160,suv,1);
glPopMatrix();
glutSwapBuffers();
}
void SetupRC()
{
glClearColor(0.0f,0.0f,0.0f,0.0f);
lightm();
glEnable(GL_DEPTH_TEST);
glEnable(GL_LIGHTING);
glLightModelf(GL_LIGHT_MODEL_LOCAL_VIEWER,1.0);
glEnable(GL_LIGHT1);
glEnable(GL_COLOR_MATERIAL);
}
void WindowSize(GLsizei w,GLsizei h)
{
GLfloat aspectRatio;
GLfloat tmb=110.0;
if(h==0)
h=1;
glViewport(0,0,w,h);
glMatrixMode(GL_PROJECTION);
glLoadIdentity();
aspectRatio=(GLfloat)w/(GLfloat)h;
if(w<=h)
glOrtho(-tmb,tmb,-tmb/aspectRatio,tmb/aspectRatio,10*tmb,-10*tmb);
else
glOrtho(-tmb*aspectRatio,tmb*aspectRatio,-tmb,tmb,10*tmb,-10*tmb);
glMatrixMode(GL_MODELVIEW);
glLoadIdentity();
}
int main(int argc,char *argv[])
{
glutInit(&argc,argv);
glutInitDisplayMode(GLUT_DOUBLE|GLUT_RGBA);
glutInitWindowSize(1024,768);
glutCreateWindow("B-NURBS");
glutDisplayFunc(RenderScene);
glutReshapeFunc(WindowSize);
glutTimerFunc(33,TimerFunction,1);
SetupRC();
glutMainLoop();
return 0;
}
参数曲面设计
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