B样条曲线曲面和NURBS曲线曲面C语言算法源程序.docx
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B样条曲线曲面和NURBS曲线曲面C语言算法源程序
学习小结:
前面学习了Bezier曲线,B样条基函数和B样条曲线的一些基础知识。
掌握关键问题是一条B样条曲线间的多段曲线的光滑连接。
因为现在是用多段Bezier曲线来描绘
一条B样条曲线,所以问题变为两段Bezier曲线间光滑连接。
两段Bezier曲线段(3次)
B1和B2光滑连接的条件:
(1).要求B1和B2有共同的连接点,即&连续。
(2).要求B1和B2在连接点处有成比例的一阶导数,即G连续。
由端点处的一阶导数
1
B1
(1)3(F3P2),B2(0)3(QiQ。
),为实现G连续,则有:
B2(0)B1
(1)即:
Q1QoRP2
这也表明,P2,B(Qo),Q三点共线。
如下图表示了一条
3次B样条曲线的所有控制多边形:
E(P1)
P2
(P
/P
用P0
10
P4
图5.3次B样条曲线和所有控制多边形
图5中,P0至P6为原始3次B样条曲线控制多边形顶点,P0至P12是计算后最终形成
样条曲线控制多边形顶点。
图6.双二次(2x2)B样条曲面
6.B样条曲线曲面和NURBS曲线曲面的C语言实现算法源程序#ifndef_mynurbs_h
#ifndefMYNURBSH
#include"gl\gl.h"
#include"math.h"
if(u==U[n+1])//特殊情况returnn;
//进行二分搜索
low=p;
high=n+1;
mid=(int)(low+high)/2;while(uU[mid])
{if(u
mid=(int)(low+high)/2;
if(u>=U[mid]&&u
}
returnmid;//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
voidBasisFunction(inti,intp,floatu,floatU[],floatN[])
{
intj,di,dp,k;
floattul,tur,left,right;
floattmpN[50][50];
for(k=0;k<=p;k++)
dp=0;
for(di=i+p-k;di>=i-k;di--){if(u>=U[di]&&u
tmpN[di][0]=1;
else
tmpN[di][0]=0;
dp+=1;
for(j=1;j{tul=U[di+j]-U[di];tur=U[di+j+1]-U[di+1];if(tul!=0)left=(u-U[di])/tul;elseleft=0;if(tur!=0)right=(U[di+j+1]-u)/tur;elseright=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>2voidDerBasisFunc(inti,intp,floatu,floatU[],floatNP[]){intj,di,dp,k;floattul,tur,left,right,saved,dl,dr;floattmpN[50][50];for(k=0;k<=p;k++){dp=0;for(di=i+p-k;di>=i-k;di--){if(u>=U[di]&&utmpN[di][0]=1;elsetmpN[di][0]=0;dp+=1;for(j=1;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;elseleft=0,dl=0;if(tur!=0)right=(U[di+j+1]-u)/tur,dr=1/tur;elseright=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*****************//计算参数u的p次基函数值并存在BC[]中voidBernsteinFunc(intp,doublet,floatBC[]){for(inti=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}}//获取p次Bezier曲线上的lines个点的值voidBezierPoint(intp,floatpx[],floatpy[],floatpz[],intlines,floattmp[][3]){floatBC[20];inti,j;for(j=0;j<=lines;j++){doublet=j/(float)lines;BernsteinFunc(p,t,BC);tmp[j][0]=tmp[j][1]=tmp[j][2]=0;for(i=0;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pw[],intvoidNBezierPoint(intp,floatpx[],floatpy[],floatpz[],floatlines,floattmp[][4]){floatx,y,z,w,BC[20];inti,j;for(j=0;j<=lines;j++){doublet=j/(float)lines;BernsteinFunc(p,t,BC);x=y=z=w=0;for(i=0;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voidBezier(intp,floatpx[],floatpy[],floatpz[],intlines){floatpt[100][3];intj;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voidNBezier(intp,floatpx[],floatpy[],floatpz[],floatw[],intlines){floatpt[100][4];intj;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py[][4],floatvoidBezierFacePoint(intp,intu,intv,floatpx[][4],floatpz[][4],floatpt[161][161][3]){floaturx[11][161],ury[11][161],urz[11][161];floattx[11],ty[11],tz[11],tmp[161][3];inti,j,k;for(j=0;j{for(i=0;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{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py[][4],floatvoidNuBezierFacePoint(intp,intu,intv,floatpx[][4],floatpz[][4],floatw[][4],floatpt[161][161][3]){floaturx[11][161],ury[11][161],urz[11][161],urw[11][161];floattx[11],ty[11],tz[11],tw[11],tmp[161][4];inti,j,k;for(j=0;j{for(i=0;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{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**************//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voidBSplineDer(intn,intp,floatU[],floatP[],floatDer[]){floatN[100],tmp;inti,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voidBSplinePoint(intn,intp,floatU[],floatP[],floatPoi[]){floatN[100],tmp;inti,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voidB3SplineControlPoint(intm,floatU[],floatP[],floatCP[]){intn,k,i,cp,p;floatPoi[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{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voidB2SplineControlPoint(intm,floatU[],floatP[],floatCP[]){intn,k,tm,i,cp,p;floatPoi[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{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voidBSpline3L(intm,floatU[],floatpx[],floatpy[],floatpz[]){floatpcx[100],pcy[100],pcz[100],drx[4],dry[4],drz[4];inti,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{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voidBSpline2L(intm,floatU[],floatpx[],floatpy[],floatpz[]){floatpcx[100],pcy[100],pcz[100],drx[3],dry[3],drz[3];inti,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{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px[],floatvoidBS3FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-3);for(j=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{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px[],floatvoidBS2FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-2);for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
tul=U[di+j]-U[di];
tur=U[di+j+1]-U[di+1];
if(tul!
=0)
left=(u-U[di])/tul;
left=0;
if(tur!
right=(U[di+j+1]-u)/tur;
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
//p为B样条函数次数P>2
voidDerBasisFunc(inti,intp,floatu,floatU[],floatNP[])
floattul,tur,left,right,saved,dl,dr;
for(di=i+p-k;di>=i-k;di--)
if(u>=U[di]&&u
for(j=1;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;elseleft=0,dl=0;if(tur!=0)right=(U[di+j+1]-u)/tur,dr=1/tur;elseright=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*****************//计算参数u的p次基函数值并存在BC[]中voidBernsteinFunc(intp,doublet,floatBC[]){for(inti=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}}//获取p次Bezier曲线上的lines个点的值voidBezierPoint(intp,floatpx[],floatpy[],floatpz[],intlines,floattmp[][3]){floatBC[20];inti,j;for(j=0;j<=lines;j++){doublet=j/(float)lines;BernsteinFunc(p,t,BC);tmp[j][0]=tmp[j][1]=tmp[j][2]=0;for(i=0;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pw[],intvoidNBezierPoint(intp,floatpx[],floatpy[],floatpz[],floatlines,floattmp[][4]){floatx,y,z,w,BC[20];inti,j;for(j=0;j<=lines;j++){doublet=j/(float)lines;BernsteinFunc(p,t,BC);x=y=z=w=0;for(i=0;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voidBezier(intp,floatpx[],floatpy[],floatpz[],intlines){floatpt[100][3];intj;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voidNBezier(intp,floatpx[],floatpy[],floatpz[],floatw[],intlines){floatpt[100][4];intj;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py[][4],floatvoidBezierFacePoint(intp,intu,intv,floatpx[][4],floatpz[][4],floatpt[161][161][3]){floaturx[11][161],ury[11][161],urz[11][161];floattx[11],ty[11],tz[11],tmp[161][3];inti,j,k;for(j=0;j{for(i=0;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{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py[][4],floatvoidNuBezierFacePoint(intp,intu,intv,floatpx[][4],floatpz[][4],floatw[][4],floatpt[161][161][3]){floaturx[11][161],ury[11][161],urz[11][161],urw[11][161];floattx[11],ty[11],tz[11],tw[11],tmp[161][4];inti,j,k;for(j=0;j{for(i=0;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{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**************//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voidBSplineDer(intn,intp,floatU[],floatP[],floatDer[]){floatN[100],tmp;inti,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voidBSplinePoint(intn,intp,floatU[],floatP[],floatPoi[]){floatN[100],tmp;inti,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voidB3SplineControlPoint(intm,floatU[],floatP[],floatCP[]){intn,k,i,cp,p;floatPoi[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{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voidB2SplineControlPoint(intm,floatU[],floatP[],floatCP[]){intn,k,tm,i,cp,p;floatPoi[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{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voidBSpline3L(intm,floatU[],floatpx[],floatpy[],floatpz[]){floatpcx[100],pcy[100],pcz[100],drx[4],dry[4],drz[4];inti,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{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voidBSpline2L(intm,floatU[],floatpx[],floatpy[],floatpz[]){floatpcx[100],pcy[100],pcz[100],drx[3],dry[3],drz[3];inti,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{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px[],floatvoidBS3FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-3);for(j=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{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px[],floatvoidBS2FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-2);for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
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;
left=0,dl=0;
right=(U[di+j+1]-u)/tur,dr=1/tur;
elseright=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
*****************
//计算参数u的p次基函数值并存在BC[]中
voidBernsteinFunc(intp,doublet,floatBC[])
for(inti=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
//获取p次Bezier曲线上的lines个点的值
voidBezierPoint(intp,floatpx[],floatpy[],floatpz[],intlines,floattmp[][3])
floatBC[20];
inti,j;
for(j=0;j<=lines;j++)
doublet=j/(float)lines;
BernsteinFunc(p,t,BC);tmp[j][0]=tmp[j][1]=tmp[j][2]=0;
for(i=0;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
pw[],int
voidNBezierPoint(intp,floatpx[],floatpy[],floatpz[],floatlines,floattmp[][4])
floatx,y,z,w,BC[20];
BernsteinFunc(p,t,BC);
x=y=z=w=0;
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
voidBezier(intp,floatpx[],floatpy[],floatpz[],intlines)
floatpt[100][3];
intj;
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
voidNBezier(intp,floatpx[],floatpy[],floatpz[],floatw[],intlines)
floatpt[100][4];
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]);
//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
py[][4],float
voidBezierFacePoint(intp,intu,intv,floatpx[][4],floatpz[][4],floatpt[161][161][3])
floaturx[11][161],ury[11][161],urz[11][161];
floattx[11],ty[11],tz[11],tmp[161][3];
inti,j,k;
for(j=0;j
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
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
voidNuBezierFacePoint(intp,intu,intv,floatpx[][4],floatpz[][4],floatw[][4],floatpt[161][161][3])
floaturx[11][161],ury[11][161],urz[11][161],urw[11][161];
floattx[11],ty[11],tz[11],tw[11],tmp[161][4];
tw[i]=w[i][j];
NBezierPoint(p,tx,ty,tz,tw,v,tmp);
for(k=0;k<=v;k++)
urw[j][k]=tmp[k][3];
tz[k]=urz[k][i];tw[k]=urw[k][i];
NBezierPoint(p,tx,ty,tz,tw,u,tmp);
********
*******
B样条曲线曲面部
**************
//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
voidBSplineDer(intn,intp,floatU[],floatP[],floatDer[])
floatN[100],tmp;
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
voidBSplinePoint(intn,intp,floatU[],floatP[],floatPoi[])
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
voidB3SplineControlPoint(intm,floatU[],floatP[],floatCP[])
intn,k,i,cp,p;
floatPoi[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{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voidB2SplineControlPoint(intm,floatU[],floatP[],floatCP[]){intn,k,tm,i,cp,p;floatPoi[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{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voidBSpline3L(intm,floatU[],floatpx[],floatpy[],floatpz[]){floatpcx[100],pcy[100],pcz[100],drx[4],dry[4],drz[4];inti,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{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voidBSpline2L(intm,floatU[],floatpx[],floatpy[],floatpz[]){floatpcx[100],pcy[100],pcz[100],drx[3],dry[3],drz[3];inti,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{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px[],floatvoidBS3FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-3);for(j=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{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px[],floatvoidBS2FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-2);for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
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
voidB2SplineControlPoint(intm,floatU[],floatP[],floatCP[])
intn,k,tm,i,cp,p;
floatPoi[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{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voidBSpline3L(intm,floatU[],floatpx[],floatpy[],floatpz[]){floatpcx[100],pcy[100],pcz[100],drx[4],dry[4],drz[4];inti,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{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voidBSpline2L(intm,floatU[],floatpx[],floatpy[],floatpz[]){floatpcx[100],pcy[100],pcz[100],drx[3],dry[3],drz[3];inti,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{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px[],floatvoidBS3FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-3);for(j=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{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px[],floatvoidBS2FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-2);for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
k=(int)i/2;
CP[i]=Poi[k];
CP[i+1]=P[tm];
tm++;
//绘制3次B样条曲线
voidBSpline3L(intm,floatU[],floatpx[],floatpy[],floatpz[])
floatpcx[100],pcy[100],pcz[100],drx[4],dry[4],drz[4];
inti,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]);
glColor3f(1.0f,0.0f,0.0f);*/
tmcp=m-7;
for(i=0;i<=tmcp;i++)
for(j=i*3;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
voidBSpline2L(intm,floatU[],floatpx[],floatpy[],floatpz[])
floatpcx[100],pcy[100],pcz[100],drx[3],dry[3],drz[3];
B2SplineControlPoint(m,U,px,pcx);
B2SplineControlPoint(m,U,py,pcy);
B2SplineControlPoint(m,U,pz,pcz);tmcp=m-5;
for(j=i*2;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
px[],float
voidBS3FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3])
inti,j,k,dp;
floattmx[50],tmy[50],tmz[50];
floattmpx[50][100],tmpy[50][100],tmpz[50][100];
floatuvx[100][100],uvy[100][100],uvz[100][100];
for(i=0;i{dp=i*(mu-3);for(j=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{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px[],floatvoidBS2FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-2);for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
dp=i*(mu-3);
for(j=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{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px[],floatvoidBS2FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-2);for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
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{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px[],floatvoidBS2FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3]){inti,j,k,dp;floattmx[50],tmy[50],tmz[50];floattmpx[50][100],tmpy[50][100],tmpz[50][100];floatuvx[100][100],uvy[100][100],uvz[100][100];for(i=0;i{dp=i*(mu-2);for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
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
voidBS2FaceControlPoint(intmu,floatU[],intmv,floatV[],floatpy[],floatpz[],floatpt[100][100][3])
for(i=0;i{dp=i*(mu-2);for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
dp=i*(mu-2);
for(j=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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
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{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voidSetGridCount(intdt,inttu,inttmk[]){inti,tm;tm=tu%dt;for(i=0;itmk[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
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++)
////设置网格数
voidSetGridCount(intdt,inttu,inttmk[])
inti,tm;
tm=tu%dt;
for(i=0;itmk[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
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
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