b样条曲面

实验四：B 样条曲面

一.实验目的

用多个B 样条曲线画出一个曲面，并能实现鼠标球滚动。

二.算法思想

B 样条曲面是B 样条曲线的拓广。一块m ⨯n 次B 样条曲面片的数学表示式：)()(),(,,00

w F u F

P w u P n j m

i m i n

j ij

∑∑===

w u , ∈［０，１］ 式中，ij P （i =0,1,2，…..,m;

j

=0,1,2,…..n ）是定义此曲面片的顶点位置向量矩阵，共计（m+1）

（n+1）个顶点。)()(,,w F u F n j m i 为B 样条基底函数，w u ,为参数。显然，m 与n 不一定相等，如m=n=3,则由4⨯4个顶点构成特征多面体，其相应的B 样条曲面片称为双三次B 样条曲面片。其中：

m i m i m k k m i k i m u c m u F )()1(!1)(10,--+-=+-=∑)!

1(!)!1(1

i m i m C i

m -++=+其中： 展开三次B 样条曲面数学表达式并写成矩阵

()()(

)

()

T

T s T

s W M w

w w w F w F w F w F UM u u u u F u F u F u F w F w F w F w F p p p p p p p p p p p p

p p p p u F u F u F u F w u Q =⎪⎪⎪⎪

⎪⎭

⎫

⎝⎛⎥⎥⎥⎥⎦⎤⎢

⎢⎢⎢

⎣⎡----=

=⎥⎥⎥⎥⎦

⎤⎢

⎢⎢⎢

⎣⎡----=⎥⎥⎥⎥⎦

⎤

⎢⎢⎢⎢⎣⎡⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡=10001133

3406313

3161)()()()(0141

030

303631331611

)()()()()()()()()()()()(),(2343212

3

432143213332

31302322212013121110

03020100

4321其中：

三.程序主要代码

#include

#include #include "ggltools.h" #include "gmatrix3d.h" #include "gvector3d.h" GMatrix3d gRotMatrix ; bool gIsLBtnDown =false ; int gMouseX =0; int gMouseY =0;

//控制点网络

GPoint3d **gCtrlGrid =NULL ; //

int gNumX=0;

int gNumY=0;

bool loadData(const char *fileName)

{

FILE *fp =fopen(fileName,"r");

if(fp == NULL)return false;

fscanf(fp,"%d %d",&gNumY,&gNumX);

printf("NumY=%d,NumX=%d\n",gNumY,gNumX);

int i,j;

float x,y,z;

gCtrlGrid = new GPoint3d *[gNumY];

for(i=0;i

{

gCtrlGrid[i]= new GPoint3d[gNumX];

for(j=0;j

{

fscanf(fp,"%f %f %f\n",&x,&y,&z);

gCtrlGrid[i][j].set (x,y,z);

printf("%.1f %.1f %.1f\t",x,y,z);

}

printf("\n");

}

fclose(fp);

return true;

}

void drawCtrlGrid()

{

int i,j;

glColor3f(1,1,1);

for(i=0;i

{

for(j=0;j

{

glBegin(GL_LINES);

glVertex3dv(gCtrlGrid[i][j]);

glVertex3dv(gCtrlGrid[i][j+1]);

glEnd();

}

}

for(j=0;j

{

for(i=0;i

{

glBegin(GL_LINES);

glVertex3dv(gCtrlGrid[i][j]);

glVertex3dv(gCtrlGrid[i+1][j]);

glEnd();

}

}

}

GPoint3d cubicBSpline(int i0,int j0,GPoint3d **ctrlGrid,double u,double v)

{

double bu[4] ,bv[4];

bu[0]= (-u*u*u+3*u*u-3*u+1)/6.0;

bu[1]= (3*u*u*u-6*u*u+4)/6.0;

bu[2]= (-3*u*u*u+3*u*u+3*u+1)/6.0;

bu[3]= (u*u*u)/6.0;

bv[0]= (-v*v*v+3*v*v-3*v+1)/6.0;

bv[1]= (3*v*v*v-6*v*v+4)/6.0;

bv[2]= (-3*v*v*v+3*v*v+3*v+1)/6.0;

bv[3]= (v*v*v)/6.0;

int i,j,k;

GPoint3d pt;

for(k=0;k<3;k++)

{

pt[k]=0;

for(i=0;i<4;i++)

{

for(j=0;j<4;j++)

{

pt[k]+=ctrlGrid[i0+i][j0+j][k]*bu[j]*bv[i];

}

}

}

return pt;

}

void drawBSpline(GPoint3d **ctrlGrid,int ny,int nx)

{

int i,j,nu,nv,iu,iv;

GPoint3d pt0,pt1,pt2,pt3;

double u,du,v,dv;

nu=10;

du=1.0/nu;

nv=10;

dv=1.0/nv;

glColor3f(1,1,0);

glPolygonMode(GL_FRONT_AND_BACK,GL_LINE);

for(i=0;i

{

for(j=0;j

{

for(iv=0,v=0;iv

{

for(iu=0,u=0;iu

{

pt0=cubicBSpline(i,j,ctrlGrid,u,v);

pt1=cubicBSpline(i,j,ctrlGrid,u,v+dv);

pt2=cubicBSpline(i,j,ctrlGrid,u+du,v+dv);

pt3=cubicBSpline(i,j,ctrlGrid,u+du,v);

glBegin(GL_QUADS);

glVertex3dv(pt0);

glVertex3dv(pt1);

glVertex3dv(pt2);

glVertex3dv(pt3);

glEnd();

}

}