【计算机图形学】四、B样条曲线的生成

1.算法

2. 源代码

#include "stdafx.h"#include "GL/glut.h"#include "stdlib.h"void init(){glClearColor(1.0,1.0,1.0,0.0);glMatrixMode(GL_PROJECTION);gluOrtho2D(0.0,600.0,0.0,400.0);}typedef struct point{float x,y;}point;void setPixel(point BsplinePt){glBegin(GL_POINTS);glVertex2f(BsplinePt.x,BsplinePt.y);glEnd();}float polyNomial(int k,int d,float u){if(d==1){if(u>=float(k)&&u<=float (k+1))return 1.0;elsereturn 0.0;}elsereturn (u-k)/(d-1)*polyNomial(k,d-1,u)+(k+d-u)/(d-1)*polyNomial(k+1,d-1,u);}void computeBsplinePt(point* BsplinePt,point* CtrlPt,float u,int nCtrlPt,int degree){int k;float Bkd;BsplinePt->x=0.0;BsplinePt->y=0.0;for(k=0;k<=nCtrlPt-1;k++){Bkd=polyNomial(k,degree,u);BsplinePt->x+=CtrlPt[k].x*Bkd;BsplinePt->y+=CtrlPt[k].y*Bkd;}}void Bspline(point* CtrlPt,int nCtrlPt,int degree){float u,du=0.001;point BsplinePt;    for(u=degree-1;u<=nCtrlPt;){computeBsplinePt(&BsplinePt,CtrlPt,u,nCtrlPt,degree);setPixel(BsplinePt);u+=du;}}void render(){glClear(GL_COLOR_BUFFER_BIT);glColor3f(1.0,0.0,0.0);point CtrlPt[5]={{50.0,50.0},{150.0,300.0},{250.0,150.0},{300.0,350.0},{500.0,50.0}};int nCtrlPts=5,degree=3;Bspline(CtrlPt,nCtrlPts,degree);glFlush();}int main(int argc, char* argv[]){glutInit(&argc,argv);glutInitDisplayMode(GLUT_SINGLE|GLUT_RGB);glutInitWindowPosition(50,100);glutInitWindowSize(600,400);glutCreateWindow("B Spline");init();glutDisplayFunc(render);glutMainLoop();return 0;}

3. 结果