#include<stdio.h>
#include<dos.h>
#include<graphics.h>
void main()
{
int gd=DETECT,gm;
int color;
int x=10,y=1,inc_x=10,inc_y=10;
int poly[10];
initgraph(&gd,&gm,"..\\bgi");
while(!kbhit())
{
x += inc_x;
if(x > getmaxx()-175)
inc_x = -5;
if(x < 0 )
inc_x = 10;
y += inc_y;
if(y > 200)
inc_y = -10;
if(y < 0 )
inc_y = 10;
cleardevice();
setcolor(WHITE);
setbkcolor(CYAN);
poly[0]=100+x;
poly[1]=50+y;
poly[2]=140+x;
poly[3]=100+y;
poly[4]=100+x;
poly[5]=155+y;
poly[6]=60+x;
poly[7]=100+y;
poly[8]=100+x;
poly[9]=50+y;
drawpoly(5,poly);
setfillstyle(SOLID_FILL,LIGHTRED);
fillpoly(5,poly);
setcolor(LIGHTBLUE);
setlinestyle(SOLID_LINE,1,3);
line(100+x,155+y,100+x,300+y);
line(100+x,155+y,110+x,300+y);
line(100+x,155+y,90+x,300+y);
setcolor(WHITE);
setlinestyle(SOLID_LINE,1,0);
line(100,480,100+x,90+y);
line(100+x,90+y,130+x,100+y);
line(100+x,90+y,70+x,100+y);
line(100+x,90+y,100+x,70+y);
delay(260);
}
setlinestyle(SOLID_LINE,0,0);
closegraph();
}
#include<dos.h>
#include<graphics.h>
void main()
{
int gd=DETECT,gm;
int color;
int x=10,y=1,inc_x=10,inc_y=10;
int poly[10];
initgraph(&gd,&gm,"..\\bgi");
while(!kbhit())
{
x += inc_x;
if(x > getmaxx()-175)
inc_x = -5;
if(x < 0 )
inc_x = 10;
y += inc_y;
if(y > 200)
inc_y = -10;
if(y < 0 )
inc_y = 10;
cleardevice();
setcolor(WHITE);
setbkcolor(CYAN);
poly[0]=100+x;
poly[1]=50+y;
poly[2]=140+x;
poly[3]=100+y;
poly[4]=100+x;
poly[5]=155+y;
poly[6]=60+x;
poly[7]=100+y;
poly[8]=100+x;
poly[9]=50+y;
drawpoly(5,poly);
setfillstyle(SOLID_FILL,LIGHTRED);
fillpoly(5,poly);
setcolor(LIGHTBLUE);
setlinestyle(SOLID_LINE,1,3);
line(100+x,155+y,100+x,300+y);
line(100+x,155+y,110+x,300+y);
line(100+x,155+y,90+x,300+y);
setcolor(WHITE);
setlinestyle(SOLID_LINE,1,0);
line(100,480,100+x,90+y);
line(100+x,90+y,130+x,100+y);
line(100+x,90+y,70+x,100+y);
line(100+x,90+y,100+x,70+y);
delay(260);
}
setlinestyle(SOLID_LINE,0,0);
closegraph();
}
denote the Bézier curve determined by any selection of points P0, P1, ..., Pn. Then to start,

![\begin{align} \mathbf{B}(t) = {} &\sum_{i=0}^n {n\choose i}(1 - t)^{n - i}t^i\mathbf{P}_i \\ = {} &(1 - t)^n\mathbf{P}_0 + {n\choose 1}(1 - t)^{n - 1}t\mathbf{P}_1 + \cdots \\ {} &\cdots + {n\choose n - 1}(1 - t)t^{n - 1}\mathbf{P}_{n - 1} + t^n\mathbf{P}_n,\quad t \in [0,1]\end{align}](http://upload.wikimedia.org/math/f/d/d/fdd94eee9ac9bd8ef46a0c8fbb003e69.png)
are the binomial coefficients.