#include <graphics.h>	
#include <stdlib.h>	
#include <stdio.h>	
#include <conio.h>	
#include <math.h>	
// this function initializes graphics mode	
// it will work only if you're using Borland C++ compiler & BGI drivers	
// if you're using another compiler you should overwrite body of this function	
void init_gr(void)	
{	
   /* request autodetection */	
   int gdriver = DETECT, gmode, errorcode;	
   /* initialize graphics mode */	
   initgraph(&gdriver, &gmode, "");	
   /* read result of initialization */	
   errorcode = graphresult();	
   if (errorcode != grOk)    /* an error occurred */	
   {	
      printf("Graphics error: %s\n", grapherrormsg(errorcode));	
      printf("Press any key to halt:");	
      getch();	
      exit(1);               /* return with error code */	
   }	
}	
// this function shuts graphics mode down	
// it will work only if you're using Borland C++ compiler & BGI drivers	
// if you're using another compiler you should overwrite body of this function	
void end_gr(void)	
{	
  closegraph();	
}	
// this function moves CP to (x,y) position	
// it will work only if you're using Borland C++ compiler & BGI drivers	
// if you're using another compiler you should overwrite body of this function	
void MoveTo(int x, int y)	
{	
  moveto(x,y);	
}	
// this function draws a line to (x,y) position	
// it will work only if you're using Borland C++ compiler & BGI drivers	
// if you're using another compiler you should overwrite body of this function	
void LineTo(int x, int y)	
{	
  lineto(x,y);	
}	
// this function draws a line from (x1,y1) to (x2,y2)	
// it will work only if you're using Borland C++ compiler & BGI drivers	
// if you're using another compiler you should overwrite body of this function	
void Line(int x1, int y1, int x2, int y2)	
{	
  line(x1,y1,x2,y2);	
}	
const N=21; // number of points	
const M=300.0; // number of steps between two points	
// coordinates of all given points	
int x[N]={50,25,50,125,200,225,275,475,590,615,615,615,600,475,275,225,200,125,50,25,50};	
int y[N]={140,100,60,40,70,90,85,75,80,85,100,115,120,125,115,110,130,160,140,100,60};	
// coefficients	
float t,xA,xB,xC,xD,yA,yB,yC,yD,a0,a1,a2,a3,b0,b1,b2,b3;	
int n,i,j,first;	
int main(void)	
{	
  // initializing graphics mode	
  init_gr();	
   /* mark the given points */	
   for (i=0;i<N;i++)	
   {	
     Line(x[i]-4,y[i]-4,x[i]+4,y[i]+4);	
     Line(x[i]+4,y[i]-4,x[i]-4,y[i]+4);	
   }	
   /* main loop */	
   first=1;	
   for(i=1;i<N-2;i++)	
   {	
     // calculating coefficients	
     xA=x[i-1]; xB=x[i]; xC=x[i+1]; xD=x[i+2];	
     yA=y[i-1]; yB=y[i]; yC=y[i+1]; yD=y[i+2];	
     a3=(-xA+3*(xB-xC)+xD)/6.0;  b3=(-yA+3*(yB-yC)+yD)/6.0;	
     a2=(xA-2*xB+xC)/2.0;        b2=(yA-2*yB+yC)/2.0;	
     a1=(xC-xA)/2.0;             b1=(yC-yA)/2.0;	
     a0=(xA+4*xB+xC)/6.0;        b0=(yA+4*yB+yC)/6.0;	
     for (j=0;j<M;j++) // drawing curve between two given points	
     {	
       t=(float)j/(float)M;	
       if (first)	
       {	
         first=0;	
         MoveTo(((a3*t+a2)*t+a1)*t+a0,((b3*t+b2)*t+b1)*t+b0);	
       } else LineTo(((a3*t+a2)*t+a1)*t+a0,((b3*t+b2)*t+b1)*t+b0);	
     }	
   }	
   /* clean up */	
   getch();	
   end_gr();	
 
   return 0;	
}