#include<graphics.h>
#include<stdlib.h>
#include<math.h>
#include<conio.h>
#include<iostream.h>

void Curve(int x1, int y1, int x2, int y2,int x3, int y3,int x4, int y4, float);
void curve(int x1, int y1, int x2, int y2,int x3, int y3,int x4, int y4, float);
void main()
{
int gdriver = DETECT, gmode, errorcode;
initgraph(&gdriver, &gmode, "c:\\la\\tc\\bgi");

int x1=500 , y1=400;
int x2=300 , y2=10;
int x3=100,  y3=300 ;
int x4=100 , y4=100;
curve(x1, y1, x2, y2, x3, y3, x4, y4, 10.0);
Curve(x1, y1, x2, y2, x3, y3, x4, y4, 100.0);
setcolor(4);
circle(x1,y1,5);
circle(x2,y2,5);
circle(x3,y3,5);
circle(x4,y4,5);
getch();
closegraph();



}

void Curve(int x1, int y1, int x2, int y2,int x3, int y3,int x4, int y4, float Step)
{
	double x,y,t,Step_Size, ax, ay, bx, by, cx, cy, dx = (float) x1, dy = (float) y1;
	Step_Size = 1.0 /Step;


	ax = -x1 + (3 * x2) - (3 * x3) + x4;
	ay = -y1 + (3 * y2) - (3 * y3) + y4;

	bx = (3 * x1) - (6 * x2) + (3 * x3);
	by = (3 * y1) - (6 * y2) + (3 * y3);

	cx = (-3 * x1) + (3 * x2);
	cy = (-3 * y1) + (3 * y2);

	moveto(x1,y1);
	for (int i = 0 ; i <= Step; i++)
	{
		t = Step_Size * i;
		x = (ax *t*t*t)  + (bx*t*t) + (cx*t) +dx;
		y = (ay *t*t*t)  + (by*t*t) + (cy*t) +dy;
		lineto(x, y);
	}
}


void curve(int x1, int y1, int x2, int y2,int x3, int y3,int x4, int y4, float Step)
{
	float x, y, u;
	float Step_Size = 1.0 /Step;
	for(int i = 0; i < Step; i++)
	{
	   u = Step_Size * i;
	   x = pow((1 - u), 3.0) * x1 + 3 * pow((1 - u), 2.0) * u * x2 + 3 * (1 - u) * u * u * x3 + u * u * u * x4;
	   y = pow((1 - u), 3.0) * y1 + 3 * pow((1 - u), 2.0) * u * y2 + 3 * (1 - u) * u * u * y3 + u * u * u * y4;
	   putpixel(x, y, 15);
	}

}