In the mathematical subfield of numerical analysis a cubic Hermite spline, named in honor of Charles Hermite (Hermite is pronounced air MEET), is a third-degree spline with each polynomial of the spline in Hermite form. The Hermite form consists of two control points and two control tangents for each polynomial.

On each subinterval, given a starting point p0 and an ending point p1 with starting tangent m0 and ending tangent m1, the polynomial can be defined by

 where t varies from 0 to 1 inclusive. The four Hermite basis functions can be defined as

to give the polynomial as  

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

struct point
	int x,y;

void main()
	int gd=DETECT,gm=VGAHI;
	cout<<"Enter control points ";
	p=new point[4];
	for (int i=0;i<4;i++)
		cout<<"Enter point P"<<i<<"(x,y)";
		for (float u=0;u<=1;u+=.001)
			float x,y;