Hermite Curves

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;
}*p;

void main()
{
	int gd=DETECT,gm=VGAHI;
	initgraph(&gd,&gm,"");
	cout<<"Enter control points ";
	p=new point[4];
	for (int i=0;i<4;i++)
	{
		cout<<"Enter point P"<<i<<"(x,y)";
		cin>>p[i].x>>p[i].y;
	}
		for (float u=0;u<=1;u+=.001)
		{
			float x,y;
			x=(2*u*u*u-3*u*u+1)*p[0].x+(-2*u*u*u+3*u*u)*p[1].x+(u*u*u-2*u*u+u)*p[2].x+(u*u*u-u*u)*p[3].x;
			y=(2*u*u*u-3*u*u+1)*p[0].y+(-2*u*u*u+3*u*u)*p[1].y+(u*u*u-2*u*u+u)*p[2].y+(u*u*u-u*u)*p[3].y;
			putpixel(x+getmaxx()/2,getmaxy()/2-y,7);
		}
	getch();
}