Midpoint circle algorithm

Midpoint circle algorithm

IT is based on the following function for testing the relationship between and arbitrary point (x,y) and a circle of radius are centered at the origin so, It we have a function of x,y then

                                f(x,y) = x^²  + y^²-r^² is equal to

if < 0 for (x,y) inside the circle

if = 0 for (x,y) on the circle

if > 0 for (x,y) outside the circle

Now consider the coordinates of the points half way between the pixel inner and outer as (x_i+1,y_i -1/2) this is called the mid point and we use it to define a decision parameter

P_i=function of (x_i+1,y_i-1/2)=((x_i+1)^²+( y_i-1/2)^²-r^²)

If P_i is -ve the midpoint is inside the circle on the other hand it P_i is the +ve the midpoint is outside the circle.

With the help of decision promoter from P_i+n for n=0 to till n point.

Program: -

#include<stdio.h>

#include<conio.h>

void pixel(int xr, int yr, int x, int y);

int main()

{

                int gd, gm, xr, yr, r, x, y, p;

                detectgraph(&gd,&gm);

                initgraph(&gd,&gm,”c://tc//bgi”);

                printf(“Enter the radius of circle”);

                scanf(“%d”,&r);

                x=0;

                y=r;

                P=1-r;

                pixel(xr, yr, x, y);

                while(x<y)

                {

                                If(p<0)

                                {

                                      x++;

                                      P=P+2*x+1;

                                }

                                else

                                {

                                     X++;

                                  y--;

                                     P=P+2*(x-y)+1;

                                }

                                rixel(xr, yr, x, y);

                }

                return 0;

}

void pixel(int xr, int yr, int x, int y)

{

                putpixel(xr+x, yr+y, white);

                putpixel(xr+x, yr-y, white);

                putpixel(xr-x, yr+y, white);

                putpixel(xr-x, yr-y, white);

                putpixel(xr+x, yr+y, white);

                putpixel(xr+x, yr-y, white);

                putpixel(xr-x, yr+y, white);

                putpixel(xr-x, yr-y, white);

}