circle using Polar Co-ordinates

Defining a circle using Polar Co-ordinates :

The second method of defining a circle makes use of polar coordinates as shown in fig:

            x=r cos θ             y = r sin θ
Where θ=current angle
r = circle radius
x = x coordinate
y = y coordinate

By this method, θ is stepped from 0 to  & each value of x & y is calculated.

Algorithm:

Step1: Set the initial variables:

            r = circle radius

            (h, k) = coordinates of the circle center
                i = step size
            θ_end=
            θ=0

Step2: If θ>θ_endthen stop.

Step3: Compute

            x = r * cos θ            y=r*sin?θ

Step4: Plot the eight points, found by symmetry i.e., the center (h, k), at the current (x, y) coordinates.

Plot (x + h, y +k)             Plot (-x + h, -y + k)
Plot (y + h, x + k)             Plot (-y + h, -x + k)
Plot (-y + h, x + k)             Plot (y + h, -x + k)
Plot (-x + h, y + k)             Plot (x + h, -y + k)

Step5: Increment θ=θ+i

Step6: Go to step (ii).

Program to draw a circle using Polar Coordinates:

#include <graphics.h>  
#include <stdlib.h>  
#define color 10  
void eightWaySymmetricPlot(int xc,int yc,int x,int y)  
{  
    putpixel(x+xc,y+yc,color);  
    putpixel(x+xc,-y+yc,color);  
    putpixel(-x+xc,-y+yc,color);  
    putpixel(-x+xc,y+yc,color);  
    putpixel(y+xc,x+yc,color);  
    putpixel(y+xc,-x+yc,color);  
    putpixel(-y+xc,-x+yc,color);  
    putpixel(-y+xc,x+yc,color);  
}  
void PolarCircle(int xc,int yc,int r)  
{  
    int x,y,d;  
    x=0;  
    y=r;  
    d=3-2*r;  
    eightWaySymmetricPlot(xc,yc,x,y);  
    while(x<=y)  
    {  
        if(d<=0)  
        {  
            d=d+4*x+6;  
        }  
        else  
        {  
            d=d+4*x-4*y+10;  
            y=y-1;  
        }  
        x=x+1;  
        eightWaySymmetricPlot(xc,yc,x,y);  
    }  
}  
int main(void)  
{  
    int gdriver = DETECT, gmode, errorcode;  
    int xc,yc,r;  
    initgraph(&gdriver, &gmode, "c:\\turboc3\\bgi");  
errorcode = graphresult();  
if (errorcode != grOk)    
    {  
        printf("Graphics error: %s\n", grapherrormsg(errorcode));  
        printf("Press any key to halt:");  
        getch();  
        exit(1);               
    }  
printf("Enter the values of xc and yc ,that is center points of circle : ");  
    scanf("%d%d",&xc,&yc);  
    printf("Enter the radius of circle : ");  
    scanf("%d",&r);  
    PolarCircle(xc,yc,r);  
    getch();  
    closegraph();  
    return 0;  
}

  

Output: