CIRCLE-GENERATING ALGORITHMS

Midpoint circle Algorithm

1. Input radius r and circle center (xc,yc) and obtain the first point on the circumference of the circle centered on the origin as (x0,y0) = (0,r)

2. Calculate the initial value of the decision parameter as P0=(5/4)-r

3. At each xk position, starting at k=0, perform the following test.

 If Pk<0 the next point along the circle centered on (0,0) is (xk+1,yk) and

Pk+1=Pk+2xk+1+1

Otherwise the next point along the circle is (xk+1,yk-1) and

Pk+1=Pk+2xk+1+1-2 yk+1 Where 2xk+1=2xk+2 and 2yk+1=2yk-2

4. Determine symmetry points in the other seven octants.

5. Move each calculated pixel position (x,y) onto the circular path centered at (xc,yc) and plot the coordinate values. x=x+xc y=y+yc 6. Repeat step 3 through 5 until x>=y.