Explain Bresenham s circle drawing algorithm,  OR   Explain midpoint circle algorithm for scan converting a circle.

Midpoint Circle Algorithm   1. Input radius r and circle center (x _c , y _c) , and obtain the first point on the circumference of a 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 x _k position, starting at k = 0, perform the following test: If p _k <0 , the next point along the circle centered on (0,0) is (x _k+1,y _k) and p _k+1 = p _k + 2x _k+1 + 1 Otherwise, the next point the circle is ( x _k + 1, y _k -1) and p _k+1 = p _k+ 2x _k+1 + 1 -2 y _k where 2x _k+1 = 2x_k +2 and 2y_k+1 = 2y _k -2.  4. Determine symmetry points in the other seven octants.  5. Move each calculated pixel position (x, y) onto the circular path centered on (x _c,y _c) and plot the coordinate values: x = x +x _c,  y = y + y _c  6. Repeat steps 3 through 5 until x > y