Numerical of Mid Point Circle Algorithm

Example-1

Draw a circle using Midpoint Circle Algorithm having radius as 10 and center of circle (100,100).

• Important points:
  • Starting d =5/4-r but as 5/4 is approximately equal to 1 so initial d would be d=1-r.
  • Plotted one pixel will generate 7 other points, because of 8 way symmetry.

The Algorithm:

S-1: Assume the coordinates of center of the circle as (h,k) and radius =r.

S-2: Find d=1-r and take x=0 & y=r as starting points.

S-3: If d >=0

• Increment x by 1 and dcrement y by 1. Calculate new d =d+2*(x-y) +5

S-4: If d <0

• Increment x by 1and keep the y unchanged, Calculate new d =d+2*(x) +3.

S-5: Stop when either x or y reaches r/squareroot(2).

S-6: All the other points would be generated by 8 way symmetry (Circle 8 way symmetr).

---

S-1; Enter the center h=100, k=100 and radius r=10.

S-2: Find d= 1-r , so d=1-10= -9  and take x = 0 , y = 10 (Initial Points as x=0 & y=radius)

S-3: If (d>=0) then x = x +1 and y = y -1 ; d = d + 2*(x-y) + 5;

S-4: if (d <0) then x =x +1 and d = d +2*x + 3;

Where to stop : x or y = 10/sqrt(2) which is 10/1.414= approx = 7. So either x or y reaches 7, the algorithm will stop.

Midpoint Circle Algorithm (r=10,h,k=100)
Step Number	X	Y	d	Pixel
1	0	10	-9	(x +h ,y +k) = 100,110
2	1	10	-9+2*1+3= – 4	101,110
3	2	10	-4+2*2+3=3	102,110
4	3	9	3+2*(3-9)+5 = -4	103,109
5	4	9	-4+2*4+3 = 7	104,109
6	5	8	7+2*(5-8)+5 = 6	105,108
7	6	7	Stop	—-

Rest of the points will be plotted using 8-Way Symmetry.  There would be 6*8=48 Points would be created in total, which on joining will look like circle.