1. UNIT-1 Bresenham’s Circle Algorithm
Computer Graphics
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UNIT-1
Bresenham’s Circle Algorithm

2. Bresenham’s Circle Algorithm
Consider only
45° ≤  ≤ 90°
General Principle
The circle function:
and

3. Bresenham’s Circle Algorithmp1 p3 yi
D(si)
D(ti)
yi - 1 p2 r xi
xi + 1
After point p1, do we choose p2 or p3?

4. Bresenham’s Circle Algorithm
Define: D(si) = distance of p3 from circle
D(ti) = distance of p2 from circle
i.e. D(si) = (xi + 1)2 + yi2 – r [always +ve]
D(ti) = (xi + 1)2 + (yi – 1)2 – r2 [always -ve]
Decision Parameter pi = D(si) + D(ti)
so if pi < 0 then the circle is closer to p3 (point above)
if pi ≥ 0 then the circle is closer to p2 (point below)

5. The Algorithm
x0 = 0
y0 = r
p0 = [12 + r2 – r2] + [12 + (r-1)2 – r2] = 3 – 2r
if pi < 0 then
yi+1 = yi
pi+1 = pi + 4xi + 6
else if pi ≥ 0 then
yi+1 = yi – 1
pi+1 = pi + 4(xi – yi) + 10
Stop when xi ≥ yi and determine symmetry points in the other octants
xi+1 = xi + 1

6. Example r = 10 p0 = 3 – 2r = -17 Initial point (x0, y0) = (0, 10) i pi 9 8 7 6 5 4 3 2 1 i pi
xi, yi
-17
(0, 10) 1
-11
(1, 10) 2 -1
(2, 10) 3 13
(3, 10) 4 -5
(4, 9) 5 15
(5, 9) 6 9
(6, 8) 7
(7,7)

7. Exercises Draw the circle with r = 12 using the Bresenham algorithm.
Draw the circle with r = 14 and center at (15, 10).

8. Decision Parameters Prove that if pi < 0 and yi+1 = yi then
pi+1 = pi + 4xi + 6
Prove that if pi ≥ 0 and yi+1 = yi – 1 then
pi+1 = pi + 4(xi – yi) + 10

9. Advantages of Bresenham circle
Only involves integer addition, subtraction and multiplication
There is no need for squares, square roots and trigonometric functions