This document describes two common algorithms for drawing circles: the Bresenham circle drawing algorithm and the midpoint circle drawing algorithm. The Bresenham algorithm considers 8-way symmetry and plots 1/8th of the circle from 90 to 45 degrees by incrementing either the x or x and -y coordinates. The midpoint circle algorithm also uses 8-way symmetry and plots from 90 to 45 degrees. It takes unit steps in the positive x direction and uses a decision parameter to determine which of two possible y coordinates is closer to the circle at each step. Both algorithms use incremental calculations to efficiently draw circles through integer operations only.

1. Circle Drawing Algorithm
WITH SOLVED EXAMPLE
Prof. Sujata L. Sonawane
Assistant Professor
Department of Artificial Intelligence and Machine Learning
P.E.S. Modern College of Engineering, Pune.

2. Circle Drawing
• Set of points that are all at a distance r from
the center position(Xc,Yc).
• Frequently used component in pictures and
graphs
• Procedure for generating full circle or circular
arcs is included in graphics packages.
• Single procedure can be used to draw circle
or elliptical curve.

3. Circle Properties
• Distance relationship in cartesian coordinates

4. • Spacing between plotted pixel positions is
not uniform
• It involves considerable equations at each
step.
• Increases the computation and processing
required by algorithm.

5. • Another way to eliminate the unequal
spacing, calculate points along the circular
boundary using polar coordinates r and
Theta.
• Circle is plotted with equally spaced points
along the circumference.

6. • For more continuous boundary on a raster
display, we can set the step size at 1/r.
• It plots pixel positions that are approximately
one unit apart.

7. Computations:
• Cartesian equation: multiplication and
square root calculation
• Parametric equation : multiplication and
trigonometric calculation
Most efficient circle drawing algorithms are
based on incremental calculations of decision
parameter, as in Bresenham line algorithm,
simple integer operations.

8. DDA Line Drawing Algorithm

11. Bresenham Circle Drawing Algorithm
• Considers 8-way symmetry
• plots 1/8th part of circle, from 90 to 45
degrees angle.

12. • To achieve best approximation to the true
circle we have to select those pixels in the
raster that fall the least distance from true
circle.
• if points are generated from 90 to 45 degree,
each new point closest to the true circle can
be found by applying either of two options:
– increment in positive x direction by one unit or
– Increment in +ve x direction and -ve y direction
both by one unit

14. • Closer pixel amongst these two can be
determined as

18. Midpoint-Circle Drawing Algorithm
• Uses eight way symmetry to generate a
circle.
• It plots 1/8th part of circle i.e. from 90 to 45
degree
• To draw a circle, we take unit steps in the
positive x direction and make use of decision
parameter to determine which of the two
possible y directions is closer to the circle
path at each step.

19. • 2 possible y positions (yi and yi+1)at sampling
position xi+1. To determine closer y
coordinate to circle, decision parameter is
used.

20. • If di<0, midpoint is inside the circle, pixel on
the scan line yi is closer to the circle
boundary.
• If di>=0, the midposition is outside or on the
circle boundary, and yi-1 is closer to the circle
boundary.
• Incremental calculation determined to obtain
successive decision parameters.

22. Questions
1. Explain Mid-point circle drawing algorithm? List its
advantages and disadvantages over DDA circle drawing
algorithm.
2. Write midpoint circle generation algorithm. Draw circle
having center (0,0) and radius 9 using this algorithm
3. Derive the Midpoint circle algorithm. Considering the
midpoint circle algorithm draw a circle with radius 10 and
center (0,0)
4. Explain midpoint circle generation algorithm by deriving the
steps.

23. THANK YOU