1. Lecture 4 Graphic Primitives, Circle

2. Drawing Circles

3. Brute Force Method

4. Cheating with 8 arcs

5. Cheating with 8 arcs Implementation

7. Digital Differential Analysis - An incremental algorithm Does not require sine or cosine table. based upon calculating the gradient of a circle at a point and using that to approximate the position of the next point.

8. Digital Differential Analysis - An incremental algorithm

9. Digital Differential Analysis - Implementation

10. Bresenham’s algorithm for circles Based on limiting the choice of the next pixel to be plotted to two alternatives, then creating and testing a decision variable to determine which alternative is actually plotted. D(Si) and D(Ti) represent the differences between the squared distance between the center of the circle and the middle of pixels S and T. Whichever is smallest corresponds to the pixel that should be plotted. To combine the two calculations into one “decision variable” is simply a matter of subtracting the two expressions:

11. Bresenham’s algorithm for circles

12. Implementation for Bresenham’s algorithm

13. Implementation for circles