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# Circle and ellipse

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### Circle and ellipse

1. 1. October 6, 2013 1 comp_dep_educ@yahoo.com
2. 2. October 6, 2013 2 A Simple Circle Drawing Algorithm Parametric Polar Representation Bresenham’s algorithm for circles Bresenham’s incremental circle algorithm Four way symmetry Eight-Way Symmetry Mid-Point Circle Algorithm Ellipses
3. 3. October 6, 2013 3 A Simple Circle Drawing Algorithm
4. 4. October 6, 2013 4
5. 5. October 6, 2013 5 However, unsurprisingly this is not a brilliant solution! Firstly, the resulting circle has large gaps where the slope approaches the vertical Secondly, the calculations are not very efficient The square (multiply) operations The square root operation – try really hard to avoid these! We need a more efficient, more accurate solution
6. 6. October 6, 2013 6 Parametric Polar Representation
7. 7. October 6, 2013 7
8. 8. October 6, 2013 8 Bresenham’s algorithm for circles
9. 9. October 6, 2013 9 Bresenham’s incremental circle algorithm
10. 10. October 6, 2013 10 Four way symmetry
11. 11. October 6, 2013 11 Eight-Way Symmetry
12. 12. October 6, 2013 12 Mid-Point Circle Algorithm
13. 13. October 6, 2013 13
14. 14. October 6, 2013 14
15. 15. October 6, 2013 15 RULE If S >0 choose pixel B Else choose A
16. 16. October 6, 2013 16 Ellipses
17. 17. October 6, 2013 17
18. 18. October 6, 2013 18