circle and ellipse
TRANSCRIPT
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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
![Page 3: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/3.jpg)
October 6, 2013 3
A Simple Circle Drawing Algorithm
![Page 4: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/4.jpg)
October 6, 2013 4
![Page 5: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/5.jpg)
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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
![Page 6: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/6.jpg)
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Parametric Polar Representation
![Page 7: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/7.jpg)
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![Page 8: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/8.jpg)
October 6, 2013 8
Bresenham’s algorithm for circles
![Page 9: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/9.jpg)
October 6, 2013 9
Bresenham’s incremental circle algorithm
![Page 10: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/10.jpg)
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Four way symmetry
![Page 11: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/11.jpg)
October 6, 2013 11
Eight-Way Symmetry
![Page 12: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/12.jpg)
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Mid-Point Circle Algorithm
![Page 13: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/13.jpg)
October 6, 2013 13
![Page 14: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/14.jpg)
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![Page 15: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/15.jpg)
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RULE
If S >0 choose pixel B
Else choose A
![Page 16: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/16.jpg)
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Ellipses
![Page 17: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/17.jpg)
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![Page 18: Circle and ellipse](https://reader034.vdocuments.net/reader034/viewer/2022050808/555da5b0d8b42a257b8b59d9/html5/thumbnails/18.jpg)
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