Circle and ellipse
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Transcript of Circle and ellipse
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
October 6, 2013 3
A Simple Circle Drawing Algorithm
October 6, 2013 4
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
October 6, 2013 6
Parametric Polar Representation
October 6, 2013 7
October 6, 2013 8
Bresenham’s algorithm for circles
October 6, 2013 9
Bresenham’s incremental circle algorithm
October 6, 2013 10
Four way symmetry
October 6, 2013 11
Eight-Way Symmetry
October 6, 2013 12
Mid-Point Circle Algorithm
October 6, 2013 13
October 6, 2013 14
October 6, 2013 15
RULE
If S >0 choose pixel B
Else choose A
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Ellipses
October 6, 2013 17
October 6, 2013 18
