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lecture08-output-primitives-part-iv

# lecture08-output-primitives-part-iv - OutputPrimitives...

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Output Primitives Part IV Ellipse Drawing

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2 General equation General equation of an ellipse: d 1 + d 2 = constant ( 29 ( 29 ( 29 ( 29 constant 2 2 2 2 2 1 2 1 = - + - + - + - y y x x y y x x
3 “Standard” equation However, we will only consider ‘standard’ ellipse: 1 2 2 = - + - y c x c r y y r x x

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4 Symmetry of an ellipse An ellipse only has a 2-way symmetry Calculation of a point (x,y) in one quadrant yields the ellipse points shown for the other three quadrants
5 Equation of an ellipse revisited Consider an ellipse centered at the origin: What is the discriminator function ? ( 29 2 2 2 2 2 2 , y x x y e r r y r x r y x f - + = 1 2 2 = + y x r y r x

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6 Equation of an ellipse revisited …and its properties: f e (x,y) <  0 for a point inside the ellipse f e (x,y)  0 for a point outside the ellipse f e (x,y) =  0 for a point on the ellipse
7 Midpoint Ellipse Algorithm Ellipse is different from circle.

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