Can elliptic arc (defined as part of an ellipse, with extent not greater than $90˚$) be represented by quadratic Bezier curve?
Can elliptic arc be represented by quadratic Bezier curve?
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geometry
bezier-curve
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1I would call that an "elliptical arc". An [elliptic curve](http://en.wikipedia.org/wiki/Elliptic_curve) is something completely different. – 2010-11-25
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0@Rahul Narain - Thanks! – 2010-11-25
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0A *rational* quadratic, yes, but I'm pretty sure not a quadratic... – 2010-11-25
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1Also, quadratic Bézier curves can only represent parabolas. To represent elliptical arcs and other cubic sections exactly, [you need rational functions](http://www.cl.cam.ac.uk/teaching/2000/AGraphHCI/SMEG/node5.html#SECTION00051000000000000000), as J.M. mentioned in your previous question. – 2010-11-25
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0See also [Representing rational quadratic Bezier with non-rational cubic](https://math.stackexchange.com/questions/1948314) – 2018-07-06
1 Answers
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No. From Computer Aided Geometric Design by T. Sederberg, chapter 2.9 Rational Bezier Curves: "A degree two polynomial Bezier curve can only represent a parabola. Exact representation of circles requires rational degree two Bezier curves."