Abstract
An upper bound of the Hausdorff distance between planar curve and conic section can be expressed by the maximum norm of error function from the conic section to the planar curve (Comput. Aided Geomet. Design, 14 (1997) 135–151). With respect to the maximum norm we characterize the necessary and sufficient condition for the conic section to be optimal approximation of the given planar curve. As an example, we approximate the cubic rational Bézier curves by conic sections using our characterization, and present the upper bound of the Hausdorff distance numerically.
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