Approximation by Conic Splines

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Approximation by Conic Splines
Abstract. We show that the complexity of a parabolic or conic spline approximating a sufficiently smooth curve with non-vanishing curvature to within Hausdorff distance ε is c1ε−1/4 + O(1), if the spline consists of parabolic arcs, and c2ε−1/5 + O(1), if it is composed of general conic arcs of varying type. The constants c1 and c2 are expressed in the Euclidean and affine curvature of the curve. We also show that the Hausdorff distance between a curve and an optimal conic arc tangent at its endpoints is increasing with its arc length, provided the affine curvature along the arc is monotone. This property yields a simple bisection algorithm for the computation of an optimal parabolic or conic spline.
Sunayana Ghosh, Sylvain Petitjean, Gert Vegter
Added 27 Dec 2010
Updated 27 Dec 2010
Type Journal
Year 2007
Where MICS
Authors Sunayana Ghosh, Sylvain Petitjean, Gert Vegter
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