Adaptive Polynomial Approximation to Circular Arcs

Abstract:

We present a new adaptive method for approximating circular arcs in polynomial form by using the s-power series. Circular arcs can be expressed in infinite series form, we obtain the order-k Hermite interpolant by truncating at the kth term. An upper bound on the error of the interpolant is available, so we can obtain the lowest degree polynomial curve that approximates a circular arc within any user-prescribed tolerance. And this degree can be further reduced through subdivision, which generates a spline approximation with Ck continuity at the joints.

• Periodical: Applied Mechanics and Materials (Volumes 50-51)
• Pages: 678-682
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.50-51.678
• Online since: February 2011
• Authors: Li Zheng Lu
• Keywords: Circular Arc, Hermite Approximation, Polynomial, S-Power Series

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