A property of parametric polynomial approximants of half circles

A method for conic approximation by polynomial curves of odd degree n with approximation order 2n was presented by Floater (1997). A half circle approximation is obtained from the special case of the conic approximation method. In this paper we show that the coefficients of the polynomial curve of odd degree approximating the half circle in the power basis are related to entries of a particular row of a Bernoulli's triangle. We obtain the scaling factor which makes the radial error function equi-oscillate five times, and the Hausdorff distance between the half circle and the polynomial approximation curve. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a method for conic approximation using polynomial curves of odd degree, showing the relationship between the coefficients of the polynomial curve and Bernoulli's triangle. The paper also determines the scaling factor for equi-oscillation and Hausdorff distance between the half circle and the polynomial approximation curve.