Circle approximation using parametric polynomial curves of high degree in explicit form
Commun. Korean Math. Soc.
Published online May 13, 2022
Young Joon Ahn
Chosun University
Abstract : In this paper we present a full circle approximation method using parametric polynomial curves with algebraic coefficients which are curvature continuous at both endpoints.
Our method yields the $n$-th degree parametric polynomial curves which have a total number of $2n$ contacts with the full circle at both endpoints and the midpoint.
The parametric polynomial approximants have algebraic coefficients involving rational numbers and radicals for degree higher than four.
We obtain the exact Hausdorff distances between the circle and the approximation curves.
Keywords : full circle approximation; parametric polynomial approximant; curvature continuous; Hausdorff distance; algebraic coefficients.
MSC numbers : 65D17
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