Communications of the
Korean Mathematical Society CKMS

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: Primary 65D17

Supported by: This study was supported by research funds from Chosun University, 2021.