Optimal parameter values for approximating conic sections by the quartic Bézier curves

摘要

The previous approximation curves of conic section by quartic Bézier curves interpolate the conic section at the specified parameter values. In this paper, by solving the minimax problem, we present the optimal parameter values for approximating conic sections by the quartic Bézier curves. The upper bound on the Hausdorff distance between the conic section and the approximation curves is minimized. The method of solving the minimax problem is changed to solve a quartic algebraic equation by delicate reasoning.