Approximation of circular arcs using quartic Bezier curves with barycentric coordinates satisfying G^2 data

Abstract

This paper proposes four methods to approximate circular arcs using quartic Bezier curves. Barycentric coordinates of two/three combination of control points are used to obtain an optimal approximation. Interior control points of quartic Bezier curves are found by satisfying G 2 data from given circular arcs. The maximum errors between circular arcs and approximated curves are calculated using Hausdorff distance approach. Four different approaches are discussed which varies in terms of accuracy, computation cost and approximation order.