Curvature approximation of circular arcs by low-degree parametric polynomials.

In this paper some new methods for curvature approximation of circular arcs by low-degree Bezier curves are presented. Interpolation by geometrically continuous (G(1)) parametric polynomials is considered. All derived approximants are given explicitly and are therefore practically applicable. Moreover, obtained results indicate that G(1) biarcs with at least G(1) continuity at the junction have smaller curvature error as parametric polynomial counterparts of the same degree. It is also shown that all considered methods provide optimal asymptotic approximation order.