Curvature-Based Optimal Polynomial Geometric Interpolation of Circular Arcs

Abstract

The problem of the optimal approximation of circular arcs by parametric polynomial curves is considered. The optimality relates to the curvature error. Parametric polynomial curves of low degree are used and a geometric continuity is prescribed at the boundary points of the circular arc. Analysis is done for cases of parabolic $G^0$, cubic $G^1$ and quartic $G^2$ interpolation. The comparison of the approximation of circular arcs based on curvature with the approximation based on radial error is provided.