The best \(G^{1}\) cubic and \(G^{2}\) quartic Bézier approximations of circular arcs
For a cubic Bézier representation of a curve approximating a circular arc, four control points are needed. Two of them coincide with the end-points of the arc (\(G^0\) condition) and two other are placed at a distance \(h\) along the tangents in these end-points (\(G^1\) condition). This gives a family of approximating curves depending on the parameter \(h\). Conditions are given to select the best one in this class in a Hausdorff sense. For quartic curves, there is one more parameter but an extra \(G^2\) condition. Again necessary and sufficient conditions are formulated to find the best approximant in Hausdorff sense. The best solutions are unique. Because of the special character of a circular arc, the Hausdorff distance can be replaced by a (signed) function that is easily computable.
\(G^{1}\) and \(G^{2}\) end-point interpolation
scientific article; zbMATH DE number 5991189