Approximation of circular arcs by Bézier curves
Best approximation of a circular arc by Bézier curves of degree four and five is investigated. Explicit forms of best approximating \(GC^3\) and \(GC^2\) quartic curves of various types are given. The existence of a \(GC^4\) quintic approximant is shown, and the explicit form of a certain best \(GC^3\) quintic approximant is given. In each case, the Hausdorff distance between the circular arc and the approximating Bézier curve is determined, and it is shown that the approximation order is twice the degree of the Bézier curve in all cases.
scientific article; zbMATH DE number 1043106