Angular Convergence during Bezier Curve Approximation

Abstract

Properties of a parametric curve in R^3 are often determined by analysis of its piecewise linear (PL) approximation. For Bezier curves, there are standard algorithms, known as subdivision, that recursively create PL curves that converge to the curve in distance . The exterior angles of PL curves under subdivision are shown to converge to 0 at the rate of $O(\sqrt{\frac{1}{2^i}})$, where i is the number of subdivisions. This angular convergence is useful for determining self-intersections and knot type.