  For Bezier curves, subdivision algorithms create control polygons as
piecewise linear (PL) approximations that converge in terms of Hausdorff
distance. We prove that the exterior angles of control polygons under
subdivision 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 topological features. We use it to show homeomorphism between a
Bezier curve and its control polygon under subdivision. The constructive
geometric proofs yield closed-form formulas to compute sufficient numbers of
subdivision iterations to obtain small exterior angles and achieve
homeomorphism.
