Topological Equivalence and Curvature Convergence: Bézier Surface

A set of control points can determine a Bézier surface and a triangulated surface simultaneously. We prove that the triangulated surface becomes homeomorphic and ambient isotopic to the Bézier surface via subdivision. We also show that the total Gaussian curvature of the triangulated surface converges to the total Gaussian curva-ture of the Bézier surface