Error Estimation of Catmull-Clark Subdivision Surfaces

The Catmull-Clark subdivision surface was designed to generalize the bi-cubic B-spline surface to the meshes of arbitrary topology. In this paper, the error bound of Catmull-Clark subdivision surface is estimated. By using the first-order difference of control points, we define the distance between two control meshes and derive an error estimation formula for Catmull-Clark subdivision surface. Meanwhile, we prove that the control meshes of Catmull-Clark surface converge in an exponential rate.