Distance between a Catmull-Clark subdivision surface and its limit mesh

In geometry processing a refined control mesh is often used to approximate a Catmull-Clark subdivision surface (CCSS). By pushing the control points to their limit positions, a limit mesh of the subdivision surface is obtained. We present a bound on the distance between a CCSS patch and its limit face in terms of the maximum norm of the second order differences of the control points. The bound shows that the limit mesh may approximate the limit surface better than the corresponding control mesh in general. Consequently, for a given error tolerance, fewer subdivision steps are needed if the refined control mesh is replaced with the corresponding limit mesh.EI