Subdivision Depth Computation for Extra-Ordinary Catmull-Clark Subdivision Surface Patches

A second order forward differences based subdivision depth computation technique for extra-ordinary Catmull-Clark subdivision surface (CCSS) patches is presented. The new technique improves a previous technique in that the computation of the subdivision depth is based on the patch’s curvature distribution, instead of its dimension. Hence, with the new technique, no excessive subdivision is needed for extra-ordinary CCSS patches to meet the precision requirement and, consequently, one can make trimming, finite element mesh generation, boolean operations, and tessellation of CCSSs more efficient.