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

Abstract

Abstract.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.

The distance of a subdivision surface to its control polyhedron

“…the estimate does not match observations and is not practically useful. Similar estimates, ever more sophisticated in the details, can be found in [3,5,4,9,10].…”

TSS BVHs: Tetrahedron Swept Sphere BVHs for Ray Tracing Subdivision Surfaces

“…The error between the subdivision mesh computed at subdivision level k and its limit surface, S(u, v), is then bounded as the following [CCY06]:…”

Beyond Catmull–Clark? A Survey of Advances in Subdivision Surface Methods

“…Zeng and Chen [ZC06] provide estimates based on the first differences of the control mesh, but these are over‐conservative and lead to a large prediction for the number of required steps. Cheng et al [CY06, CCY06, CC06] make improved estimates based on second differences instead. Huang and Wang [HW07b] find optimal convergence rates for these second differences, but still predict a large number of subdivision steps compared to typical use in practice.…”