Approximating Catmull-Clark Subdivision Surfaces with Bicubic Patches

摘要

We present a simple and computationally efficient algorithm for approximating Catmull-Clark subdivision surfaces using a minimal set of bicubic patches. For each quadrilateral face of the control mesh, we construct a geometry patch and a pair of tangent patches. The geometry patches approximate the shape and silhouette of the Catmull-Clark surface and are smooth everywhere except along patch edges containing an extraordinary vertex where the patches are C~0. To make the patch surface appear smooth, we provide a pair of tangent patches that approximate the tangent fields of the Catmull-Clark surface. These tangent patches are used to construct a continuous normal field (through their cross-product) for shading and displacement mapping. Using this bifurcated representation, we are able to define an accurate proxy for Catmull-Clark surfaces that is efficient to evaluate on next-generation GPU architectures that expose a programmable tessellation unit.