Curvature-continuous bicubic subdivision surfaces for polar configurations.

摘要

Subdivision surfaces are popular in animation as a way of smoothing coarse control meshes. On the other hand, the Computer-Aided Design (CAD) industry typically prefers the simplicity and predictability of NURBS when constructing high-quality surfaces for the manufacture of cars and planes. Since a single NURBS patch is capable only of modeling the topologies of planes, cylinders, and torii, it is complex to use a NURBS atlas to construct a surface of arbitrary topology that is curvature-continuous everywhere. While popular subdivision algorithms of low parametric degree, like Catmull-Clark and Loop subdivision, are not inherently restricted in topology, they suffer from shape artifacts at so-called "extraordinary vertices". This makes them unattractive for CAD. Subdivision theory requires a (bi)degree of at least 6 in order for stationary subdivision to be non-trivially curvature-continuous and mitigate some of these shape artifacts. We circumvent this restriction by designing a curvature-continuous non-stationary bicubic subdivision algorithm which has the implementational simplicity of stationary algorithms. We hope techniques such as ours make subdivision surfaces more attractive for high-quality constructions in CAD.