Title: "Differentiable Parameterization of Catmull-Clark Subdivision Surfaces"
Authors: Ioana Boier-Martin and Denis Zorin
Citation: Proceedings of the Symposium on Geometry Processing, Nice, France, July 2004.
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Abstract: Subdivision-based representations are recognized as important
tools for the generation of high-quality surfaces for Computer Graphics. In
this paper we describe two parameterizations of Catmull-Clark subdivision
surfaces that allow a variety of
algorithms designed for other types of parametric surfaces (i.e., B-splines) to be directly applied to subdivision surfaces. In contrast with the natural parameterization of subdivision surfaces characterized by diverging first order derivatives around extraordinary vertices of valence higher than four, the derivatives associated with our proposed methods are defined everywhere on the surface. This is especially important for Computer-Aided Design (CAD) applications that seek to address the limitations of NURBS-based representations through the more flexible subdivision framework.