Differentiable Parameterization of Catmull-Clark Subdivision Surfaces

Boier-Martin, Ioana; Zorin, Denis

Differentiable Parameterization of Catmull-Clark Subdivision Surfaces

Files

159-168.pdf (1.64 MB)

Date

2004

Authors

Boier-Martin, Ioana
Zorin, Denis

Publisher

The Eurographics Association

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.

        @inproceedings{:10.2312/SGP/SGP04/159-168
,
booktitle = {Symposium on Geometry Processing
},
editor = {Roberto Scopigno and Denis Zorin
},
title = {{Differentiable Parameterization of Catmull-Clark Subdivision Surfaces
}},
author = {Boier-Martin, Ioana and 
Zorin, Denis
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-13-4
},
DOI = {/10.2312/SGP/SGP04/159-168
}
}