Constructing an Interpolatory Subdivision Scheme from Doo-Sabin Subdivision

Abstract

This paper presents an interpolatory subdivision scheme derived from the Doo-Sabin subdivision scheme. We first present the relations among three curve subdivision schemes, namely a four point interpolatory subdivision scheme, a cubic B-spline curve subdivision scheme, and the Chaikin's algorithm that generates uniform quadratic B-spline curves. By generalizing these relations to the surface case, we derive an interpolatory surface subdivision scheme from the Doo-Sabin subdivision scheme, a generalization of the Chaikin's algorithm to surface subdivision. In the new subdivision scheme, we also introduce a variable tension parameter that is dependent to local control vertices. The variable tension parameter can be used to effectively control the resulting limit surface of the proposed subdivision scheme.

DOI: 10.1109/CAD/Graphics.2011.80

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Cite this paper

@article{Deng2011ConstructingAI, title={Constructing an Interpolatory Subdivision Scheme from Doo-Sabin Subdivision}, author={Chongyang Deng and Weiyin Ma}, journal={2011 12th International Conference on Computer-Aided Design and Computer Graphics}, year={2011}, pages={215-222} }