Abstract
Popular subdivision algorithms like Catmull-Clark and Loop are
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almost everywhere, but suffer from shape artifacts and reduced smoothness exactly near the so-called "extraordinary vertices" that motivate their use. Subdivision theory explains that inherently, for standard stationary subdivision algorithms, curvature-continuity and the ability to model all quadratic shapes requires a degree of at least bi-6. The existence of a simple-to-implement
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subdivision algorithm generating surfaces of good shape and piecewise degree bi-3 in the polar setting is therefore a welcome surprise. This paper presents such an algorithm, the underlying insights, and a detailed analysis. In bi-3
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polar subdivision the weights depend, as in standard schemes, only on the valence, but the valence at one central polar vertex increases to match Catmull-Clark-refinement.
Funder
National Science Foundation
Publisher
Association for Computing Machinery (ACM)
Subject
Computer Graphics and Computer-Aided Design
Cited by
17 articles.
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