Bi-3 C 2 polar subdivision
| Autor: | Ashish Myles, Jörg Peters |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Surface (mathematics)
Loop (graph theory) Pure mathematics Degree (graph theory) business.industry Topology Computer Graphics and Computer-Aided Design Vertex (geometry) Computer Science::Graphics Quadratic equation Piecewise Subdivision surface Almost everywhere Finite subdivision rule business ComputingMethodologies_COMPUTERGRAPHICS Mathematics Subdivision |
| Zdroj: | ACM Transactions on Graphics. 28:1-12 |
| ISSN: | 1557-7368 0730-0301 |
| DOI: | 10.1145/1531326.1531354 |
| Popis: | Popular subdivision algorithms like Catmull-Clark and Loop are C 2 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 C 2 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 C 2 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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