Abstract
This paper presents a new subdivision scheme that operates over an infinite triangulation, which is regular except for a single extraordinary vertex. The scheme is based on the quartic three-directional Box-spline scheme, and is guaranteed to generate C2 limit functions whenever the valency n of the extraordinary vertex is in the range 4≤n≤20. The new scheme differs from the commonly used subdivision schemes by the fact that it applies special subdivision rules near edges of the original triangulation, which emanate from the extraordinary vertex, and not only in the vicinity of the extraordinary vertex.
Original language | English |
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Pages (from-to) | 157-178 |
Number of pages | 22 |
Journal | Computer Aided Geometric Design |
Volume | 23 |
Issue number | 2 |
DOIs | |
State | Published - Feb 2006 |
Bibliographical note
Funding Information:* Corresponding author. E-mail address: [email protected] (A. Levin). 1 The paper is part of the first author’s PhD Thesis. 2 The first and the fourth authors were partially supported by the Emmy Noether Research Institute for Mathematics, Bar-Ilan University and the Minerva Foundation, Germany, and by the Excellency Center “Group theoretic methods in the study of algebraic varieties” of the National Science Foundation of Israel.
Funding
* Corresponding author. E-mail address: [email protected] (A. Levin). 1 The paper is part of the first author’s PhD Thesis. 2 The first and the fourth authors were partially supported by the Emmy Noether Research Institute for Mathematics, Bar-Ilan University and the Minerva Foundation, Germany, and by the Excellency Center “Group theoretic methods in the study of algebraic varieties” of the National Science Foundation of Israel.
Funders | Funder number |
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Emmy Noether Research Institute for Mathematics, Bar-Ilan University | |
National Science Foundation of Israel | |
Minerva Foundation |
Keywords
- Polynomial generation
- Smoothness
- Subdivision schemes