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.
|Number of pages||22|
|Journal||Computer Aided Geometric Design|
|State||Published - Feb 2006|
Bibliographical noteFunding Information:
* Corresponding author. E-mail address: email@example.com (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.
- Polynomial generation
- Subdivision schemes