C2 subdivision over triangulations with one extraordinary point

Avi Zulti; Adi Levin; David Levin; Mina Teicher

doi:10.1016/j.cagd.2005.06.001

C² subdivision over triangulations with one extraordinary point

Avi Zulti, Adi Levin^*, David Levin, Mina Teicher

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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
Pages (from-to)	157-178
Number of pages	22
Journal	Computer Aided Geometric Design
Volume	23
Issue number	2
DOIs	https://doi.org/10.1016/j.cagd.2005.06.001
State	Published - Feb 2006

Keywords

Polynomial generation
Smoothness
Subdivision schemes

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10.1016/j.cagd.2005.06.001

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title = "C2 subdivision over triangulations with one extraordinary point",

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.",

keywords = "Polynomial generation, Smoothness, Subdivision schemes",

author = "Avi Zulti and Adi Levin and David Levin and Mina Teicher",

note = "Funding Information: * Corresponding author. E-mail address: adi.levin@cadent.co.il (A. Levin). 1 The paper is part of the first author{\textquoteright}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.",

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C² subdivision over triangulations with one extraordinary point

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Keywords

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