C2 subdivision over triangulations with one extraordinary point

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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 languageEnglish
Pages (from-to)157-178
Number of pages22
JournalComputer Aided Geometric Design
Issue number2
StatePublished - Feb 2006


FundersFunder number
Emmy Noether Research Institute for Mathematics, Bar-Ilan University
National Science Foundation of Israel
Minerva Foundation


    • Polynomial generation
    • Smoothness
    • Subdivision schemes


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