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Bivariate non-uniform subdivision schemes based on L-systems

Gérot, Cédric; Ivrissimtzis, Ioannis


Cédric Gérot


L–systems have been used to describe non-uniform, univariate, subdivision schemes, which offer more flexible refinement processes than the uniform schemes, while at the same time are easier to analyse than the geometry driven non-uniform schemes. In this paper, we extend L–system based nonuniform subdivision to the bivariate setting. We study the properties that an L–system should have to be the suitable descriptor of a subdivision refinement process. We derive subdivision masks to construct the regular parts of the subdivision surface as cubic B-spline patches. Finally we describe stencils for the extraordinary vertices, which after a few steps become stationary, so that the scheme can be studied through simple eigenanalysis. The proposed method is illustrated through two new subdivision schemes, a Binary-Ternary, and a Fibonacci scheme with average refinement rate below two.


Gérot, C., & Ivrissimtzis, I. (2023). Bivariate non-uniform subdivision schemes based on L-systems. Applied Mathematics and Computation, 457, Article 128156.

Journal Article Type Article
Acceptance Date May 29, 2023
Online Publication Date Jun 27, 2023
Publication Date Nov 15, 2023
Deposit Date Jun 15, 2023
Publicly Available Date Jun 28, 2024
Journal Applied Mathematics and Computation
Print ISSN 0096-3003
Electronic ISSN 1873-5649
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 457
Article Number 128156
Public URL
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