Bivariate non-uniform subdivision schemes based on L-systems

Gérot, Cédric; Ivrissimtzis, Ioannis

Abstract

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.

Citation

Gérot, C., & Ivrissimtzis, I. (2023). Bivariate non-uniform subdivision schemes based on L-systems. Applied Mathematics and Computation, 457, Article 128156. https://doi.org/10.1016/j.amc.2023.128156

• 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
• DOI: https://doi.org/10.1016/j.amc.2023.128156
• Public URL: https://durham-repository.worktribe.com/output/1170982
• Publisher URL: http://www.journals.elsevier.com/applied-mathematics-and-computation/