Bivariate non-uniform subdivision schemes based on L-systems

Cédric Gérot and Ioannis Ivrissimtzis

Applied Mathematics and Computation, 2023, vol. 457, issue C

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 non-uniform 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.

Keywords: bivariate non-uniform subdivision; L–systems; non-uniform B-spline refinement; eigenanalysis around EVs (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:457:y:2023:i:c:s0096300323003259

DOI: 10.1016/j.amc.2023.128156

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