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Article Dans Une Revue Applied Mathematics and Computation Année : 2023

Bivariate non-uniform subdivision schemes based on L-systems

Résumé

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.
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Dates et versions

hal-04169693 , version 1 (24-07-2023)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Cédric Gérot, Ioannis Ivrissimtzis. Bivariate non-uniform subdivision schemes based on L-systems. Applied Mathematics and Computation, 2023, 457 (November), pp.128156. ⟨10.1016/j.amc.2023.128156⟩. ⟨hal-04169693⟩
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