A uniform non-linear subdivision scheme reproducing polynomials at any non-uniform grid

Sergio López-Ureña

Applied Mathematics and Computation, 2024, vol. 479, issue C

Abstract: In this paper, we introduce a novel non-linear uniform subdivision scheme for the generation of curves in Rn, n≥2. This scheme is distinguished by its capacity to reproduce second-degree polynomial data on non-uniform grids without necessitating prior knowledge of the grid specificities. Our approach exploits the potential of annihilation operators to infer the underlying grid, thereby obviating the need for end-users to specify such information. We define the scheme in a non-stationary manner, ensuring that it progressively approaches a classical linear scheme as the iteration number increases, all while preserving its polynomial reproduction capability.

Keywords: Uniform non-stationary subdivision scheme; Polynomial reproduction; Non-uniform grid; Annihilation operators; Asymptotically equivalent schemes; Quasilinear schemes (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003503

DOI: 10.1016/j.amc.2024.128889

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