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

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  • López-Ureña, Sergio

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.

Suggested Citation

  • López-Ureña, Sergio, 2024. "A uniform non-linear subdivision scheme reproducing polynomials at any non-uniform grid," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    • Handle: RePEc:eee:apmaco:v:479:y:2024:i:c:s0096300324003503
    DOI: 10.1016/j.amc.2024.128889
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    1. Conti, Costanza & López-Ureña, Sergio & Romani, Lucia, 2022. "Annihilation operators for exponential spaces in subdivision," Applied Mathematics and Computation, Elsevier, vol. 418(C).
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