English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we introduce a novel non-linear uniform subdivision scheme forthe generation of curves in $\mathbb{R}^n$, $n\geq2$. This scheme isdistinguished by its capacity to reproduce second-degree polynomial data onnon-uniform grids without necessitating prior knowledge of the gridspecificities. Our approach exploits the potential of annihilation operators toinfer the underlying grid, thereby obviating the need for end-users to specifysuch information. We define the scheme in a non-stationary manner, ensuringthat it progressively approaches a classical linear scheme as the iterationnumber increases, all while preserving its polynomial reproduction capability.  The convergence is established through two distinct theoretical methods.Firstly, we propose a new class of schemes, including ours, for which weestablish $\mathcal{C}^1$ convergence by combining results from the analysis ofquasilinear schemes and asymptotically equivalent linear non-uniformnon-stationary schemes. Secondly, we adapt conventional analytical tools fornon-linear schemes to the non-stationary case, allowing us to again concludethe convergence of the proposed class of schemes.  We show its practical usefulness through numerical examples, showing that thegenerated curves are curvature continuous.

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