Convergence of Wachspress coordinates: from polygons to curved domains

Jiří Kosinka, Michael Barton

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Given a smooth, strictly convex planar domain, we investigate point-wise convergence of the sequence of Wachspress coordinates defined over finer and finer inscribed polygonal approximations of the domain. Based on a relation between the discrete Wachspress case and the limit smooth case given by the Wachspress kernel defined by Warren et al., we show that the corresponding sequences of Wachspress interpolants and mappings converge as 𝓞(h2) for a sampling step size h of the boundary curve of the domain as h → 0. Several examples are shown to numerically validate the results and to visualise the behaviour of discrete interpolants and mappings as they converge to their smooth counterparts. Empirically, the same convergence order is observed also for mean value coordinates. Moreover, our numerical tests suggest that the convergence of interpolants and mappings is uniform both in the Wachspress and mean value cases. © 2014 Springer Science+Business Media New York.
Original languageEnglish (US)
Pages (from-to)489-505
Number of pages17
JournalAdvances in Computational Mathematics
Volume41
Issue number3
DOIs
StatePublished - Aug 8 2014

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Convergence of Wachspress coordinates: from polygons to curved domains'. Together they form a unique fingerprint.

Cite this