Convergence of Wachspress coordinates: from polygons to curved domains

Handle URI:
http://hdl.handle.net/10754/563698
Title:
Convergence of Wachspress coordinates: from polygons to curved domains
Authors:
Kosinka, Jiří; Barton, Michael ( 0000-0002-1843-251X )
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.
KAUST Department:
Numerical Porous Media SRI Center (NumPor); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Publisher:
Springer Science + Business Media
Journal:
Advances in Computational Mathematics
Issue Date:
8-Aug-2014
DOI:
10.1007/s10444-014-9370-3
Type:
Article
ISSN:
10197168
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorKosinka, Jiříen
dc.contributor.authorBarton, Michaelen
dc.date.accessioned2015-08-03T12:06:50Zen
dc.date.available2015-08-03T12:06:50Zen
dc.date.issued2014-08-08en
dc.identifier.issn10197168en
dc.identifier.doi10.1007/s10444-014-9370-3en
dc.identifier.urihttp://hdl.handle.net/10754/563698en
dc.description.abstractGiven 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.en
dc.publisherSpringer Science + Business Mediaen
dc.subjectBarycentric coordinatesen
dc.subjectBarycentric mappingen
dc.subjectConvergenceen
dc.subjectInterpolationen
dc.titleConvergence of Wachspress coordinates: from polygons to curved domainsen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalAdvances in Computational Mathematicsen
dc.contributor.institutionComputer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, Cambridge, CB3 0FD, United Kingdomen
kaust.authorBarton, Michaelen
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