Convergence of barycentric coordinates to barycentric kernels

Handle URI:
http://hdl.handle.net/10754/596178
Title:
Convergence of barycentric coordinates to barycentric kernels
Authors:
Kosinka, Jiří; Barton, Michael ( 0000-0002-1843-251X )
Abstract:
We investigate the close correspondence between barycentric coordinates and barycentric kernels from the point of view of the limit process when finer and finer polygons converge to a smooth convex domain. We show that any barycentric kernel is the limit of a set of barycentric coordinates and prove that the convergence rate is quadratic. Our convergence analysis extends naturally to barycentric interpolants and mappings induced by barycentric coordinates and kernels. We verify our theoretical convergence results numerically on several examples.
KAUST Department:
Numerical Porous Media SRI Center (NumPor)
Citation:
Convergence of barycentric coordinates to barycentric kernels 2016 Computer Aided Geometric Design
Publisher:
Elsevier BV
Journal:
Computer Aided Geometric Design
Issue Date:
12-Feb-2016
DOI:
10.1016/j.cagd.2016.02.003
Type:
Article
ISSN:
01678396
Additional Links:
http://linkinghub.elsevier.com/retrieve/pii/S0167839616300048
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorKosinka, Jiříen
dc.contributor.authorBarton, Michaelen
dc.date.accessioned2016-02-14T14:13:45Zen
dc.date.available2016-02-14T14:13:45Zen
dc.date.issued2016-02-12en
dc.identifier.citationConvergence of barycentric coordinates to barycentric kernels 2016 Computer Aided Geometric Designen
dc.identifier.issn01678396en
dc.identifier.doi10.1016/j.cagd.2016.02.003en
dc.identifier.urihttp://hdl.handle.net/10754/596178en
dc.description.abstractWe investigate the close correspondence between barycentric coordinates and barycentric kernels from the point of view of the limit process when finer and finer polygons converge to a smooth convex domain. We show that any barycentric kernel is the limit of a set of barycentric coordinates and prove that the convergence rate is quadratic. Our convergence analysis extends naturally to barycentric interpolants and mappings induced by barycentric coordinates and kernels. We verify our theoretical convergence results numerically on several examples.en
dc.language.isoenen
dc.publisherElsevier BVen
dc.relation.urlhttp://linkinghub.elsevier.com/retrieve/pii/S0167839616300048en
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computer Aided Geometric Design. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computer Aided Geometric Design, 12 February 2016. DOI: 10.1016/j.cagd.2016.02.003en
dc.subjectBarycentric coordinatesen
dc.subjectBarycentric kernelen
dc.subjectConvergenceen
dc.titleConvergence of barycentric coordinates to barycentric kernelsen
dc.typeArticleen
dc.contributor.departmentNumerical Porous Media SRI Center (NumPor)en
dc.identifier.journalComputer Aided Geometric Designen
dc.eprint.versionPost-printen
dc.contributor.institutionJohann Bernoulli Institute, University of Groningen, The Netherlandsen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorBarton, Michaelen
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