A Müntz type theorem for a family of corner cutting schemes

Handle URI:
http://hdl.handle.net/10754/577066
Title:
A Müntz type theorem for a family of corner cutting schemes
Authors:
Ait-Haddou, Rachid; Sakane, Yusuke; Nomura, Taishin
Abstract:
Dimension elevation process of Gelfond–Bézier curves generates a family of control polygons obtained through a sequence of corner cuttings. We give a Müntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Müntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the convergence of the corresponding dimension elevation algorithms.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Elsevier BV
Journal:
Computer Aided Geometric Design
Issue Date:
Feb-2013
DOI:
10.1016/j.cagd.2012.12.001
Type:
Article
ISSN:
0167-8396
Sponsors:
This work was partially supported by the MEXT Global COE project. Osaka University, Japan.
Appears in Collections:
Articles; Visual Computing Center (VCC)

Full metadata record

DC FieldValue Language
dc.contributor.authorAit-Haddou, Rachiden
dc.contributor.authorSakane, Yusukeen
dc.contributor.authorNomura, Taishinen
dc.date.accessioned2015-09-10T09:28:17Zen
dc.date.available2015-09-10T09:28:17Zen
dc.date.issued2013-02en
dc.identifier.issn0167-8396en
dc.identifier.doi10.1016/j.cagd.2012.12.001en
dc.identifier.urihttp://hdl.handle.net/10754/577066en
dc.description.abstractDimension elevation process of Gelfond–Bézier curves generates a family of control polygons obtained through a sequence of corner cuttings. We give a Müntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Müntz condition in the problem raises the question of a possible connection between the density questions of nested Chebyshev spaces and the convergence of the corresponding dimension elevation algorithms.en
dc.description.sponsorshipThis work was partially supported by the MEXT Global COE project. Osaka University, Japan.en
dc.publisherElsevier BVen
dc.subjectCorner cutting schemesen
dc.subjectBézier curvesen
dc.subjectGelfond–Bézier curvesen
dc.subjectMüntz spacesen
dc.subjectDensity of Müntz spacesen
dc.titleA Müntz type theorem for a family of corner cutting schemesen
dc.typeArticleen
dc.contributor.departmentVisual Computing Center (VCC)en
dc.identifier.journalComputer Aided Geometric Designen
dc.contributor.institutionOsaka Univ, Ctr Adv Med Engn & Informat, Osaka 5608531, Japanen
dc.contributor.institutionOsaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, Osaka 5600043, Japanen
dc.contributor.institutionOsaka Univ, Grad Sch Engn Sci, Dept Mech Sci & Bioengn, Osaka 5608531, Japanen
kaust.authorAit-Haddou, Rachiden
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.