Gelfond–Bézier curves

Handle URI:
http://hdl.handle.net/10754/577065
Title:
Gelfond–Bézier curves
Authors:
Ait-Haddou, Rachid; Sakane, Yusuke; Nomura, Taishin
Abstract:
We show that the generalized Bernstein bases in Müntz spaces defined by Hirschman and Widder (1949) and extended by Gelfond (1950) can be obtained as pointwise limits of the Chebyshev–Bernstein bases in Müntz spaces with respect to an interval [a,1][a,1] as the positive real number a converges to zero. Such a realization allows for concepts of curve design such as de Casteljau algorithm, blossom, dimension elevation to be transferred from the general theory of Chebyshev blossoms in Müntz spaces to these generalized Bernstein bases that we termed here as Gelfond–Bernstein bases. The advantage of working with Gelfond–Bernstein bases lies in the simplicity of the obtained concepts and algorithms as compared to their Chebyshev–Bernstein bases counterparts.
KAUST Department:
Visual Computing Center (VCC)
Publisher:
Elsevier BV
Journal:
Computer Aided Geometric Design
Issue Date:
Feb-2013
DOI:
10.1016/j.cagd.2012.10.002
Type:
Article
ISSN:
0167-8396
Sponsors:
This work was partially supported by the MEXT Global COE project at 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.accessioned2015-09-10T09:28:14Zen
dc.date.available2015-09-10T09:28:14Zen
dc.date.issued2013-02en
dc.identifier.issn0167-8396en
dc.identifier.doi10.1016/j.cagd.2012.10.002en
dc.identifier.urihttp://hdl.handle.net/10754/577065en
dc.description.abstractWe show that the generalized Bernstein bases in Müntz spaces defined by Hirschman and Widder (1949) and extended by Gelfond (1950) can be obtained as pointwise limits of the Chebyshev–Bernstein bases in Müntz spaces with respect to an interval [a,1][a,1] as the positive real number a converges to zero. Such a realization allows for concepts of curve design such as de Casteljau algorithm, blossom, dimension elevation to be transferred from the general theory of Chebyshev blossoms in Müntz spaces to these generalized Bernstein bases that we termed here as Gelfond–Bernstein bases. The advantage of working with Gelfond–Bernstein bases lies in the simplicity of the obtained concepts and algorithms as compared to their Chebyshev–Bernstein bases counterparts.en
dc.description.sponsorshipThis work was partially supported by the MEXT Global COE project at Osaka University, Japan.en
dc.publisherElsevier BVen
dc.subjectPolyimide hollow fibresen
dc.subjectIn-line cross-linkingen
dc.subjectDiamine cross-linkeren
dc.subjectH2 separationen
dc.subjectGas separationen
dc.titleGelfond–Bézier curvesen
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
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