A Müntz type theorem for a family of corner cutting schemes

Rachid Ait-Haddou; Yusuke Sakane; Taishin Nomura

doi:10.1016/j.cagd.2012.12.001

A Müntz type theorem for a family of corner cutting schemes

Rachid Ait-Haddou^*
, Yusuke Sakane
, Taishin Nomura

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

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.

Original language	English
Pages (from-to)	240-253
Number of pages	14
Journal	Computer Aided Geometric Design
Volume	30
Issue number	2
DOIs	https://doi.org/10.1016/j.cagd.2012.12.001
State	Published - 2013
Externally published	Yes

Bibliographical note

Funding Information:
This work was partially supported by the MEXT Global COE project. Osaka University, Japan. The authors would like to thank the anonymous referees for their careful revision of the manuscript and helpful comments.

Keywords

Bézier curves
Corner cutting schemes
Density of Müntz spaces
Gelfond-Bézier curves
Müntz spaces

ASJC Scopus subject areas

Modeling and Simulation
Automotive Engineering
Aerospace Engineering
Computer Graphics and Computer-Aided Design

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10.1016/j.cagd.2012.12.001

Cite this

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title = "A M{\"u}ntz type theorem for a family of corner cutting schemes",

abstract = "Dimension elevation process of Gelfond-B{\'e}zier curves generates a family of control polygons obtained through a sequence of corner cuttings. We give a M{\"u}ntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the M{\"u}ntz 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.",

keywords = "B{\'e}zier curves, Corner cutting schemes, Density of M{\"u}ntz spaces, Gelfond-B{\'e}zier curves, M{\"u}ntz spaces",

author = "Rachid Ait-Haddou and Yusuke Sakane and Taishin Nomura",

note = "Funding Information: This work was partially supported by the MEXT Global COE project. Osaka University, Japan. The authors would like to thank the anonymous referees for their careful revision of the manuscript and helpful comments.",

year = "2013",

doi = "10.1016/j.cagd.2012.12.001",

language = "English",

volume = "30",

pages = "240--253",

journal = "Computer Aided Geometric Design",

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T1 - A Müntz type theorem for a family of corner cutting schemes

AU - Ait-Haddou, Rachid

AU - Sakane, Yusuke

AU - Nomura, Taishin

N1 - Funding Information: This work was partially supported by the MEXT Global COE project. Osaka University, Japan. The authors would like to thank the anonymous referees for their careful revision of the manuscript and helpful comments.

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

KW - Bézier curves

KW - Corner cutting schemes

KW - Density of Müntz spaces

KW - Gelfond-Bézier curves

KW - Müntz spaces

UR - https://www.scopus.com/pages/publications/84872169317

U2 - 10.1016/j.cagd.2012.12.001

DO - 10.1016/j.cagd.2012.12.001

M3 - Article

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SN - 0167-8396

VL - 30

SP - 240

EP - 253

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 2

ER -

A Müntz type theorem for a family of corner cutting schemes

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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