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

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 (US)
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 - Feb 2013
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was partially supported by the MEXT Global COE project. Osaka University, Japan.

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10.1016/j.cagd.2012.12.001

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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.",

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

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AU - Ait-Haddou, Rachid

AU - Sakane, Yusuke

AU - Nomura, Taishin

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: This work was partially supported by the MEXT Global COE project. Osaka University, Japan.

PY - 2013/2

Y1 - 2013/2

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.

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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

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