A Müntz type theorem for a family of corner cutting schemes

Rachid Ait-Haddou, Yusuke Sakane, Taishin Nomura

Research output: Contribution to journalArticlepeer-review

7 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 languageEnglish (US)
Pages (from-to)240-253
Number of pages14
JournalComputer Aided Geometric Design
Volume30
Issue number2
DOIs
StatePublished - Feb 2013
Externally publishedYes

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