A Müntz type theorem for a family of corner cutting schemes

R. Ait-Haddou, Y. Sakane, T. Nomura
Computer Aided Geometric Design, volume 30, issue 2, pp. 240-253, (2013)

A Müntz type theorem for a family of corner cutting schemes

Keywords

Corner cutting schemes, Bzier curves, GelfondBzier curves, Mntz spaces, Density of Mntz spaces

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.

Code

DOI: 10.1016/j.cagd.2012.12.001

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