Article ID Journal Published Year Pages File Type
441191 Computer Aided Geometric Design 2013 14 Pages PDF
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.

► Identify a family of corner cutting schemes as dimension elevation process of Gelfond–Bézier curves. ► Give a Müntz type condition for the convergence of the dimension elevated control polygons to the underlying curve. ► Discuss the emergence of the Müntz condition in the problem and its possible implications for the density of infinite nested Chebyshev spaces.

Related Topics
Physical Sciences and Engineering Computer Science Computer Graphics and Computer-Aided Design
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