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)|
|Number of pages||14|
|Journal||Computer Aided Geometric Design|
|State||Published - Feb 2013|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: This work was partially supported by the MEXT Global COE project. Osaka University, Japan.