A Muntz type theorem for a family of corner cutting schemes

作者：Ait Haddou Rachid^*; Sakane Yusuke; Nomura Taishin

来源：Computer Aided Geometric Design, 2013, 30(2): 240-253.

DOI：10.1016/j.cagd.2012.12.001

• Corner cutting schemes
• Bezier curves
• Gelfond-Bezier curves
• Muntz spaces
• Density of Muntz spaces

Dimension elevation process of Gelfond-Bezier curves generates a family of control polygons obtained through a sequence of corner cuttings. We give a Muntz type condition for the convergence of the generated control polygons to the underlying curve. The surprising emergence of the Muntz 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.

• 出版日期2013-2