A Muntz type theorem for a family of corner cutting schemes

被引：8

作者：

Ait-Haddou, Rachid ^{[1
,3
]}

Sakane, Yusuke ^{[2
]}

Nomura, Taishin ^{[1
,3
]}

机构：

[1] Osaka Univ, Ctr Adv Med Engn & Informat, Osaka 5608531, Japan

[2] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, Osaka 5600043, Japan

[3] Osaka Univ, Grad Sch Engn Sci, Dept Mech Sci & Bioengn, Osaka 5608531, Japan

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2013年 / 30卷 / 02期

关键词：

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

D O I：

10.1016/j.cagd.2012.12.001

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

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. (C) 2012 Elsevier B.V. All rights reserved.

引用

页码：240 / 253

页数：14

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