High accuracy Hermite approximation for space curves in Rd

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:325

Article

Rababah, Abedallah

关键词: Hermite approximation;    space curves;    approximation order;    high accuracy;    computer aided geometric design;   

DOI  :  10.1016/j.jmaa.2006.02.054

来源: Elsevier

【 摘 要 】

In this article, it is shown that a space curve in R-d can be approximated by a piecewise polynomial curve of degree m with order (m + 1) + [(m + 1)/(2d - 1)] rather than m + 1. Moreover, we show that the optimal order (m + 1) + [(m - 1)/(d - 1)] is possible for a particular set of curves of nonzero measure. Analogous results were shown to be true for Taylor polynomial interpolation in [A. Rababah, High order approximation method for curves, Comput. Aided Geom. Design 12 (1995) 89-102]. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free