HIGH ACCURATE RATIONAL APPROXIMATION OF PARAMETRIC CURVES

被引：43

作者：

DEGEN, WLF

机构：

[1] Mathematisches Institut B, Universität Stuttgart, D-7000 Stuttgart 80

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 1993年 / 10卷 / 3-4期

关键词：

HIGH ACCURACY APPROXIMATION; APPROXIMATION ORDER; CUBIC RATIONAL CURVES; ASYMPTOTIC EXPANSION; AFFINE AND PROJECTIVE CURVATURE;

D O I：

10.1016/0167-8396(93)90043-3

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Similar to the work of de Boor, Hollig and Sabin [de Boor et al. '87) and Rababah [Rababah '92a] we construct a cubic approximant for a segment of a given curve. However, using a rational cubic instead of a polynomial one, a third order contact can be attained at both endpoints. It is shown that this rises the approximation order up to eight. A detailed analysis of the asymptotic behaviour (as the segment's length tends to zero) is given. It leads to a purely geometric condition for the existence of that rational cubic approximant.

引用

页码：293 / 313

页数：21

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