Nonexistence of rational rotation-minimizing frames on cubic curves

被引：36
|
作者：
Han, Chang Yong [1 ]
机构：
[1] Kyung Hee Univ, Dept Appl Math, Yongin 446701, Gyeonggi Do, South Korea
来源：
COMPUTER AIDED GEOMETRIC DESIGN | 2008年 / 25卷 / 4-5期
关键词：
Pythagorean-hodograph curve; rotation-minimizing frame; Euler-Rodrigues frame; rational frame; cubic curve;
D O I：
10.1016/j.cagd.2007.09.006
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
We prove there is no rational rotation-minimizing frame (RMF) along any non-planar regular cubic polynomial curve. Although several schemes have been proposed to generate rational frames that approximate RMF's, exact rational RMF's have been only observed on certain Pythagorean-hodograph curves of degree seven. Using the Euler-Rodrigues frames naturally defined on Pythagorean-hodograph curves, we characterize the condition for the given curve to allow a rational RMF and rigorously prove its nonexistence in the case of cubic curves. (C) 2007 Elsevier B.V. All rights reserved.
引用
收藏
页码：298 / 304
页数：7
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