High accuracy approximation of helices by quintic curves

被引：40

作者：

Yang, XN ^{[1
]}

机构：

[1] Zhejiang Univ, Dept Math, Hangzhou 310027, Peoples R China

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2003年 / 20卷 / 06期

基金：

中国国家自然科学基金;

关键词：

helix; Bezier curves; rational Bezier curves; interpolation; parametrization;

D O I：

10.1016/S0167-8396(03)00074-8

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

In this paper we present methods for approximating a helix segment by quintic Bezier curves or quintic rational Bezier curves based on the geometric Hermite interpolation technique in space. The fitting curve interpolates the curvatures as well as the Frenet frames of the original helix at both ends. We achieve a high accuracy of the approximation by giving a proper parametrization of the curve, and the approximation order of the height function along the helix axis is 9 provided that the screw angle of the helix is fixed. Numerical examples are also presented to illustrate the efficiency of the new method. (C) 2003 Elsevier B.V. All rights reserved.

引用

页码：303 / 317

页数：15

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