Cubic trigonometric polynomial curves with a shape parameter

被引：145

作者：

Han, XL ^{[1
]}

机构：

[1] Cent S Univ, Dept Appl Math, Changsha 410083, Peoples R China

来源：

COMPUTER AIDED GEOMETRIC DESIGN | 2004年 / 21卷 / 06期

关键词：

trigonometric polynomial; trigonometric curve; B-splines; shape parameter;

D O I：

10.1016/j.cagd.2004.03.001

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

Cubic trigonometric polynomial curves with a shape parameter are presented in this paper. The trigonometric polynomial curves are C(2) continuous and G(3) continuous with a non-uniform knot vector. With a uniform knot vector, the trigonometric polynomial curves are C(3) continuous for the shape parameter lambda not equal 1 and C(5) continuous for lambda = 1. With the shape parameter, the trigonometric polynomial curves can be close to the cubic B-spline curves or closer to the given control polygon than the cubic B-spline curves. The trigonometric polynomial curves also can be decreased to quadratic trigonometric polynomial curves which can represent ellipses. The trigonometric Bezier curve and trigonometric polynomial interpolation are also discussed. (C) 2004 Elsevier B.V. All rights reserved.

引用

页码：535 / 548

页数：14