A generalized curve subdivision scheme of arbitrary order with a tension parameter

被引：37
作者：
Fang, Mei-e [1 ,2 ]
Ma, Weiyin [1 ]
Wang, Guozhao [3 ]
机构：
[1] City Univ Hong Kong, Dept MEEM, Hong Kong, Hong Kong, Peoples R China
[2] Hongzhou Dianzi Univ, Sch Comp Sci, Hangzhou, Zhejiang, Peoples R China
[3] Zhejiang Univ, Dept Math, Hangzhou 310003, Zhejiang, Peoples R China
来源：
COMPUTER AIDED GEOMETRIC DESIGN | 2010年 / 27卷 / 09期
基金：
美国国家科学基金会;
关键词：
Generalized subdivision; Tension parameter; Generalized B-spline curve; Trigonometric spline curves; Hyperbolic spline curves; Analytic curves; B-SPLINE CURVES; C-CURVES; SURFACES; ALGORITHM;
D O I：
10.1016/j.cagd.2010.09.001
中图分类号：
TP31 [计算机软件];
学科分类号：
081202 ; 0835 ;
摘要：
This article presents a generalized subdivision scheme of arbitrary order with a tension parameter for curve design. The scheme is built upon refinement of a family of generalized B-splines that unify classic B-splines with algebraic-trigonometric B-splines and algebraic-hyperbolic B-splines. The scheme of order k produces Ck-2-continuous limit curves representing such splines. Many known subdivisions are special cases of the proposed subdivision scheme. By assigning an appropriate initial tension parameter, many analytic curves commonly used in engineering applications, such as Lissajous curves, conics, trigonometric function curves, hyperbolic function curves. catenary curves and helixes, etc., can also be exactly defined under the generalized subdivision scheme. Numerous examples are also provided to illustrate how the initial tension parameter and the control points are assigned for reproducing such analytic curves. (C) 2010 Elsevier B.V. All rights reserved.
引用
收藏
页码：720 / 733
页数：14
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