带形状参数的四次Ball曲线

山东大学学报(工学版) ›› 2011, Vol. 41 ›› Issue (2): 23-28.

带形状参数的四次Ball曲线

刘华勇,李璐,张大明

安徽建筑工业学院数理系, 安徽合肥 230601

收稿日期:2010-09-02 出版日期:2011-04-16 发布日期:2010-09-02
作者简介:刘华勇(1972- ),男,安徽合肥人,讲师,硕士,主要研究方向为计算机辅助几何设计和图形学.Email:aiaiwj@126.com
基金资助:
安徽省教育厅自然科学基金资助项目(KJ2010B050, 2010SQRL093, KJ2009A019Z)

Quadratic Ball curve with multiple shape parameters

LIU Hua-yong, LI Lu, ZHANG Da-ming

Department of Sciences and Physics, Anhui Institute of Architecture ＆ Industry, Hefei 230601, China

Received:2010-09-02 Online:2011-04-16 Published:2010-09-02

摘要/Abstract

摘要：

为了明确形状参数对三次Ball曲线形状的影响,给出一个含有参数λ、u的四次多项式基函数,分析了此基函数的性质。同时定义基于该组基函数带有形状参数的多项式曲线,讨论了两段曲线连续拼接的条件。在保持控制多边形不变的情况下,可以通过改变形状参数来调整曲线形状,使得曲线具有更强的表达能力。曲线不仅具有三次Ball曲线的特性,而且具有形状的可调性和更好的逼近性。计算实例表明:该方法是有效的,可以广泛地应用于计算机辅助设计中对曲线形状调整。

关键词: 计算机应用, 广义Ball曲线, 形状参数, 曲线设计

Abstract:

To investigate effects of shape parameters on the cubic Ball curve shape, a polynomial basis function of 4th degree with shape control parameters λ,u was presented. It is an extension of basis function of the cubic Ball basis fanction. Based on these basis functions, the guadnic Ball curve with two parameters was defined. The continuity condition of twopieces of curves was also discussed. This curve not only inherited the outstanding properties of the cubic Ball curve, but also was adjustable in shape and fit close to the control polygon. Its shape can be adjusted by two parameters in the same control points, which makes the curve have more powerful expression ability. Some practical examples which were adjustable in shape parameter verify the applicability in the computer aided design.

Key words: computer application, generalized Ball curve, shape parameter, curve design

刘华勇,李璐,张大明. 带形状参数的四次Ball曲线[J]. 山东大学学报(工学版), 2011, 41(2): 23-28.

LIU Hua-yong, LI Lu, ZHANG Da-ming. Quadratic Ball curve with multiple shape parameters[J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2011, 41(2): 23-28.

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