与给定多边形相切的四次可调Ball闭曲线  

Closed adjustable quartic Ball curves with given tangent polygon

作　　者：郭坤[1] 刘植[1,2] 江平[1] 

机构地区：[1]合肥工业大学数学学院,安徽合肥230009 [2]合肥工业大学计算机与信息学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2010年第8期1271-1273,1276,共4页Journal of Hefei University of Technology：Natural Science

基　　金：教育部博士点新教师基金资助项目(2008JYXJ0828);安徽省高校优秀青年人才基金资助项目(2009SQRZ008);合肥工业大学科学研究发展基金资助项目(2010HGXJ0084);安徽省自然科学基金资助项目(090416232)

摘　　要：文章讨论了与给定多边形相切的分段四次可调Ball曲线的构造方法,在每相邻两切点之间构造2段四次Ball曲线。所构造的曲线C1连续,选择适当的形状参数可达到C2连续,而且对切线多边形都是保形的;Ball曲线段的控制点由切线多边形的顶点直接计算产生,曲线可以在一定范围内局部修改;实例表明使用文中的方法灵活、方便、有效。This paper proposes an approach for constructing planar piecewise closed adjustable quartic Ball curve with all edges tangent to a given control polygon,that is to construct two quartic Ball curves between every two tangential points.The curve segments are joined with C1continuity and if appropriate shape parameter are given,they are joined with C2continuity.The segmented Ball curves are all shape preserving to their tangent polygon.The control points of the Ball curve segments are computed simply by the vertices of the given tangent polygon.Local modifications in a certain range for these curves are possible.The effectiveness as well as adaptability of the method is manifested by experimental results.

关 键 词：分段四次Ball曲线 切线多边形 保形曲线 

分 类 号：O174.41[理学—数学] TP391.72[理学—基础数学]