摘要
为了拓展曲线曲面的表示方法,提出一种曲线造型工具——H-Bzier曲线.在讨论三次H-Bzier曲线性质的基础上,提出了三次H-Bzier曲线的任意分割算法,即对三次H-Bzier曲线上任意一点p(t*)(0≤t*≤α),求该点把曲线分成的2个子曲线段pt*(t)(0≤t≤t*)与pα-t*(t)(0≤t≤α-t*)的控制参数和控制顶点;给出了三次H-Bzier曲线与三次Bzier曲线的拼接条件,以及三次H-Bzier曲线在曲面造型中应用的例子.采用该算法所得结果简单、直观,有效地增强了三次H-Bzier方法控制及表达曲线形状的能力.
H-Bezier curves, as a new kind of curve modeling tool, are presented in this paper, aiming at extending the representation of curves and surfaces. Based on the analysis of the properties of cubic H-Bezier curves, a subdivision algorithm is proposed to compute the control parameters and control points of the two subcurves Pt^＊（t）（0≤t≤t^＊） and Pa-t^＊（t）（0≤t≤a-t^＊）） subdivided by any point p（t^＊）（0≤t^＊≤a） of cubic H-Bezier curves. The connection conditions between cubic H-Bezier curves and cubic Bezier curves are derived the applications of cubic H-Bezier curves in the surface modeling are given. The obtained results, which are simple and intuitionistic, can effectively improve the shape representation and control of cubic H-Bezier curves.
出处
《计算机辅助设计与图形学学报》
EI
CSCD
北大核心
2009年第5期584-588,共5页
Journal of Computer-Aided Design & Computer Graphics
基金
国家自然科学基金(60773043,60473114)
教育部博士点基金(20070359014)
安徽省自然科学基金(070416273X)
安徽省教育厅科技创新团队基金(2005TD03)
