期刊论文

中文

计算机应用与软件

1000-386X

2012

29

1

149-151,190

10.3969/j.issn.1000-386X.2012.01.042

湖南省科技重大专项（2010J05） 稳定人才基金项目（09WD47）

本校为第一机构

通过分析Bezier曲面局部凸的充要条件与控制顶点网格形状的关系,在几何上将网格的形状与曲面的凸性之间建立联系,导出Bezier曲面局部凸的几个充要条件。将凸性分析的结论应用到Bezier曲面拼接中,得到Bezier曲面保凸拼接的条件,并且证明带有公共边界线的两个局部凸Bezier曲面的C~n(n≥1)拼接后,仍然是凸的且凸性相同。最后,给出几个三次Bezier曲面保凸拼接实例。

The relation has been set up for the figure of the grid and the convexity of surface in terms of geometry concept by analysing the relationship between the necessary and sufficient conditions of local convex on Bezier surface and the figure of control vertices grid,a couple of necessary and sufficient conditions for local convex on Bezier surface are then educed.The conclusion of convexity analysis is applied to Bezier surfaces splicing,the condition of convexity-preserving splicing for Bezier surfaces is derived.Moreover,it is proved that afte...