Bezier曲面的凸性分析及保凸拼接  

ANALYSING CONVEXITY OF Bezier SURFACE AND THE CONVEX-PRESERVING SPLICING

作　　者：方逵[1] 邓四清[2] 姚杰[1] 吴泉源[3] 

机构地区：[1]湖南农业大学信息科学技术学院,湖南长沙410128 [2]韶关学院数学与信息科学学院,湖南韶关512005 [3]国防科技大学计算机学院,湖南长沙410073

出　　处：《计算机应用与软件》2012年第1期149-151,190,共4页Computer Applications and Software

基　　金：湖南省科技重大专项(2010J05);稳定人才基金项目(09WD47)

摘　　要：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Cn(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 after splicing,for two local convex Bezier surfaces with common boundary,their Cn（n≥1） are still convex with same convexities.In the end of the paper,a few examples of cubic Bezier surfaces convex-preserving splicing are given.

关 键 词：BEZIER曲面 控制网格顶点 凸性 保凸拼接 

分 类 号：TP3[自动化与计算机技术—计算机科学与技术]