(4,5)次可展Bézier曲面  

(4,5)-developable Bézier surfaces and properties

作　　者：孟雅琴[1] 叶正麟[1] 赵红星[2] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072 [2]榆林学院,陕西榆林719000

出　　处：《西北大学学报（自然科学版）》2004年第2期133-136,共4页Journal of Northwest University（Natural Science Edition）

基　　金：陕西省自然科学研究计划资助项目(200CSL08)

摘　　要：目的　为生成一(4,5)次可展B啨zier曲面,并构造出G1合成可展曲面。方法　按照G.Au mann构造可展B啨zier曲面的方法,在两个平行平面(即设计平面)上分别选取4次和5次B啨zier曲线作为设计曲线生成一可展曲面。结果　得到了两条设计曲线的控制多边形应满足的几何位置关系,并详细讨论了此可展曲面上平行于设计平面的截曲线对于设计曲线的保凸性、保形性及奇异性(尖点)的条件;在两个设计平面上分别指定了型值点列后,可构造出G1合成可展B啨zier曲面,它的两条边界曲线插值指定的型值点列。结论　通过边界曲线的设计和适当选取匹配系数,可设计出所需形状的可展曲面,满足诸如凸性、弯曲、角点线或尖点线等要求。Aim Generate a (4,5) developable Bézier surface and construct G^1 combining developable Bézier surface.Methods Using G.Aumann′s method, the geometric positional relationship that the two control polygons should satisfy is presented in case the ruled surface is developable. Results The conditions of the shape preserving, convexity preserving and singularity properties of parallel transversal curves on the developable surface are also specifically discussed. The method to generate a G^1 developable Bézier surface that interpolates the given sequence of points on the intersecting curving is given. Conclusion Therefore,using existing techniques of constructing G^1 Bézier curves by designing the boundary curve and selecting suitable matching coefficients, the giving shape developable surface that satisfies the requirement for convexity, bending and so on can be constructed.

关 键 词：可展曲面 Bēzier曲面片 设计曲线 边界曲线 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]