非流形几何造型及其布尔运算研究

Research about Non-Manifold Modeling System and It's Boolean Operation

简述了非流形造型的基本原理及其采用的基本操作 ,以及非流形几何造型布尔运算 ,侧重在其基本理论 ,包括 :推广的Euler公式 ,集合属籍分类函数 ,正则集与正则集合运算 ;最后介绍了非流形造型布尔运算的 5个基本运算步骤 ,即求交 ,新面环的生成与剖分 ,拓扑元素分类 ,连面成壳与连壳成体 ,以及悬点、悬边、悬面的生成 .实践证明算法是有效。

At first, describes the basic principal of non manifold geometric modeling , the data structure,and some basic operations of the system used,then describes the basic theory of Boolean operation in non manifold geometric modeling which consists of extended EULER formula, set ownship classification function, regular set and regular set operation. Finally, the five basic operation steps of Boolean operation are described,that is,①intersection, include the intersection of edge with edge, edge with face, edge with volume, face with face, face with volume. ②the formation of new loops and their partition into new sub loops and sub faces . ③the topology elements classification. ④linking the face into shells and linking shells into volumes. ⑤the formation of lamina elements which include lamina vertex, lamina edges, lamina faces.