一种三维空间9-交模型的简化方法

9-交模型是一种表达三维空间拓扑关系的常用方法,但存在着冗余度大等问题。本文在Z latanova简化9-交模型工作的基础上,定义了点、线、面和体等简单三维空间对象,对它们之间的拓扑关系进行了研究。排除各种不可能的情况,共总结出24种可能的9-交结果以及80种点线面体之间的拓扑关系,并进行归类得到55种拓扑分析操作,从而大大简化了原模型。以线与体的拓扑关系分析为例,给出了根据简化以后的9-交模型进行拓扑分析操作的具体算法实现。

Method for Simplifying 3D Spatial Nine-Intersection Model

The topological relations between 3D objects are very important for the study of the spatial operations and algorithms of 3D objects.A nine-intersection model is a common one used to represent the topological relations between 3D spatial objects,but it has a problem of great redundancy.Based on the work of Zlatanova,the simple 3D spatial objects such as point,line,region and body are defined and the topological relations between them are investigated.All the impossible relations are excluded.24 possible nine-intersection results and eighty topological relations between points,line,region and body are concluded.All the 80 topological relations are categorized to get 55 different topological operations.In this way,the original nine-interscetion model is greatly simplified.Taking the topological relations between the line and the body as an example,algorithms based on the simplified 9-intersection model are designed.