三维空间中简单线与体之间的拓扑关系研究  

Study on the 3D spatial topological relationships between simple line and volume

作　　者：李姣姣[1,2] 李光强[1,2] 徐锐[1] 

机构地区：[1]中南大学信息物理工程学院,长沙410083 [2]矿山空间信息技术国家测绘局重点实验室,河南焦作454003

出　　处：《测绘科学》2009年第6期221-223,共3页Science of Surveying and Mapping

基　　金：矿山空间信息技术国家测绘局重点实验室(编号:KLM200824)

摘　　要：三维空间对象的拓扑关系对于研究三维空间对象的操作及其算法至关重要。本文在详细研究拓扑关系的9-交和4-交模型的基础上,指出了它们在表达简单线与体拓扑关系上的局限性,9-交模型的线性相关性以及4-交模型的不完备性。进而提出简单线与体拓扑关系表达的扩展4-交模型,运用扩展4-交模型详细分析了简单线与体的拓扑关系,并给出图示。接着对所提扩展4-交模型线性无关性及完备性进行了论证。最后对所提出的扩展4-交模型进行了总结性说明。The research of topological relationships between 3 D spatial objects is significant for the spatial manipulation and algorithms. After making a detail research on the 9 - intersection model and the 4-intersection model, their deficiency about the topological relationships between simple line and volume was pointed out. The 9-intersection model is linear correlative and the 4-intersection model is completeness in describing spatial topological relationships between simple line and volume. Furthermore, an extended 4-intersection model was proposed in this paper. Then a detailed analysis between simple line and volume was done. The picture which describes the topological relationships was also given. The linear correlative and completeness of the extended 4-intersection model were argued. Finally, a conclusion was given.

关 键 词：空间拓扑关系 扩展4-交模型 线性相关性 

分 类 号：P231.5[天文地球—摄影测量与遥感]