中文摘要：

四面体格网（TEN）模型是一种重要的空间数据构模方法,侧重于三维空间对象内部的表达,但是存在着数据量大、计算速度慢的问题。三维拓扑关系是三维GIS的重要研究内容,为此,该文提出了面向TEN的三维拓扑关系计算方法。基于点集拓扑学理论,将TEN分解为内部、边界和外部3个集合,并使用9交模型描述了TEN/TEN的8种拓扑关系;设计了面向TEN的三维拓扑关系计算流程,详细阐述了面向TEN的三维拓扑关系计算的核心算法;基于提出的三维拓扑关系算法,设计了面向TEN的拓扑关系计算实验。实验结果表明：该文提出的面向TEN的三维拓扑关系计算方法,能够满足TEN之间拓扑关系计算的需求。

英文摘要：

As an important spatial data model, tetrahedron network（TEN）model has advantage in representation of the interior of 3D objects and disadvantage in large volume of data and slow computation speed. Because 3D topological relationship calculation was the focus of 3D GIS, a topological relationship calculation algorithm for TEN model was proposed in this paper. TEN was divided into three sets inclu- ding interior set, boundary set and exterior set based on point set theory. Eight topological relationships were expressed based on 9IM（nine intersection model）. Flow chart of 3D topological relationship calcula- tion method for TEN model was given and the core algorithms were described in detail. A prototype sys- tem was developed and topological relationship calculation results were showed. From the topological rela- tionship calculation results, we can conclude that the proposed algorithm can calculate topological rela- tionship between TEN.