中文摘要：

三维空间实体及其间拓扑关系的语义描述和形式化描述是三维GIS空间数据建模的重要理论基础．以点集拓扑学为基础，基于空间剖分用单纯形和单纯复形对空间实体进行形式化描述，利用代数运算和集合运算相结合的方法计算出实体内部和边界及相互之间的交集，运用维度扩展法判断交集的维数，提出基于单纯复形的维度扩展的41模型．为了进一步区分拓扑不同胚的空间实体，给出了基于Euler示性数的41模型．相比传统的41或91模型，基于维度扩展和分离数的空间拓扑关系描述模型进一步细化了三维空间实体的拓扑关系．

英文摘要：

Formal description and representation of topological relations between 3D spatial features is one of the key issues in developing 3D GIS. The criteria on the description and determination of topological relations are topological invariants, which may be dimension, separations, and Euler-Poincare characteristics etc. Some basic issues of modeling topological relations using these invariants are concentrated on. With the introduction of the concept of pure k- complex（0≤k≤3） , formal description of spatial features in the GIS is given. An approach is proposed to describe the topological relations between 3D spatial features with topological components of k-complex（0≤k≤3） , i.e. boundary and interior. The topological relations for the pair of k-complex were examined with dimension-extend 4-intersection prior to the calculation of Euler-Poincare characteristics. The model based on dimension-extend and Euler-Poincare characteristics can distinguish the topological relations of 3D spatial features more aecurately than the classic 4/9-intersection model.