三维地籍空间数据一致性计算和验证是保证三维地籍数据准确性的关键，其本质是三维地籍对象几何与拓扑关系计算。现有三维地籍对象几何与拓扑关系计算依赖具体坐标，不同维度地籍对象几何与拓扑关系计算缺乏统一的计算框架，增加了以混合维度拓扑关系计算为主要特征的三维地籍空间数据一致性计算和验证的复杂度，影响计算效率的提升。针对上述问题，本研究拟基于齐次几何代数理论，构建一种新的三维地籍对象几何与拓扑关系多维统一表达和计算模型。利用齐次几何代数中外积运算的维度扩展特性，研究不同维度地籍对象多维统一的几何表达方法；利用齐次几何代数中连接不同维度对象的多重向量结构，研究三维地籍对象几何与拓扑关系集成的一体化表达方法；利用齐次几何代数在多维统一计算方面的坐标无关性优势，研究三维地籍对象几何与拓扑关系的多维统一计算框架。本项目研究可以有效降低三维地籍对象几何与拓扑关系计算复杂度，提升一致性计算效率。

Consistency in data validation for three-dimensional (3D) cadastral objects is the key to ensure the accuracy of 3D cadastral spatial data. The essence of consistency in 3D cadastral data validation is the calculation of geometry and topology for 3D cadastral objects. Existing methods of geometric and topological calculation depend on objects’ coordinates, which leads to a disunited calculation framework for geometry and topology in different dimensional cadastral objects. These methods increase the complexity of consistency in 3D cadastral data validation and reduce the calculation efficiency. To solve the above problems, theories of homogeneous geometric algebra (HGA) are introduced into 3D cadastral objects modeling. A new multi-dimensional unified expression and calculation model for 3D cadastral object’s geometry and topology are proposed based on HGA. A multi-dimensional unified expression method for 3D basic cadastral objects will be researched using advantages of outer product operation in dimensions extension. Integration expression methods for both geometry and topology of 3D cadastral objects are designed using the multivector structure in HGA which can connect objects in different dimensions. A multi-dimensional unified geometric and topological calculation framework for 3D cadastre is designed take advantage of HGA’s characteristics in multi-dimensional calculation. Results of this study are willing to simplify the calculation structure for 3D cadastral object’s geometry and topology and improve the efficiency of calculation.