Spatial Data Transformation and Fusion Expression Based on Geometric Algebra

With the advancement of geographic spatial data observation and collection technologies, three-dimensional geographic spatial data serving various industries has become increasingly abundant. However, geographic spatial data from different sources exhibit significant differences in data organization structures, data storage logic, data formats, and more. These differences pose substantial challenges to the integration and fusion of multi-source heterogeneous spatial data. Addressing the aforementioned issues, this paper proposes a method for geographic spatial data transformation and fusion expression based on geometric algebra. Basic operators in geometric algebra, such as inner product, outer product, and geometric product, are utilized to design various types of geometric space transformation classes and data transformation operation interface classes. The storage structure for geographic spatial data is constructed based on the multivector structure in geometric algebra. A geographic spatial data transformation system, developed based on the data transformation method presented in this article, is used for validation through the parsing and integration of CityGML data and DXF data. The research results of this article can provide new solutions for the conversion and fusion of current multi-source heterogeneous spatial data.