Theory and method of spatial-temporal unified data model construction based on geometric algebra introduction to the popularization of project results

GIS data model is the basis of GIS data expression, organization, collection, analysis and transmission, and it is always the frontier and hotspot of GIS research.However, the existing GIS data model focuses on the expression of space or geometry, and the expression of time often adopts the discrete way, which leads to the imperfect expression of space, weak expression of time, insufficient expression of semantic and physical attribute and lack of expression of space-time relation.As an algebraic method to describe geometric problems, geometric algebra has the characteristics of unification of geometry and algebra, unification of time and space, multidimensional unification and unification of space-time expression and computation, and it is an effective mathematic tool to help GIS data model break through the above obstacles. According to the above questions, this project mainly answers the following 4 scientific questions: Can we use the scientific space-time view and geometric algebra method to construct the spatial-temporal integrated GIS data model from top to bottom? Can the method of geometric algebra achieve the unified expression of continuous and discrete geographical space-time and multidimensional unified expression? Can the new GIS data model be compatible with the existing GIS data model? Can the new GIS data Model support the geo-analytic model from the underlying mathematics level? After five years of research, the project has made some substantial progress, and has a clearer understanding of the above scientific problems, specifically expressed in: 1 the mapping transformation mechanism of spatial space-time and geometric algebra space is studied, and a conceptual model for temporal and spatial representation of geographical objects and dynamic geographical processes is formed. The fusion geometric expression and algebraic operation are constructed, discrete object and continuous process, geometric structure and spatial relation of geographical information total element expression; 2 the spatial-temporal data model of “six-factor” geometric algebra is constructed, which refers to geographical semantics, spatio-temporal location, geometrical form, evolutionary process, factor relationship and attribute characteristics.Thus, the spatio-temporal data model based on geometric algebra has richer connotations, which is helpful to integrate the dimension structure, geometric measurement and topological structure of vector data, to express the dimension structure of spatiotemporal field data, to facilitate the fusion of network object topology and constraint characteristics … 3 The multiple vector tree (mvtree) data structure of expression-organization-storage-retrieval-computing structure is designed.Tree structure, as the most commonly used structured storage, has many advantages, such as hierarchical expression and operation, fast retrieval speed, etc.Therefore, in practical applications, the nodes are given pointers to their siblings to facilitate the linear operation of the data.But the multiple vector tree structure of the project, the node level is built on the basis of the outer product operation, the value on the node can be obtained by operation, which greatly improves the flexibility of the structure and makes its application range more extensive. 4 The computational engine that can be used in parallel computation of geometric algebra GIS algorithm is developed.Using this engine, the user can realize the development of GIS algorithm through simple script instruction.Compared with the traditional script GIS system, the data type used by this computing engine has more versatility, the user does not need to spend too much time on the data conversion, and the operator operation is more intuitive, it can facilitate the development of GIS algorithm for the majority of geographers.At the same time, in order to cope with the decrease of the efficiency caused by the dimension enhancement of geometric algebra algorithm, the engine uses a number of optimization strategies, which makes it not inferior to the traditional Euclidean geometry algorithm in its running efficiency. 5 for the support of the geographic analysis model, this project constructs, the transformation and the coupling operation of the geometric algebra of the geographic model from three different perspectives of data coupling, model integration and model transformation.Data coupling mainly utilizes the advantage of geometric algebra in expression. Reduce the number of data conversion in the process of the model, and the adaptability of the data expression is also conducive to the development of the high dynamic model; the integration of the model is mainly based on the analysis of the data and flow of the geometrical algebra operators, Using the computing engine of the 4 results, it is easy to realize the coupling between the models; the reconstruction of the model is mainly the transformation of the geometric algebra of the existing models, and the project also makes a series of exploratory work on the method of solving the geo-model based on geometric algebra.

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