Study On Spatio-temporal Topological Relationship Expression And Computation Based On Conformal Geometric Algebra

Spatio-temporal topology analysis is an important research issue in Geographical Information Science. At present, spatio-temporal topological relations are commonly expressed via qualitative methods, which have certain problems such as content duplication, information redundancy and lack of the ability to calculate spatio-temporal topological relations directly. Researches about spatio-temporal topological relationship computation are also limited, and do not yet have a systematic theory or methodology. The expressions of spatio-temporal objects and spatio-temporal topological relations are separated because of the constraint from the underlying mathematical theory foundation, and it is difficult to define relatively complete analysis operators for spatio-temporal topological relationship unified expression and computation.For the deficiencies of the existing spatio-temporal topological relationship expressing and computing methods, and around the needs of spatio-temporal object expression and spatio-temporal topology analysis, this dissertation introduces Conformal Geometric Algebra theory, which has the ability of multidimensional unified expressing and geometric computing, from a unified perspective of multidimensional space-time. A unified expressing model for spatio-temporal objects of different types and dimensions is established. On this basis, formal expressing methods and a unified computing framework for spatio-temporal topological relationship are also proposed. The research provides theoretical and methodological support for expressing and computing the spatio-temporal topological relations between geographic objects, and has effectively promoted spatio-temporal topological relationship expressing and analyzing capabilities of GIS. The main research contents of this dissertation are as follows:(1) Unified expressing model for multidimensional spatio-temporal objects based on Conformal Geometric Algebra. In order to solve the problem that expression patterns of spatio-temporal objects of different types and dimensions are not unified, Conformal Geometric Algebra theory is introduced and then complex spatio-temporal objects of different dimensions are decomposed into several simple geometric shapes. Space-time is constructed and spatio-temporal objects are expressed via inner product and outer product in Conformal Geometric Algebra. On the basis of multivector, a unified expressing model for spatio-temporal objects is established finally. (2) Spatio-temporal topological relationship formal expression supported by Conformal Geometric Algebra. Based on the above unified expressing model for multidimensional spatio-temporal objects, spatio-temporal topological relations are formally expressed via the multi-branch decision tree method, which is not only qualitative but also quantitative. The topological relations between simple spatio-temporal objects are judged via topology rule sets. On this basis, those between complex spatio-temporal objects are deduced as well. As a result, the expressions of spatio-temporal objects and spatio-temporal topological relations become an organic unity.(3) Spatio-temporal topological relationship unified computing framework supported by Conformal Geometric Algebra. On the basis of spatio-temporal topological relationship formal expression, the algorithm structures and implementation processes of spatio-temporal topological relationship computing methods are discussed in the framework of Conformal Geometric Algebra. Practical operator and algorithm sets are established, and spatio-temporal topological relationship unified computing framework STTR-CF, which includes computational engine and interfaces, is designed and implemented.(4) Application demonstration and case verification. Land use spatio-temporal topology analysis with the help of computational interfaces supplied by STTR-CF is proposed. The feasibility, effectiveness and computational correctness of STTR-CF are verified by comparing its computational results with other methods’.The research shows that CGA-based spatio-temporal object unified expressing model has dimensional unity and self-adaptability in structure, simplicity and semantic clarity in expression, and the ability to support spatio-temporal topological relationship expression and computation. STTR-CF, spatio-temporal topological relationship unified computing framework designed and implemented in this dissertation, is able to build the right solutions for specific needs and problems, which effectively promotes spatio-temporal integrated analysis and application. The work of this research provides a feasible and new way for the study on spatio-temporal topological relationship expression and computation, and has important scientific significance and practical value.