Abstract
Geographic objects usually change their locations, shape and characteristics over time. Change in one object can trigger a series of changes in the adjacent objects and their topological relationships. The spatio-temporal topological relations analysis of geographic objects is an important issue in the development of a more temporally aware geographical information science. Research on, and applications of spatial topology are mature, yet the methods to exploit spatio-temporal topology are still far from the reach of GIS users. Such research has probed the definition of time, and explored the formalization of spatio-temporal topology from different perspectives. However, almost all methods and representations are mathematical or logical methods represented in qualitative ways. Conformal geometric algebra (CGA) is a new tool for unified multidimensional representation and geometric computation, from a unified perspective of multidimensional space-time. In this research, we pursue a logic based on the concept of a unified representational model based on CGA for spatio-temporal objects and their spatio-temporal topological relations formally expressed by a multi-branch decision tree, which is not only qualitative but also quantitative. The research provides theoretical and methodological support for expressing and computing the spatio-temporal topological relations among any set of geographic objects. This ability effectively promotes the expression of spatio-temporal topological relationships and enhances the analytical capabilities of GIS for dealing with both space and time.
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Acknowledgements
This research was funded by the National Natural Science Foundation of China (41471313). We thank M. Chen, X. Jiang, and Q. Wang, three graduated graduate students, for their research results, which provided a good foundation for this study.
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This article is part of the Topical Collection on Geometric Algebra for Computing, Graphics and Engineering edited by Yu Zhaoyuan, Dietmar Hildenbrand, Kit Ian Kou, and Eckhard Hitzer.
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Wang, Y., Zhang, F. An Unified CGA-Based Formal Expression of Spatio-Temporal Topological Relations for Computation and Analysis of Geographic Objects. Adv. Appl. Clifford Algebras 29, 59 (2019). https://doi.org/10.1007/s00006-019-0971-2
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DOI: https://doi.org/10.1007/s00006-019-0971-2