An Unified CGA-Based Formal Expression of Spatio-Temporal Topological Relations for Computation and Analysis of Geographic Objects

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.