Towards the next-generation GIS: a geometric algebra approach

ABSTRACT Due to the increasing complexity of GIS data and service modes, there is an urgent need for the next generation of GIS with new representation and computation methods. A number of spatiotemporal models, analytical and visualization methods, as well as system architectures have been proposed. However, previous studies failed to integrate basic geographical theories with latest computing technologies. Without a well-defined body of underlying theories, new models and methods are limited in scope and not able to meet the ultimate requirements of the next-generation GIS, which demands multidimensional, highly dynamic and semantic-rich representations and computational power. Geometric algebra (GA) provides an ideal tool for the expression and calculation of multidimensional geometric objects, and has proved to be effective for GIS representation and computation applications in our previous studies. We propose to use GA as the basic mathematical language for the establishment of the next-generation GIS. We present the framework of a GA-based next-generation GIS and describe the representation space, data structure, and computational models in this paper. A few issues that have not been sufficiently addressed by previous studies are discussed in detail with potential solutions proposed. These include multi-scale representations, modelling of geographic processes, simulation of geographic interactions, and multi-element modelling. The GA-based next-generation GIS uses an integrated structure consisting of a theoretical architecture, model for information expression, and computational methods. Implementation of the approach aims to improve GIS capacities in applications such as global spatiotemporal modelling and analysis, regional geographic modelling and simulation, smart city applications, and many others