CAUSTA: Clifford Algebra‐based Unified Spatio‐Temporal Analysis

Abstract

Abstract Introducing Clifford algebra as the mathematical foundation, a unified spatio‐temporal data model and hierarchical spatio‐temporal index are constructed by linking basic data objects, like pointclouds and Spatio‐Temporal Hyper Cubes of different dimensions, within the multivector structure of Clifford algebra. The transformation from geographic space into homogeneous and conformal space means that geometric, metric and many other kinds of operators of Clifford algebra can be implemented and we then design the shortest path, high‐dimensional Voronoi and unified spatial‐temporal process analyses with spacetime algebra. Tests with real world data suggest these traditional GIS analysis algorithms can be extended and constructed under Clifford Algebra framework, which can accommodate multiple dimensions. The prototype software system CAUSTA (Clifford Algebra based Unified Spatial‐Temporal Analysis) provides a useful tool for investigating and modeling the distribution characteristics and dynamic process of complex geographical phenomena under the unified spatio‐temporal structure.