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CAUSTA: Clifford Algebra‐based Unified Spatio‐Temporal Analysis
Author(s) -
Yuan Linwang,
Yu Zhaoyuan,
Chen Shaofei,
Luo Wen,
Wang Yongjun,
Lü Guonian
Publication year - 2010
Publication title -
transactions in gis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.721
H-Index - 63
eISSN - 1467-9671
pISSN - 1361-1682
DOI - 10.1111/j.1467-9671.2010.01221.x
Subject(s) - geometric algebra , multivector , clifford algebra , universal geometric algebra , algebra over a field , computer science , theoretical computer science , spacetime , algebra representation , mathematics , cellular algebra , pure mathematics , physics , quantum mechanics
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.