Clifford algebra and GIS spatial analysis algorithms - The case study of geographical network and voronoi analysis

Introducing Clifford Algebra as the mathematical foundation, we proposed a unified multi-dimensional GIS data model, constructed by linking data objects of different dimensions within the multivector structure of Clifford algebra. Then, algorithms for geographical network analysis (such as shortest path, minimum unicom and maximum flow analysis) and high-dimensional voronoi diagram were constructed. We use both simulation and real world data to test the usability and performance of our algorithms. The result gives very positive prospect of implement GIS analysis algorithms under Clifford Algebra framework. In that way, traditional GIS analyses algorithms can be extended not only accommodate various dimensions but also get beneficial on performance.