Multi-dimensional Unified Algorithm And Application Of Voronoi Based On Conformal Geometric Algebra

As an important part in GIS spatial analysis, V-neighborhood analysis plays an important role in other complex geographic analysis such as space partition, structural analysis. In total, many studies focus on two-dimensional V-neighborhood analysis algorithm, three-dimensional and even higher dimensional algorithms are also discussed. However, existing three-dimensional and higher dimensional V-neighborhood algorithm, aiming at the specific application areas, lack the universality and disunity among different dimensions, and Delaunay and Voronoi generated by these algorithms are short of integrative description to topology and attribute information. It is difficult to support effectively high dimensional space analysis and even geographical analysis. As GIS is developing from the two-dimension to three-dimension and temporal GIS, it is particularly important to promote the V-neighborhood analysis with the dimension adaptability, unity of different dimensions.The combination of advantages of conformal transformation and geometric algebra in conformal geometric algebra can provide a unified, simple expression and computing framework for different types and different dimensional geometric objects. This paper tries to introduce conformal geometric algebra for the building of V-Construction neighborhood algorithm. Draw multidimensional unified objects expression and operation structure of conformal geometric algebra, the unique organization of objects and attributes, multi-dimensional integrated structure of V-neighborhood algorithm framework is proposed. And basing on this V-neighborhood algorithm, adaptive interpolation and local interpolation are further constructed. Above algorithms unify the expression and computing of different dimensions objects, basic topology involved in V-neighborhood analysis in the underlying of the mathematics. So the proposed algorithm structure can be extended to other more complex applications algorithm, to better to support complex analysis.Based on the meteorological data of China cities, two-dimensional to four-dimensional unified V-neighborhood algorithm is achieved. Compared with the traditional V-neighborhood algorithm, there proposed V-neighborhood algorithm has advantages of unity in different dimensions and no boundary constraints. And adaptive interpolation algorithm makes the spatial structure of the known data retained well, while local interpolation algorithm makes the local characteristics of the known data better. Then the three-dimensional community case simulation study shows that the interpolation algorithm of this paper has better interpolation results, and that indicate V-neighborhood algorithm structure based conformal geometric algebra has good generality and extending. That provides an effective reference to build a simple, efficient, high-dimensional space analysis, and multi-dimensional integration geographical analysis algorithm.