Multi-factor Coupled PDE Model and Algorithm for Spatial Partition

In order to study spatial partition of the non-convex discrete spatial data, established mathematical model coupling the convexity, data size and dispersion of the dataset. Non-convex discrete spatial data was divided in the limited area by Laves divided identity 3⁶, and then by the partial derivatives relationship of the terrain surface between the differential unit and the data density, the spacing and number of cells was calculated coupled discrete.Last visualization and compared analysis through building DEM showed that: coupled model can calculate out the spacing and number of non-convex discrete spatial data, also achieved seamless mosaic of divided units for different resolution; and while test data from 110 groups to 440 groups, the time cost of this paper was only 1/10-1/3 of 4⁴ divided identifies and Delaunay, and was linear growth with the data multiplied increased, besides the convergence was better, however it took growth with discrete degrees increased.