Modified Voronoi Diagram and Algorithms for its Application in Practice

The scope of application of the Voronoi diagram is quite diverse: artificial intelligence, urban systems, marketing, computer science and others. This is because the so-called spatial relationships are effectively solved using a Voronoi diagram. The classical Voronoi diagram method assumes homogeneity of objects, which, obviously, is far from reality and therefore limits not only the scope of its application, but also its possibilities. When adding potential power about objects, a potential scheme is added to the traditional Voronoi diagram, after which the modified Voronoi method additionally acquires the functions of optimal planning of the urban system, economic space, finding a safe path, etc. The article presents a method for constructing a modified Voronoi diagram and discusses algorithms for its practical use.