Tereshchenko,V., Chudakov,S.
Abstract:
The paper is devoted to the development and of an efficient algorithmic model for solving a set of interrelated computational geometry problems. To do this, a unified algorithmic environment with unified data structures is created, which allows to implement complex use cases efficiently with respect to computational resources. We build the environment on the basis of the "divide and conquer" strategy. Once a convex hull is key to a set of computational geometry problems, we offer a concatenable queue data structure to maintain it. The data structure is implemented in a form of a binary tree. This allows to perform operations needed in algorithm for a set of problems in $O(log n)$ time. Furthermore we offer a way to execute the algorithms both sequentially and in parallel. In the future the algorithmic environment can be improved to support other computational models with similar properties for solving problems. As an example, the Voronoi diagram or the Delaunay triangulation can be considered.