APPLICATION OF THE COMPUTATIONAL GEOMETRY ALGORITHMS IN THE SOFTWARE PACKAGE MATHEMATICA

Abstract

Computational geometry is a branch of computer science that discusses algorithms for solving geometric problems. It considers such tasks as triangulation, building a convex hull, determining whether one object belongs to another, finding their intersection, etc. Computational geometry algorithms operate with the geometric objects with the point, a segment, a polygon, and circles. Two important algorithms of computational geometry that have many applications are Delaunay triangulation and the Voronoi
diagram. The Voronoi splitting is used in computational materials science to create synthetic polycrystalline aggregates. In computer graphics is used for randomly splitting surfaces. These algorithms are used in a gold method or the area stealing method for interpolating a function in 2D. In this paper, are shown three implementations of the Delaunay triangulation and Voronoi diagram in the software package Mathematica.