Constructing the Internal Voronoi Diagram of Polygonal Figure Using the Sweepline Method

Abstract

The problem of constructing the internal Voronoi diagram of a polygonal figure—a polygon with polygonal holes—is considered. A method based on the plane sweep paradigm is proposed. Direct construction of only the internal part of the Voronoi diagram allows us to reduce the amount of computations and increase robustness compared to known solutions. Another factor in reducing the computational complexity is the use of the property of pairwise incidence of linear segments formed by the sides of the polygonal figure. To take these features into account, it is proposed to build a data structure called sweep line status in the form of an ordered set of sites’ areas of responsibility. This structure is implemented as a combination of a balanced tree and a bidirectional list. Computational experiments illustrate the numerical reliability and efficiency of the proposed method.