Voronoi diagrams

Matej Kristan (2017) Voronoi diagrams. EngD thesis.

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Abstract

In the thesis we first describe the definition of a Voronoi diagram and several properties of Voronoi diagrams in the plane. We also define triangulations of the plane and the concept of a Delaunay triangulation, and present the connection between Voronoi diagrams and Delaunay triangulations. We then present three different algorithms for constructing a Voronoi diagram in the plane, and provide a more detailed description of Fortune’s algorithm which is an example of a sweep line algorithm. Sweep line algorithms are especially widespread in computational geometry and are used for solving various problems in Euclidean space. We selected Fortune’s algorithm for constructing Voronoi diagrams, and implemented it in the Java programming language. The performance of our implementation of the algorithm was checked on several randomly generated datasets and on a dataset of geographic coordinates of public charging stations for electric cars in Slovenia.

Item Type:

Thesis (EngD thesis)

Keywords:

Voronoi diagram, two-dimensional Voronoi diagram, sweep line, computational geometry, Fortune’s algorithm, Euclidean space

Number of Pages:

Language of Content:

Slovenian

Mentor / Comentors:

Name and Surname	ID	Function
prof. dr. Neža Mramor Kosta	242	Mentor

Link to COBISS:

http://www.cobiss.si/scripts/cobiss?command=search&base=51012&select=(ID=1537667779)

Institution:

University of Ljubljana

Department:

Faculty of Computer and Information Science

Item ID:

4021

Date Deposited:

04 Dec 2017 14:07

Last Modified:

18 Dec 2017 11:44

URI:

http://eprints.fri.uni-lj.si/id/eprint/4021

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