Ravninska Delaunayeva triangulacija

ŠTEVANČEC, TADEJ (author), Mramor Kosta, Nežka (mentor)

Delaunayeva triangulacija predstavlja eno izmed fundamentalnih podatkovnih struktur v računski geometriji. V diplomskem delu predstavimo ravninsko Delaunayevo triangulacijo in opišemo njeno konstrukcijo. Za izgradnjo Delaunayeve triangulacije v ravnini obstaja več vrst algoritmov, najbolj so razširjeni naključni inkrementalni. Naredili smo implementacijo algoritma Bowyer-Watson v programskem jeziku Java in preverili njegovo delovanje na več naborih naključno zgeneriranih točk. Mnogo algoritmov za izgradnjo Delaunayeve triangulacije je na tak ali drugačen način odvisnih od števila povezav, ki jim pripada posamezna točka. Primerjali smo teoretična pričakovanja za najvišjo in povprečno stopnjo točke v triangulaciji z rezultati, ki jih je vrnil naš algoritem.

• Language: Slovenian
• Keywords: računska geometrija, ravninska triangulacija, ravninska Delaunayeva triangulacija, naključni inkrementalni algoritem, algoritem Bowyer-Watson, stopnja točke, pričakovana najvišja stopnja točke
• Work type: Undergraduate thesis
• Organization: FRI - Faculty of Computer and Information Science
• Year: 2016
• PID: 20.500.12556/RUL-84109
• Publication date in RUL: 08.07.2016

Secondary language

• Language: English
• Title: Plane Delaunay triangulation

Abstract

Delaunay triangulation is one of the fundamental data structures in computational geometry. In the thesis we present the planar Delaunay triangulation and describe its construction. Several types of algorithms for building a two-dimensional Delaunay triangulation exist, the most popular are randomized incremental algorithms. We implemented the Bowyer-Watson algorithm in the programming language Java and tested it on a number of samples of randomly generated point sets. The expected degree of a vertex in a triangulation is an important parameter in many algorithms for constructing triangulations. Theoretical expectations for average and maximal vertex degrees are compared with the obtained values.

• Keywords: computational geometry, planar triangulation, planar Delaunay triangulation, randomized incremental algorithm, Bowyer-Watson algorithm, vertex degree, expected maximum vertex degree