5677 KB194 KB0 KB2014Smogavec, GregorŽalik, BorutXIV, 131 str., 30 cmCOBISSID:18055958URN:URN:NBN:SI:doc-C9P263EDslG. Smogavecvisokošolska delaalgorithmsalgoritmicomputer geometryconstrained Delaunay triangulationDisertacijemedial axisMnogokotnikiomejena Delaunayeva triangulacijaračunalniška geometrijaRačunalniška grafikaskeletonsrednja osSteiner pointsSteinerjeva točkeAproksimacijski algoritem gradnje srednje osi enostavnih mnogokotnikov, temelječ na omejeni Delaunayevi triangulaciji| doktorska disertacija|In this doctoral dissertation a new method for approximating a polygon's medial axis is introduced. As shown by experiments, the new method is more efficient than the existing methods. Firstly the definition of the main problem is given. This is fol-lowed by the description of fields, where the medial axis is used, and finished with the hypotheses. In the next chapter, the connection between the Voronoi diagram and the Delaunay triangulation is mentioned, which is followed by the description of the constrained Delaunay triangulation. In the next chapter, algorithms for medial axis construction are described and classified into groups of exact and approximate algorithms. This is followed by definitions and an overview of existing methods. The core of this doctoral dissertation is composed of the description of a new algorithm for medial axis construction of a simple polygon. In this chapter, the triangulation, heuristics and the step for medial axis construction out of the triangles circumcentres are described. The next chapter is devoted to the analysis of our algorithm. Here the time and space complexity are derived and the comparison of our algorithm with the existing ones is given. This is followed by the description of a metric, which evaluates the exactness of a polygon's medial axis. The doctoral dissertation is concluded with evaluation of the hypotheses and an overview of the scientific contributionsV doktorski disertaciji uvedemo nov postopek gradnje aproksimativne srednje osi, ki je učinkovitejši od obstoječih metod. Naprej opredelimo problem, področja upo-rabe in podamo hipotezi. V nadaljevanju na kratko razložimo Voronoijev diagram in opozorimo na povezavo med njim in Delaunayjevo triangulacijo, ki jo razširimo še z opisom omejene Delaunayjeve triangulacije. Zatem se osredotočimo na algoritme gradnje srednje osi, ki jih delimo na eksaktne in aproksimacijske. Sledijo definicije in pregled dosedanjih rešitev. V jedru doktorske disertacije opišemo nov algoritem za konstrukcijo aproksimacije srednje osi mnogokotnika. V tem poglavju opišemo naš algoritem za triangulacijo enostavnega mnogokotnika, uporabljeno hevristiko in korak generiranja srednje osi iz središč dobljenih trikotnikov. Sledi analiza algoritma, kjer izpeljemo prostorsko in časovno zahtevnost, in primerjava našega algoritma z obstoječimi metodami. Razvijemo tudi novo metriko za oceno kakovosti aproksimacije. Doktorsko disertacijo zaključimo s pregledom opravljenega dela in opozorimo na izvirne znanstvene prispevkeTEXTvisokošolska delatheses and dissertationsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza v Mariboru, Fakulteta za elektrotehniko računalništvo in informatiko