doktorska disertacija
Povzetek
V 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 prispevke.
Ključne besede
računalniška geometrija;algoritmi;skeleton;srednja os;omejena Delaunayeva triangulacija;Steinerjeva točke;Računalništvo;Disertacije;Računalniška grafika;
Podatki
Jezik: |
Slovenski jezik |
Leto izida: |
2014 |
Tipologija: |
2.08 - Doktorska disertacija |
Organizacija: |
UM FERI - Fakulteta za elektrotehniko, računalništvo in informatiko |
Založnik: |
G. Smogavec] |
UDK: |
004.925.8(043.3) |
COBISS: |
18055958
|
Št. ogledov: |
1269 |
Št. prenosov: |
122 |
Ocena: |
0 (0 glasov) |
Metapodatki: |
|
Ostali podatki
Sekundarni jezik: |
Angleški jezik |
Sekundarni naslov: |
APPROXIMATION ALGORITHM FOR MEDIAL AXIS COMPU-TATION ON SIMPLE POLYGONS USING CONSTRAINED DELAUNAY TRIANGULATION |
Sekundarni povzetek: |
In this doctoral dissertation a new method for approximating a polygonʼs 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 polygonʼs medial axis. The doctoral dissertation is concluded with evaluation of the hypotheses and an overview of the scientific contributions. |
Sekundarne ključne besede: |
computer geometry;algorithms;skeleton;medial axis;constrained Delaunay triangulation;Steiner points; |
URN: |
URN:SI:UM: |
Vrsta dela (COBISS): |
Doktorsko delo/naloga |
Komentar na gradivo: |
Univ. v Mariboru, Fak. za elektrotehniko, računalništvo in informatiko |
Strani: |
XIV, 131 str. |
ID: |
8729500 |