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Title:
ISKANJE NAJBLIŽJE TOČKE V 3D PROSTORU
Authors:
ID
Balažic, David
(
Author
)
ID
Žalik, Borut
(
Mentor
)
More about this mentor...
Files:
UN_Balazic_David_2016.pdf
(1,97 MB)
MD5: DDF3BAB154CD3F7448463E0D360E109C
Language:
Slovenian
Work type:
Undergraduate thesis
Typology:
2.11 - Undergraduate Thesis
Organization:
FERI - Faculty of Electrical Engineering and Computer Science
Abstract:
Iskanje najbližje točke je temeljni problem v računalniški geometriji. Diplomsko delo obravnava Bentleyev algoritem z delitvijo prostora na celice v različici za 3D prostor ter razširitev z rekurzivno delitvijo celic na podcelice. Algoritem je preizkušen na različnih množicah točk, tako sintetičnih kot praktičnih. Za primerjavo so testirani tudi naivna metoda iskanja ter metoda z osmiškim drevesom. Ugotovljeno je, da je Bentleyev algoritem učinkovit na različnih vhodnih podatkih in ima v večini primerov linearno časovno zahtevnost tako pri predobdelavi podatkov kot pri iskanju vseh najbližjih sosedov. Metoda z rekurzivno delitvijo celic izboljša hitrost iskanja na množicah z močno neenakomerno porazdelitvijo točk v prostoru, kjer prejšnja dosega slabše rezultate.
Keywords:
algoritmi
,
računalniška geometrija
,
najbližja točka
,
delitev prostora
Place of publishing:
[Maribor
Publisher:
D. Balažic
Year of publishing:
2016
PID:
20.500.12556/DKUM-57627
UDC:
004.921.021(043.2)
COBISS.SI-ID:
19466006
NUK URN:
URN:SI:UM:DK:8B3XVZWI
Publication date in DKUM:
18.03.2016
Views:
1627
Downloads:
114
Metadata:
Categories:
KTFMB - FERI
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Secondary language
Language:
English
Title:
THE CLOSEST POINT SEARCH IN 3D SPACE
Abstract:
A closest point search is a basic problem in the computational geometry. This diploma thesis deals with the Bentley cell-based space partitioning algorithm and an extension of it with recursive subdivision of the cells. The algorithm is tested on different point distributions in the 3D space, both synthetic and from the real world. For comparison the naive method and an octree-based method were also tested. It was found that the Bentley algorithm performs well on different datasets and in most cases has a linear time complexity both for preprocessing and searching all nearest neighbors. The recursive method improves searching speed on inputs with strongly non-uniform distributions, where the former algorithm performs worse.
Keywords:
algorithm
,
computational geometry
,
closest point
,
spatial subdivision
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