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Two-Dimensional Convex Hull Algorithm Using the Iterative Orthant Scan
KTH, School of Computer Science and Communication (CSC).
KTH, School of Computer Science and Communication (CSC).
2017 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Tvådimensionell Convex Hull Algoritm Med Iterativ Orthant Scan (Swedish)
Abstract [en]

Finding the minimal convex polygon on a set of points in space is of great interest in computer graphics and data science. Furthermore, doing this efficiently is financially preferable. This thesis explores how a novel variant of bucketing, called the Iterative orthant scan, can be applied to this problem. An algorithm implementing the Iterative orthant scan was created and implemented in C++ and its real-time and asymptotic performance was compared to the industry standard algorithms along with the traditional textbook convex hull algorithm. The worst-case time complexity was shown to be a logarithmic term worse than the best teoretical algorithm. The real-time performance was 47.3% better than the traditional algorithm and 66.7% worse than the industry standard for a uniform square distribution. The real-time performance was 61.1% better than the traditional algorithm and 73.4% worse than the industry standard for a uniform triangular distribution. For a circular distribution, the algorithm performed 89.6% worse than the traditional algorithm and 98.7% worse than the industry standard algorithm. The asymptotic performance improved for some of the distributions studied. Parallelization of the algorithm led to an average performance improvement of 35.9% across the tested distributions. Although the created algorithm exhibited worse than the industry standard algorithm, the algorithm performed better than the traditional algorithm in most cases and shows promise for parallelization.

Abstract [sv]

Att hitta den minsta konvexa polygonen för en mängds punkter är av intresse i ett flertal områden inom datateknik. Att hitta denna polygon effektivt är av ekonomiskt intresse. Denna rapport utforskar hur metoden Iterative orthant scan kan appliceras på problemet att hitta detta konvexa hölje. En algoritm implementerades i C++ som utnyttjar denna metod och dess prestanda jämfördes i realtid såsom asymptotiskt mot den traditionella och den mest använda algoritmen. Den nya algoritmens asymptotiska värsta fall visades vara ett logaritmiskt gradtal sämre än den bästa teoretiska algoritmen. Realtidsprestandan av den nya algoritmen var 47,3% bättre än den traditionella algoritmen och 66,7% sämre än den mest använda algoritmen för fyrkantsdistribution av punkterna. Realtidsprestandan av den nya algoritmen var 61,1% bättre än den traditionella algoritmen och 73,4% sämre än den mest använda algoritmen för triangulär distribution av punkterna. För cirkulär distribution var vår algoritm 89,6% sämre än den traditionella algoritmen och 98,7% sämre än den vanligaste algoritmen. Parallellisering av vår algoritm ledde i medel till en förbättring på 35,9%. För vissa typer av fördelningar blev denna prestanda bättre. Även då algoritmen hade sämre prestanda än den vanligaste algoritmen, så är det ett lovande steg att prestandan var bättre än den traditionella algoritmen.

Place, publisher, year, edition, pages
2017. , p. 50
Keywords [en]
Convex hull, parallelization, OpenMP, Iterative orthant scan, computer graphics, minimal polygon
National Category
Computer Sciences
Identifiers
URN: urn:nbn:se:kth:diva-208351OAI: oai:DiVA.org:kth-208351DiVA, id: diva2:1105811
Presentation
2017-06-30, E51, Osquars backe 14, Stockholm, 14:05 (English)
Supervisors
Examiners
Available from: 2017-06-19 Created: 2017-06-05 Last updated: 2018-01-13Bibliographically approved

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