A constructive approach to sweep algorithms for Voronoi diagrams

Simple item page
dc.contributor.authorHeuberger, Philipp A. (Philipp AndreĢ)en_US
dc.date.accessioned2024-08-14T16:50:27Z
dc.date.available2024-08-14T16:50:27Z
dc.date.copyright1991en_US
dc.date.issued1991
dc.degree.departmentDepartment of Computer Science
dc.degree.levelMaster of Science M.Sc.en
dc.description.abstractConstructing the Voronoi diagram where the given sites are points in the Euclidean space veils the discrete problem of determining the finite set of siteless subsets of the original sites. The function siteless incorporates all geometric and the function subset all combinatorial concerns. The set of all siteless subsets is called the Voronoi set. Independent of dimension, our precise definition of the Voronoi diagram is based on the Voronoi set. Thus, the finite Voronoi set is a convenient abstraction of the infinite Voronoi diagram separating geometric from combinatorial concerns. Furthermore, this thesis describes a constructive approach to Voronoi sweep algorithms. In a first attempt, we derive a brute-force algorithm demonstrating our methodology of strengthening program conditions. Then, two efficient algorithms for the plane are presented: the sweephull and the sweepcircle Voronoi algorithm. The sweepcircle algorithm is a companion of Fortune's sweepline algorithm, where the sweepline has been replaced by a sweepcircle. The sweephull algorithm, a generalized form of both sweepline and sweepcircle algorithms, is based on our improved underĀ­standing of the relationship between the convex hull and the Voronoi diagram.
dc.format.extent102 pages
dc.identifier.urihttps://hdl.handle.net/1828/18127
dc.rightsAvailable to the World Wide Weben_US
dc.titleA constructive approach to sweep algorithms for Voronoi diagramsen_US
dc.typeThesisen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
HEUBERGER_Philipp_Andre_MSC_1991_525340.pdf
Size:
22.71 MB
Format:
Adobe Portable Document Format
Download

Collections

Electronic Theses and Dissertations (ETD)
 
University of Victoria Libraries

We acknowledge and respect the LəkĢ“Ź·É™Å‹É™n (Songhees and Esquimalt) Peoples on whose territory the university stands, and the LəkĢ“Ź·É™Å‹É™n and WĢ±SƁNEĆ Peoples whose historical relationships with the land continue to this day.