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dc.contributorHuemer, Clemens
dc.contributorClaverol Aguas, Mercé
dc.contributor.authorDe Las Heras Parrilla, Andrea
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2021-10-27T10:14:52Z
dc.date.available2021-10-27T10:14:52Z
dc.date.issued2021-10
dc.identifier.urihttp://hdl.handle.net/2117/354664
dc.description.abstractIn this thesis we study properties for spherical Voronoi diagrams of order $k$, SV_k(U)$ using different tools: the geometry of the sphere, a labeling for the edges of $SV_k(U)$, and the inversion transformation. Among the obtained properties, we show that $SV_k(U)$ has a small orientable cycle double cover, and we identify configurations that cannot appear in $SV_k(U)$ for small values of $k$. We generalize the construction of spherical Voronoi diagrams defined by Hyeon-Suk Na, Chung-Nim Lee and Otfried Cheong (2002) for order one to any order. We use that construction to prove that the numbers of faces, edges and vertices in $SV_k(U)$ are constant for fixed values of $k$ and $|U|$, i.e., do not depend on the positions of the points of $U$ on the sphere. Also, several connections and differences between Voronoi diagrams in the plane and in the sphere are addressed in this thesis.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Geometria
dc.subject.lcshDiscrete geometry
dc.subject.otherSpherical Voronoi diagrams
dc.subject.otherHigher order Voronoi diagram in the sphere
dc.subject.otherDouble cover
dc.subject.otherEdge labeling
dc.subject.otherInversion transformation
dc.subject.otherAlternating hexagon
dc.titleProperties for Voronoi diagrams of arbitrary order in the sphere
dc.typeMaster thesis
dc.subject.lemacGeometria discreta
dc.subject.amsClassificació AMS::52 Convex and discrete geometry::52C Discrete geometry
dc.identifier.slugFME-1956
dc.rights.accessOpen Access
dc.date.updated2021-10-19T05:22:20Z
dc.audience.educationlevelMàster
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)


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