Rank-1 lattices in computer graphics [Elektronische Ressource] / Sabrina Dammertz

Rank 1LatticesinComputerGraphicsSabrinaDammertz,geb.inRavensburgInstitutfur¨ Medieninformatik,2009DissertationzurErlangungdesDoktorgradesDr.rer.nat.derFakultat¨ fur¨¨IngenieurwissenschaftenundInformatikderUniversitatUlmAmtierenderDekan: Prof.Dr.MichaelWeberGutachter: Dr.AlexanderKeller Prof.Dr.MichaelWeberTagderPromotion: 14.07.2009AbstractSampling is fundamental to computer graphics, as samples are used both for representingdata and computing averages in the process of forming images. In this context rank 1 lat tices are explored with respect to image and texture representation, simulation, and imagesynthesis. We also contribute the necessary algorithmic and theoretical investigations tofind rank 1 lattices, which are suitable for specific requirements. Opposite to common be lief, it turns out that rank 1 lattices improve graphics applications quite notably and resultinmoreefficientalgorithms,too.iiiivAcknowledgementsManythanksto• Holgerforhislonglastingcollaboration,support,andpatience• AlexanderKellerforhisguidance,encouragement,andsupportforthisPhD• mentalimagesforthefinancialsupport• theoldandnewcomputergraphicsgroup• Johannes Hanika and Leonhard Grunschloss¨ for proof reading, and giving valuablefeedback• Carsten Wachter¨ , Matthias Raab, Martin Bader, Leonhard Grunschloss,¨ JohannesHanika,ManuelFinckh,andStefanMenzformanyhelpfuldiscussions• myfamilyvviContents1 Introduction 11.1 LatticeStructureofPseudo RandomNumberGenerators . . . . . . .