Bounding Volumes in Computer Graphics Master thesis

Zadání Prostudujte publikované metody, které používají obalová tělesa a jejich hierarchie v počítačové grafice. Zaměřte se ná ulohyřešení globální iluminace a detekce kolizí. V písemnéčásti vypracujte porovnání vybran´ych metod a teoreticky zpracujte nově navženou metodu. V praktickéčásti práce vyzkoušejte některé z těchto metod a porovnejte v´ysledky získané při vyhodnocení experimentálních scén. Task Investigate published methods that use bounding volumes and their hierarchies in the computer graphics. Focus on the problems of global illumination and collision detection. In written part compare selected methods and theoretically examine new method. In practical part implement some of these methods and compare results obtained on experimental scenes. 2 Prohlášení Prohlašuji, ˇ ze tato práce je m´ym p ˚ uvodním autorsk´ym dílem, které jsem vypracoval samostatně. Všechny zdroje, prameny a literaturu, které jsem při vypracování používal a z nichž jsemčerpal, v práciřádně cituji s uvedenímúplného odkazu na příslušn´y zdroj. Declaration I declare that this thesis is my original work and that I have written it independently. All sources and literature that I have used during elaboration of the thesis are cited with complete reference to the corresponding source. Acknowledgement First of all I would like to thank Jiří Sochor, the supervisor of the thesis, for numerous advices and invaluable discussions during my work on it. This work would not be possible without Karel Zikan who has drawn my attention to the subject and provided support during the research as well as enormous amount of help in many mathematical topics. My thanks go also to Henry Sowizral of Sun Microsystems for support during first implementation of these ideas. I would also like to thank researchers from SUNY at Stony Brook who kindly provided their implementation for comparison purposes, namely Martin Held, James Klosowski and Joseph Mitchell. The work on this thesis would be much harder without existence of Debian GNU/Linux distribution. Each letter in this thesis (and then some more) was typed on a keyboard attach to this system. 3 Abstract In this thesis we show how the techniques based on bounding volume hierarchies can be used to solve various problems in computer graphics. We concentrate mainly on the problem of collision detection and a more general task of proximity computation. We employ a special class of bounding volumes – fixed directions hulls – to implement time and memory efficient algorithms for these problems. The fixed directions hulls are analyzed in a detail and some rarely used …