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Euclidean Shortest Paths on Polyhedra

By The Raymond and Beverly Sackler

Abstract

First of all, I would like to express my most sincere gratitude and appreciation to my advisor Micha Sharir, for his invaluable encouragement and support, and for endless patience and delicate instruction. His guidance is not only an inseparable part of this research, which could not have been accomplished without it, but it is also the crucial factor that has made my graduate studies so enjoyable. I am much obliged to Joe Mitchell for sharing his ideas with me; it has been a pleasure working with him. I am also very grateful to Haim Kaplan for many helpful discussions and constructive ideas, and I would like to thank Joseph O’Rourke and John Hershberger for their help in significant parts of this research. Last but not least, I would like to thank my family for their support over the years; especially, I would like to express eternal gratitude to my beloved wife Jenny, who has patiently endured numerous lectures on shortest paths in geometric environments. In this thesis we develop optimal-time algorithms for computing shortest paths on polyhedral surfaces in three dimensions. Specifically

Year: 2014
OAI identifier: oai:CiteSeerX.psu:10.1.1.413.8055
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