Date of Award
Department of Computer Science
Robert L. Drysdale
Voronoi diagrams are a geometric structure containing proximity information useful in efficiently answering a number of common geometric problems associated with a set of points in the plane.. They have applications in fields ranging from crystallography to biology. Diagrams of sites other than points and with different distance metrics have been studied. This paper examines the Voronoi diagram of a set of lines, which has escaped study in the computational geometry literature. The combinatorial and topological properties of the closest and farthest Voronoi diagrams are analyzed and O(n^2) and O(n log n) algorithms are presented for their computation respectively.
Henle, Mark C., "Closest and Farthest-Line Voronoi Diagrams in the Plane" (2007). Dartmouth College Undergraduate Theses. 52.