Recent developments in the theory of arrangements of surfaces

Abstract

We review recent progress in the study of arrangements of surfaces in higher dimensions. This progress involves new and nearly tight bounds on the complexity of lower envelopes, single cells, zones, and other substructures in such arrangements, and the design of efficient algorithms (near optimal in the worst case) for constructing and manipulating these structures. We then present applications of the new results to a variety of problems in computational geometry and its applications, including motion planning, Voronoi diagrams, union of geometric objects, visibility, and geometric optimization. © Springer-Verlag Berlin Heidelberg 1999.