The basic techniques used in computational geometry are all covered: polygon triangualtions, convex hulls, Voronoi diagrams, arrangements, geometric searching, and motion planning.Expand

Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers.Expand

An optimal algorithm is presented for constructing an arrangement of hyperplanes in arbitrary dimensions and is shown to improve known worst-case time complexities for five problems: computing all order-k Voronoi diagrams, computing the λ-matrix, estimating halfspace queries, degeneracy testing, and finding the minimum volume simplex determined by a set of points.Expand

An algorithm is presented that constructs a representation for the cell complex defined by n hyperplanes in optimal $O(n^d )$ time in d dimensions, which is shown to lead to new methods for computing $\lambda $-matrices, constructing all higher-order Voronoi diagrams, halfspatial range estimation, degeneracy testing, and finding minimum measure simplices.Expand

A worst-ease lower bound of N(n 4) for explicitly computing the boundary of the visibility polygon from a line segment in the presence of other line segments is established, and an optimal algorithm to construct the boundary is designed.Expand

COMBINATORIAL AND DISCRETE GEOMETRY Finite Point Configurations, J. Pach Packing and Covering, G. Fejes Toth Tilings, D. Schattschneider and M. Senechal Helly-Type Theorems and Geometric… Expand

It is proven that at least two adjacent box sides are flush with edges of the hull of the convex hull, and this characterization enables the anO(n3) algorithm to find all minimal boxes for a set ofn points.Expand