This well-accepted introduction to computational geometry is a textbook for high-level
undergraduate and low-level graduate courses. The focus is on algorithms and hence the …

We give a simple lazy randomized incremental algorithm to compute≤ k-levels in
arrangements of x-monotone Jordan curves in the plane, and in arrangements of planes in …

Abstract Voronoi diagrams were introduced by R. Klein (1988) as an axiomatic basis of
Voronoi diagrams. We show how to construct abstract Voronoi diagrams in time O (n log n) …

The Delaunay tree is a hierarchical data structure which is defined from the Delaunay
triangulation and, roughly speaking, represents a triangulation as a hierarchy of balls. It …

Given n points in three dimensions, we show how to answer halfspace range reporting
queries in O (log n+ k) expected time for an output size k. Our data structure can be …

In the plane the post-office problem, which asks for the closest site to a query site, and
retraction motion planning, which asks for a one-dimensional retract of the free space of a …

We present an edge labeling of order-k Voronoi diagrams,\(V_k (S)\), of point sets S in the
plane, and study properties of the regions defined by them. Among them, we show that\(V_k …

We present the first optimal randomized algorithm for constructing the order-k Voronoi
diagram of n points in two dimensions. The expected running time is O (n log n+ nk), which …

We examine some benefits of using the medial axis as a centerline for rivers and lakes. One
benefit, automatic centerline generation, has been used for many years. We show that …

We use here the results on the influence graph1 to adapt them for particular cases where
additional information is available. In some cases, it is possible to improve the expected …