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 …

There are many problems in computational geometry for which the best know algorithms
take time Θ (n2)(or more) in the worst case while only very low lower bounds are known. In …

This paper describes a new probabilistic roadmap (PRM) path planner that is:(1) single-
query—instead of pre-computing a roadmap covering the entire free space, it uses the two …

This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM)
planner that is: single-query—instead of pre-computing a roadmap covering the entire free …

We present a data structure that can store a set of disjoint fat objects ind-space such that
point location and bounded-size range searching with arbitrarily shaped ranges can be …

We present an efficient and simple paradigm for motion planning amidst fat obstacles. The
paradigm fits in the cell decomposition approach to motion planning and exploits workspace …

We investigate the concept of a median among a set of trajectories. We establish criteria that
a “median trajectory” should meet, and present two different methods to construct a median …

Motion planning is a fundamental problem in robotics. It comes in a variety of forms, but the
simplest version is as follows. We are given a robot system B, which may consist of several …

The traditional worst-case analysis often fails to predict the actual behavior of the running
time of geometric algorithms in practical situations. One reason is that worst-case scenarios …

Let C be a set of geometric objects in Rd. The combinatorial complexity of the union of C is
the total number of faces of all dimensions on its boundary. We survey the known upper …