Let p and q be two imprecise points, given as probability density functions on R, and let R be a set of n line segments (obstacles) in R. We study the problem of approximating the probability that p and q can see each other; that is, that the segment connecting p and q does not cross any segment of R. To solve this problem, we approximate each density function by a weighted set of polygons; a n...

Geometric problems are central in many areas of science and engineering. Computational geometry, the study of combinatorial and algorithmic problems in a geometric setting, and in particular triangulations have tremendous practical applications in areas such as computer graphics, computer vision and imaging, scientific visualization, geographic information systems, astronomy, computational biol...

We consider the problem of performing polygonal map overlay and the re nement step of spatial overlay joins. We show how to adapt algorithms from computational geometry to solve these problems for massive data sets. A performance study with arti cial and real-world data sets helps to identify the algorithm that should be used for given input data.

In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of n definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the combinatorial parts of similar bounds known in the case of semi-algebraic and semi-Pfaffian sets, and as a result vastly increases the applicability of results on combinat...

This report describes an approach to locating an object in an r-dimensional scene. The location problem is reduced to a problem in computational geometry, then solved by linear programming methods.

Several fundamental problems in Computational Geometry come from the eld of Facility Location. In this paper we consider some problems that belong to the interplay between these two areas. Given a set S of points in the plane: (1) nd a polygonal chain with one corner belonging to S such that minimizes the maximum distance, (2) nd a polygonal chain with k corners belonging to S such that minimiz...