Marc J. van Kreveld

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Motivated by the problem of labeling maps, we investigate the problem of computing a large non-intersecting subset in a set of n rectangles in the plane. Our results are as follows. In O(n log n) time, we can nd an O(logn)-factor approximation of the maximum subset in a set of n arbitrary axis-parallel rectangles in the plane. If all rectangles have unit(More)
Let F be a polyhedral terrain with n vertices. We show how to preprocess F such that for any two query points on F it can be decided whether there exists a path on F between the two points whose height decreases monotonically. More generally, the minimum total ascent or descent along any path between the two points can be computed. It is also possible to(More)
General Terms: add here 1. INTRODUCTION A large proportion of the resources available on the worldwide web refer to information that may be regarded as geographically located. Thus most activities and enterprises take place in one or more places on the Earth's surface and there is a wealth of survey data, images, maps and reports that relate to specific(More)
Assume that a set of imprecise points is given, where each point is specified by a region in which the point may lie. We study the problem of computing the smallest and largest possible convex hulls, measured by length and by area. Generally we assume the imprecision region to be a square, but we discuss the case where it is a segment or circle as well. We(More)
Two novel applications of the plane sweep paradigm are demonstrated, namely, for the computation of extended viewsheds on gridded DEMs and for class interval selection on TIN-based DEMs. In both cases, the e ciency of the plane sweep algorithm is signi cantly better than a straightforward approach. The algorithms are presented by rst giving the plane sweep(More)
A rectangular cartogram is a type of map where every region is a rectangle. The size of the rectangles is chosen such that their areas represent a geographic variable (e.g., population). Good rectangular cartograms are hard to generate: The area specifications for each rectangle may make it impossible to realize correct adjacencies between the regions and(More)