The existence of Macbeath regions is a classical theorem in convex geometry (“A Theorem on nonhomogeneous lattices”, Annals of Math, 1952). We refer the reader to the survey of I. Barany for several applications [3]. Recently there have been some striking applications of Macbeath regions in discrete and computational geometry. In this paper, we study Macbeath’s problem in a more general setting...

The examination of differences in intra-hemispheric coherence and a novel method based on computational geometric algorithms between the left and right hemispheres of the same EEG. The Coherence and Computational geometry methods are computed from the same EEG segment and especially in the alpha and beta activities. The Results of the application of Coherence and Computational geometry methods ...

Arrangements of lines and pseudolines are important and appealing objects for research in discrete and computational geometry. We show that there are at most 2 n 2 simple arrangements of n pseudolines in the plane. This improves on previous work by Knuth who proved an upper bound of 3( n 2) ∼= 2 n in 1992 and the first author who obtained 2 n 2 in 1997. The argument uses surprisingly little geo...

Kurt Mehlhorn’s foundational results in computational geometry provide not only a basis for practical geometry systems such as Leda and CGAL, they also, in the spirit of Euclid, provide a sound basis for geometric truth. This article shows how Mehlhorn’s ideas from computational geometry have influenced work on the logical basis for constructive geometry. In particular there is a sketch of new ...

Given a family of objecte in the plane, the line transversal problem is to compute a line that intersects every member of the family. In this paper we examine a variation of the line transversal problem that involves computing a shortest line segment that intersects every member of the family. In particular, we give O(nlogn) time algorithms for computing a shortest transversal of a family of n ...