Dominique Schmitt

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Given a set S of line segments in the plane, we introduce a new family of partitions of the convex hull of S called segment triangu-lations of S. The set of faces of such a triangulation is a maximal set of disjoint triangles that cut S at, and only at, their vertices. Surprisingly , several properties of point set triangulations extend to segment(More)
Let S be a finite set of n points in the plane in general position. We prove that every inclusion-maximal family of subsets of S separable by convex pseudo-circles has the same cardinal (n 0)+(n 1)+(n 2)+(n 3). This number does not depend on the configuration of S and is the same as the number of subsets of S separable by true circles. Buzaglo, Holzman, and(More)
Given a set V of n points in the plane, no three of them being collinear, a convex inclusion chain of V is an ordering of the points of V such that no point belongs to the convex hull of the points preceding it in the ordering. We call k-set of the convex inclusion chain, every k-set of an initial subsequence of at least k points of the ordering. We show(More)