Hannes Krasser

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The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction(More)
We extend the order type data base of all realizable order types in the plane to point sets of cardinality 11. More precisely, we provide a complete data base of all combinatorial different sets of up to 11 points in general position in the plane. In addition, we develop a novel and efficient method for a complete extension to order types of size 12 and(More)
Oswin Aichholzer Institute for Theoretical Computer Science Graz University of Technology Inffeldgasse 16b, A-8010 Graz, Austria oaich@igi.tu-graz.ac.at Franz Aurenhammer Institute for Theoretical Computer Science Graz University of Technology Inffeldgasse 16b, A-8010 Graz, Austria auren@igi.tu-graz.ac.at Hannes Krasser Institute for Theoretical Computer(More)
Let TS be the set of all crossing-free straight line spanning trees of a planar n-point set S. Consider the graph TS where two members T and T ′ of TS are adjacent if T intersects T ′ only in points of S or in common edges. We prove that the diameter of TS is O(log k), where k denotes the number of convex layers of S. Based on this result, we show that the(More)
We define general Laman (count) conditions for edges and faces of polygonal partitions in the plane. Several well-known classes, including k-regular partitions, k-angulations, and rank-k pseudo-triangulations, are shown to fulfill such conditions. As an implication, nontrivial perfect matchings exist between the edge sets (or face sets) of two such(More)