Voronoi Diagrams Revisited Rolf Klein∗ Elmar Langetepe∗ Zahra Nilforoushan† Abstract Abstract Voronoi diagrams [21] were designed as a unifying concept that should include as many concrete types of diagrams as possible. To ensure that abstract Voronoi diagrams, built from given sets of bisecting curves, are finite graphs, it was required that any two bisecting curves intersect only finitely oft...

Embeddings of several graph classes into hypercubes have been widely studied. Unfortunately, almost all investigated graph classes are regular graphs such as meshes, complete trees, pyramids. In this paper, we present a general method for one-to-one embedding irregular graphs into their optimal hypercubes based on extended-edge-bisectors of graphs. An extended-edge-bisector is an edge-bisector ...

We present an exact algorithm for computing the precise Hausdorff distance between two general polyhedra represented as triangular meshes. The locus of candidate points, events where the Hausdorff distance may occur, is fully classified. These events include simple cases where foot points of vertices are examined as well as more complicated cases where extreme distance evaluation is needed on t...

Hingeless plastic ankle-foot orthoses (PAFOs) achieve ankle motion by flexing about the ankle joint. Instantaneous centers of rotation (ICRs) in dorsi- and plantarflexion movements, used as a measure of PAFO axes of movement, were measured to evaluate their fit to ankle motion. Thirty different PAFOs were fabricated and their stiffness modified in three stages. They were dorsi- and plantarflexe...

For a given triangle there are many points associated with the triangle that lie in its interior; examples include the incenter (which can be found by the intersection of the angle bisectors) and the centroid (which can be found by the intersection of the medians). Using this point one can naturally subdivide the triangle into either three or six “daughter” triangles. We can then repeat the sam...

We discuss the interpretation of distortions to stellar spectral lines with particular attention to line bisectors in the presence of an orbiting planetary companion. We present a simple model whereby light reflected by the companion can cause temporal variations to the observed line profiles. These distortions have a characteristic signature depending on the inclination angle of the system. Fo...

Given a set S of n points in general position, we consider all k-th order Voronoi diagrams on S, for k = 1, . . . , n, simultaneously. We deduce symmetry relations for the number of faces, number of vertices and number of circles of certain orders. These symmetry relations are independent of the position of the sites in S. As a consequence we show that the reduced Euler characteristic of the po...

This paper concentrates on the InCircle predicate which is used for the computation of the Voronoi diagram of smooth closed curves. The predicate decides the position of a query object relative to the Voronoi circle of three given ones. We focus on (nonintersecting) ellipses but our method extends to arbitrary closed smooth curves, given in parametric representation. We describe an efficient al...

After having investigated the equidistant surfaces (”perpendicular bisectors” of two points) in S2×R space (see [6]) we consider the analogous problem in H2×R space from among the eight Thurston geometries. In [10] the third author has determined the geodesic curves, geodesic balls of H2×R space and has computed their volume, has defined the notion of the geodesic ball packing and its density. ...