Now showing items 21-40 of 56

    • IconRegion inter-visibility in terrains  [Presentation]

      Van Kreveld, Marc; Moet, Esther; Van Oostrum, René (2004)
      A polyhedral terrain is the image of a piecewise linear continuous function de ned over the triangles of a triangulation in the xy- plane. Given a terrain with n vertices, two simply-connected regions (subsets of the ...
    • IconOn fencing problems  [Presentation]

      Miori, Cinzia; Peri, Carla; Segura Gomis, Salvador (2004)
      Fencing problems deal with the bisection of a convex body in a way that some geometric measures are optimized. We study bisections of planar bounded convex sets by straight line cuts and also bisections by hyperplane cuts ...
    • IconComputing the Fréchet distance between piecewise smooth curves  [Presentation]

      Rote, Günter (2004)
      We consider the Fréchet distance between two curves which are given as a sequence of m+n curved pieces. If these pieces are sufficiently well-ehaved, we can compute the Fréchet distance in O(mn log(mn)) time. The ...
    • IconFinding a door along a wall with an error afflicted robot  [Presentation]

      Kamphans, Tom; Langetepe, Elmar (2004)
      We consider the problem of finding a door in a wall with a blind robot, that does not know the distance to the door or whether the door is located left hand or right hand to its start point. This problem can be solved with ...
    • IconGeometric data structures for multihierarchical XML tagging of manuscripts  [Presentation]

      Jaromczyk, Jerzy W.; Moore, Neil (2004)
      This paper shows an application of computational geometry methods to the preparation of image-based digital library editions. We present a formalism for describing non-hierarachical markup of manuscripts in terms of ...
    • IconLower bounds for the polygon exploration problem  [Presentation]

      Hagius, Roland; Icking, Christian; Langetepe, Elmar (2004)
      We improve the best known lower bound for the polygon exploration problem from 1.2071 to 1.2825.
    • IconPointed encompassing trees  [Presentation]

      Hoffmann, Michael; Speckmann, Bettina; Tóth, Csaba D. (2004)
      It is shown that for any set of disjoint line segments in the plane there exists a pointed binary encompassing tree, that is, a spanning tree on the segment endpoints that contains all input segments, has maximal degree ...
    • IconCompetitive search ratio of graphs and polygons  [Presentation]

      Fleischer, Rudolf; Kamphans, Tom; Klein, Rolf; Langetepe, Elmar; Trippen, Gerhard (2004)
      We consider the problem of searching for a goal in an unknown environment, which may be a graph or a polygonal environment. The search ratio is the worst-case ratio before the goal is found while moving along some search ...
    • IconGeometric dilation of closed planar curves: a new lower bound  [Presentation]

      Ebbers-Baumann, Annette; Grüne, Ansgar; Klein, Rolf (2004)
      Given any simple closed curve C in the Euclidean plane, let w and D denote the minimal and the maximal caliper distances of C, correspondingly. We show that any such curve C has a geometric dilation of at least arcsin( ...
    • IconOn the number of pseudo-triangulations of certain point sets  [Presentation]

      Aichholzer, Oswin; Orden Martín, David; Santos Leal, Francisco; Speckmann, Bettina (2004)
      We compute the exact number of pseudo-triangulations for two prominent point sets, namely the so-called double circle and the double chain. We also derive a new asymptotic lower bound for the maximal number of pseudotriangulations ...
    • IconSimilarity search in semialgebraic pattern spaces  [Presentation]

      Knauer, Christian (2004)
      We describe a general technique to construct data structures for similarity search in semialgebraic pattern spaces. These spaces capture most known combinations of geometric patterns (e.g., point sets, polygons, polygonal ...
    • IconComputing the convex hull of disks using only their chirotope  [Presentation]

      Habert, Luc; Pocchiola, Michel (2004)
      We show that the convex hull of a collection of n pairwise disjoint disks in the plane is computable in O(n log n) time using only the chirotope of the collection of disks. The method relies mainly on the development of ...
    • IconOptimizing a 2D function satisfying unimodality properties  [Presentation]

      Demaine, Erik D.; Langerman, Stefan (2004)
    • IconPoint set stratification and minimum weight structures  [Presentation]

      Abellanas Oar, Manuel; Claverol Aguas, Mercè; Hurtado Díaz, Ferran (2004)
      Three different concepts of depth in a point set are considered and compared: Convex depth, location depth and Delaunay depth. As a notion of weight is naturally associated to each depth definition, we also present results ...
    • IconOptimal spanners for axis-aligned rectangles  [Presentation]

      Asano, Tetsuo; Berg, Mark de; Cheong, Otfried; Everett, Hazel; Haverkort, Herman; Katoh, Naoki; Wolff, Alexander (2004)
    • IconSmoothed number of extreme points under uniform noise  [Presentation]

      Damerow, Valentina; Sohler, Christian (2004)
      We analyze the maximal expected number of extreme points of a point set P in Rd that is slightly perturbed by random noise. We assume that each point in P is uniformly distributed in an axis-aligned hypercube of side ...
    • IconOn relative isodiametric inequalities  [Presentation]

      Cerdán Sala, Antonio; Miori, Cinzia; Segura Gomis, Salvador (2004)
      We consider subdivisions of convex bodies G in two subsets E and G\E. We obtain several inequalities comparing the relative volume 1) with the minimum relative diameter and 2) with the maximum relative diameter. In the ...
    • IconA completion of hypotheses method for 3D-geometry. 3D-extensions of Ceva and Menelaus theorems  [Presentation]

      Roanes Macías, Eugenio; Roanes Lozano, Eugenio (2004)
      A method that automates hypotheses completion in 3D-Geometry is presented. It consists of three processes: defi ning the geometric objects in the confi guration; determining the hypothesis conditions of the confi ...
    • IconFinding planar regions in a terrain  [Presentation]

      Funke, Stefan; Malamatos, Theocharis; Ray, Rahul (2004)
      We consider the problem of computing large connected regions in a triangulated terrain of size n for which the normals of the triangles deviate by at most some small fixed angle. In previous work an exact near-quadratic ...
    • IconMinimum weight pseudo-triangulations  [Presentation]

      Gudmundsson, Joachim; Levcopoulos, Christos (2004)
      We consider the problem of computing a minimum weight pseudo-triangulation of a set S of n points in the plane. We first present an O(n log n)-time algorithm that produces a pseudo-triangulation of weight O(wt(M(S))· log ...