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This heavily-illustrated book contains twenty-eight major articles that present a comprehensive picture of the current state of discrete and computational geometry. Many of the articles solve long-outstanding problems in the field.
This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry , and presents a comprehensive picture of the current state of the field. The articles in this volume, a number of which solve long-outstanding problems in the field, were chosen by the editors of DCG for…mehr

Produktbeschreibung
This heavily-illustrated book contains twenty-eight major articles that present a comprehensive picture of the current state of discrete and computational geometry. Many of the articles solve long-outstanding problems in the field.
This commemorative book contains the 28 major articles that appeared in the 2008 Twentieth Anniversary Issue of the journal Discrete & Computational Geometry , and presents a comprehensive picture of the current state of the field.
The articles in this volume, a number of which solve long-outstanding problems in the field, were chosen by the editors of DCG for the importance of their results, for the breadth of their scope, and to show the intimate connections that have arisen between discrete and computational geometry and other areas of both computer science and mathematics. Apart from the articles, the editors present an expanded preface, along with a set of photographs of groups and individuals who have played a major role in the history of the field during the past twenty years.
  • Produktdetails
  • Verlag: Springer, Berlin
  • Artikelnr. des Verlages: 12282647
  • Erscheinungstermin: 13. November 2008
  • Englisch
  • Abmessung: 235mm x 155mm x 34mm
  • Gewicht: 991g
  • ISBN-13: 9780387873626
  • ISBN-10: 0387873627
  • Artikelnr.: 24953041
Autorenporträt
Jacob Goodman, Richard Pollack and János Pach are each distinguished professors and authors in their own right, and together they are the pre-eminent founders and editors-in-chief of the journal, Discrete & Computational Geometry. Over the 20 years since the founding of this premiere journal, it has become synonymous with the field of discrete and computational geometry itself.
Inhaltsangabe
Preface.- There are Not too Many Magic Configurations.- Computing the Detour and Spanning Ratio of Paths, Trees, and Cycles in 2D and 3D.- Robus Shape Fitting via Peeling and Grating Coresets.- Siegel's LEmaa and Sum-Distinct Sets.- Slicing Convex Sets and Measures by a Hyperplane.- A Centrally Symmetric Version of the Cyclic Polytope.- On Projections of Semi-Algebraic Sets Defined by Few Quadratic Inequalities.- Enumeration in Convex Geometries and Associated Polytopal Subdivisions of Spheres.- Isotopic Implicit Surface Meshing.- Line Transversals to Disjoint Balls.- Generating all Vertices of a Polyhedron is Hard.- Norm Bounds for Ehrhart Polynominal Roots.- Helly-Type Theorems for Line Transversals to Disjoint Unit Balls.- Grid Vertex-Unfolding Orthogonal Polyhedra.- Empty Convex Hexagons in Planar Point Sets.- Affinely Regular Polygons are Extremals of Area Functionals.- Improved Output-Sensitive Snap Rounding.- Pure Point Diffractive Substitution Delone Sets Have the Meyer Property.- Metric Combinatorics of Convex Polyhedra: Cut Loci and Nonoverlapping Unfoldings.- Empty Simplices of Polytopes and Graded Betti Numbers.- Rigidity and the Lower Bound Theorem for Doubly Cohen Macaulay Complexes.- Finding the Homology of Submanifolds with HIgh Confidence from Random Samples.- Odd Crossing Number and Crossing Number are Not the Same.- Visibility Graphs of Point Sets in the Plane.- Decomposability of Polytopes.- An Inscribing Model for Random Polytopes.- An Optimal-Time Algorithm for Shortest Paths on a Convex Polytope in Three Dimensions.- Genral-Dimensional Constrained Delaunay nad Constrained Regular Triangulation, I: Combinatorial Properties.