Twentieth Anniversary Volume: Discrete & Computational Geometry /

• Corporate Author: SpringerLink (Online service)
• Other Authors: Pollack, Richard. (Editor), Pach, Jǹos. (Editor), Goodman, Jacob E. (Editor)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Subjects: Mathematics.; Computational complexity.; Computer graphics.; Geometry, algebraic.; Computer science > Mathematics.; Discrete groups.; Algebraic Geometry.; Computational Mathematics and Numerical Analysis.; Computer Graphics.; Discrete Mathematics in Computer Science.; Convex and Discrete Geometry.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-0-387-87363-3

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. Formed during the past few decades by the merger of the classical...

Table of Contents:

• 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<U+0013>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.