Combinatorial and Computational Geometry
by Edited by Jacob E. Goodman , Janos Pach , Emo WelzlEdition: 1st
Format: Paperback
Pub. Date: 2011-06-02
Publisher(s): Cambridge University Press
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Summary
During the past few decades, the gradual merger of Discrete Geometry and the newer discipline of Computational Geometry has provided enormous impetus to mathematicians and computer scientists interested in geometric problems. This volume, which contains 32 papers on a broad range of topics of current interest in the field, is an outgrowth of that synergism. It includes surveys and research articles exploring geometric arrangements, polytopes, packing, covering, discrete convexity, geometric algorithms and their complexity, and the combinatorial complexity of geometric objects, particularly in low dimension.
Table of Contents
| Geometric approximation via core sets | |
| Applications of graph and hypergraph theory in geometry | |
| Convex geometry of orbits | |
| The Hadwiger transversal theorem for pseudolines | |
| Betti number bounds, applications, and algorithms | |
| Shelling and the h-vector of the (extra-)ordinary polytope | |
| On the number of mutually touching cylinders | |
| Edge-antipodal 3-polytopes | |
| A conformal energy for simplicial surfaces | |
| On the size of higher-dimensional triangulations | |
| The carpenter's ruler folding problem | |
| A survey of folding and unfolding in computational geometry | |
| On the rank of a tropical matrix | |
| The geometry of biomolecular solvation | |
| Inequalities for zonotopes | |
| Quasiconvex programming | |
| De Concini-Procesi wonderful arrangement models - a discrete geometer's point of view | |
| Thinnest covering of a circle by eight, nine, or ten congruent circles | |
| On the complexity of visibility problems with moving viewpoints | |
| Cylindrical partitions of convex bodies | |
| Tropical halfspaces | |
| Two proofs for Sylvester's problem using an allowable sequence of permutations | |
| A comparison of five implementations of 3d Delaunay tessellation | |
| Bernstein's basis and real root isolation | |
| On some extremal problems in combinatorial geometry | |
| A long non-crossing path among disjoint segments in the plane | |
| On a generalization of Schoenhardt's polyhedron | |
| On Hadwiger numbers of direct products of convex bodies | |
| Binary space partitions - recent developments | |
| Erdos-Szekeres theorem: upper bounds and related results | |
| On the pair-crossing number | |
| Geometric random walks: a survey | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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