## Combinatorial and Computational GeometryJacob E. Goodman, Janos Pach, Emo Welzl This volume, containing 32 papers on a broad range of topics of current interest in the field, is an outgrowth of the synergism of Discrete and Computational Geometry. 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.There are points of contact with many applied areas such as mathematical programming, visibility problems, kinetic data structures, and biochemistry, and with algebraic topology, geometric probability, real algebraic geometry, and combinatorics. |

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### Contents

Geometric Approximation via Coresets 1 | 29 |

Convex Geometry of Orbits | 51 |

The Hadwiger Transversal Theorem for Pseudolines | 79 |

Betti Number Bounds Applications and Algorithms | 87 |

Shelling and the hVector of the Extraordinary Polytope | 97 |

On the Number of Mutually Touching Cylinders | 121 |

EdgeAntipodal 3Polytopes | 129 |

A Conformal Energy for Simplicial Surfaces | 135 |

I | 305 |

A Discrete | 333 |

Thinnest Covering of a Circle by Eight Nine or Ten Congruent Circles | 361 |

On the Complexity of Visibility Problems with Moving Viewpoints | 377 |

Cylindrical Partitions of Convex Bodies | 399 |

Two Proofs for Sylvesters Problem Using an Allowable Sequence | 433 |

The Bernstein Basis and Real Root Isolation | 459 |

Extremal Problems Related to the SylvesterGallai Theorem | 479 |

On the Size of HigherDimensional Triangulations | 149 |

The Carpenters Ruler Folding Problem | 155 |

A Survey of Folding and Unfolding in Computational Geometry | 167 |

On the Rank of a Tropical Matrix | 213 |

The Geometry of Biomolecular Solvation | 243 |

Inequalities for Zonotopes | 277 |

A Long Noncrossing Path Among Disjoint Segments in the Plane | 495 |

On Hadwiger Numbers of Direct Products of Convex Bodies | 517 |

Recent Developments | 529 |

Upper Bounds and Related Results | 557 |

A Survey | 577 |

### Other editions - View all

Combinatorial and Computational Geometry Jacob E. Goodman,Janos Pach,Emo Welzl No preview available - 2011 |

### Common terms and phrases

algebraic algorithm arrangement models axis-aligned ball Barvinok Bernstein basis binary space partitions boundary BSP tree building set cell CGAL circles combinatorial computational geometry configuration construction contains convex body convex hull convex sets coordinates coreset corresponding cross d-dimensional defined Delaunay Demaine denote dimension Discrete Comput disjoint Edelsbrunner elements endpoint Eppstein example facet Figure finite folding function Geom graph halfspace hyperplane inequality input integer intersection lattice Lemma line segments linear lower bound Math matrix mesh minimal minimum Minkowski sum nested set NP-hard optimal ordinary oriented matroid origami Pach partition complexity permutation plane polygon polyhedron polynomial positive problem Proc proof Proposition protein proved pseudoline quasiconvex functions quasiconvex program radius random Real Root Isolation Section short edges simplices smallest enclosing ball space sphere structure Sturmfels subset subspace tess3 tetrahedra Theorem Toth triangulation tropical convex hull tropical polytopes upper bound vector vertex vertices zonotopes