Combinatorial and Computational Geometry

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Jacob E. Goodman, Janos Pach, Emo Welzl
Cambridge University Press, Aug 8, 2005 - Computers - 616 pages
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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
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