Combinatorial and Computational GeometryJacob E. Goodman, Janos Pach, Emo Welzl Cambridge University Press, 8. aug. 2005 - 616 sider 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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Indhold
Applications of Graph and Hypergraph Theory in Geometry | 31 |
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 Extra ordinary Polytope | 97 |
On the Number of Mutually Touching Cylinders | 121 |
EdgeAntipodal 3Polytopes | 129 |
A Conformal Energy for Simplicial Surfaces | 135 |
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 |
A Long Noncrossing Path Among Disjoint Segments in the Plane | 495 |
On the Size of HigherDimensional Triangulations | 147 |
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 |
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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Combinatorial and Computational Geometry Jacob E. Goodman,Janos Pach,Emo Welzl Ingen forhåndsvisning - 2011 |
Almindelige termer og sætninger
algebraic algorithm angle apply axis-aligned ball Barvinok rank Betti numbers binary space partitions cell CGAL columns combinatorial computational geometry configuration construction contains convex body convex hull convex sets coreset cylinder d-dimensional defined Delaunay Delaunay triangulation Demaine denote dimension Discrete Comput disjoint Edelsbrunner elements endpoint Eppstein Erdős example facet Figure finite folding function Geom graph h-vector halfspace hypergraph hyperplane inequality input intersection Kapranov rank lattice Lemma line segments linear lower bound Math matrix maximum minimal minimum NP-hard O'Rourke optimal origami partition complexity permutation plane polygon polyhedra polyhedron polynomial positive problem proof Proposition protein proved pseudoline quasiconvex functions quasiconvex program radius random Section semialgebraic set short edges simplex simplices smallest enclosing ball space sphere structure Sturmfels subset subspace tetrahedra Theorem Tóth triangulation tropical convex hull tropical halfspace tropical polytope tropical rank upper bound vector vertex vertices zonotopes