Counting facets and incidences

DOI10.1007/BF02187848zbMath0747.68092OpenAlexW2037597410WikidataQ56454603 ScholiaQ56454603MaRDI QIDQ1189286

Boris Aronov, Pankaj K. Agarwal

Publication date: 26 September 1992

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131201

zbMATH Keywords

arrangementsfacetstight bounds

Mathematics Subject Classification ID

Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.) (52B05) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Arrangements of points, flats, hyperplanes (aspects of discrete geometry) (52C35)

Related Items (10)

Two theorems on point-flat incidences ⋮ Castles in the air revisited ⋮ Many-face complexity in incremental convex arrangements ⋮ Nondegenerate spheres in four dimensions ⋮ On a Question of Bourgain about Geometric Incidences ⋮ A bichromatic incidence bound and an application ⋮ A new technique for analyzing substructures in arrangements of piecewise linear surfaces ⋮ Robot motion planning and the single cell problem in arrangements ⋮ On the complexity of a single cell in certain arrangements of surfaces related to motion planning ⋮ On the sum of squares of cell complexities in hyperplane arrangements

Cites Work

• Unnamed Item
• The complexity of many cells in arrangements of planes and related problems
• On the lattice property of the plane and some problems of Dirac, Motzkin and Erdős in combinatorial geometry
• Extremal problems in discrete geometry
• The upper envelope of piecewise linear functions and the boundary of a region enclosed by convex plates: Combinatorial analysis
• Combinatorial complexity bounds for arrangements of curves and spheres
• On the maximal number of edges of many faces in an arrangement
• The complexity of cells in three-dimensional arrangements
• On the sum of squares of cell complexities in hyperplane arrangements
• Castles in the air revisited
• Triangles in space or building (and analyzing) castles in the air
• Partitioning Space for Range Queries

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