On the zone of a surface in a hyperplane arrangement
Copyright policy )On the zone of a surface in a hyperplane arrangement
For a collection of \(n\) hyperplanes in \(\mathbb{R}^ d\) the complex of all open cells and their lower dimensional faces is called an arrangement. The collection of all those cells which are met by a set \(\sigma\) is called its zone and its complexity is the number of all the faces. Asymptotic estimates for the complexity are given the simplest, for the case that \(\sigma\) is the boundary of a convex set or an algebraic surface, is \(O(n^{d-1}\log n)\).
- Tel Aviv University Israel
- New York University United States
- DigiZeitschriften Germany
- Canadian Friends Of Tel-Aviv University Canada
- Courant Institute of Mathematical Sciences United States
510.mathematics, Computer graphics; computational geometry (digital and algorithmic aspects), zone theorem, algebraic surface, hyperplane arrangement, Article, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
510.mathematics, Computer graphics; computational geometry (digital and algorithmic aspects), zone theorem, algebraic surface, hyperplane arrangement, Article, Arrangements of points, flats, hyperplanes (aspects of discrete geometry), Combinatorial properties of polytopes and polyhedra (number of faces, shortest paths, etc.)
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