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Pseudo-characteristic functions for convex polyhedra. (English) Zbl 1072.52002

For a convex \(n\)-polytope \(P\) in \(\mathbb{R}^n\), the authors present an algorithm to construct polynomials of degree \(2r\) that determine approximately whether a point \(p\) lies in- or outside of \(P\). (Here \(r\) is a positive integer, where the order of the approximation can be made arbitrarily small by taking \(r\) sufficiently large.) They give concrete examples for dimensions 2, 3, and 4 (e.g., in the latter case investigating the equilateral simplex).

MSC:

52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
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