Mexican Conference on Discrete Mathematics and Computational Geometry Isoperimetric Enclosures
نویسندگان
چکیده
Let S be a set of n > 2 points in the plane whose convex hull has perimeter t. Given a number P ≥ t, we study the following problem: Of all curves of perimeter P that enclose S, which is the curve that encloses the maximum area? In this paper, we give a complete characterization of this curve. We show that there are cases where this curve cannot be computed exactly and provide an O(n logn)-time algorithm to obtain an approximation of this curve, with arbitrary precision, having the same combinatorial structure.
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