منابع مشابه
Steaming on Convex Hulls
This is a sea story about using a simple classroom example to save a great deal of money, as well as to convince beginning Postgraduate Naval School operations research students—experienced, skeptical military officers—that mathematical analysis can yield immediate results. The application is planning a ship’s transit from one point to another in a fixed amount of time, given that the ship can ...
متن کاملFormalizing Convex Hulls Algorithms
We study the development of formally proved algorithms for computational geometry. The result of this work is a formal description of the basic principles that make convex hull algorithms work and two programs that implement convex hull computation and have been automatically obtained from formally verified mathematical proofs. A special attention has been given to handling degenerated cases th...
متن کاملOn the Smoothed Complexity of Convex Hulls
We establish an upper bound on the smoothed complexity of convex hulls in R under uniform Euclidean (`2) noise. Specifically, let {p1, p2, . . . , pn} be an arbitrary set of n points in the unit ball in R and let pi = pi + xi, where x1, x2, . . . , xn are chosen independently from the unit ball of radius δ. We show that the expected complexity, measured as the number of faces of all dimensions,...
متن کاملClassifier Conditions based on Convex Hulls
We introduce a novel representation of classifier conditions based on convex hulls. A classifier condition is represented by a sets of points in the problem space. These points identify a convex hull that delineates a convex region of the problem space. The condition matches all the problem instances inside such region. We apply XCSF with convex conditions to function approximation problems and...
متن کاملA Note on Approximate Convex Hulls
Bentley, Faust and Preparata [1] presented a linear time algorithm for computing an approximate convex hull in two-dimensional space. They compute a polygon with vertices in the given set of points in the plane such that the polygon is arbitrarily close to the convex hull of the point set. Soisalon-Soininen [2] modified the approximation scheme of [1] and, among other things, gave a criterion w...
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ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1998
ISSN: 0179-5376
DOI: 10.1007/pl00009331