Computational geometry: an introduction
Computational geometry: an introduction
Algorithms
A New Convex Hull Algorithm for Planar Sets
ACM Transactions on Mathematical Software (TOMS)
Fast linear expected-time alogorithms for computing maxima and convex hulls
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
The traveling salesman: computational solutions for TSP applications
The traveling salesman: computational solutions for TSP applications
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This paper is concerned with a simple, rather intuitive preprocessing step that is likely to improve the average-case performance of any convex hull algorithm. For n points randomly distributed in the unit square, we show that a simple linear pass through the points can eliminate all but &Ogr;(√n) of the points by showing that a simple superset of the remaining points has size c√n + &ogr;(√n). We give a full implementation of the method, which should be useful in any practical application for finding convex hulls. Most of the paper is concerned with an analysis of the number of points eliminated by the procedure, including derivation of an exact expression for c. Extensions to higher dimensions are also considered.