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Convex Hull

The convex hull of a set of points in dimensions is the intersection of all convex sets containing . For points , ..., , the convex hull is then given by the expressionComputing the convex hull is a problem in computational geometry. The indices of the points specifying the convex hull of a set of points in two dimensions is given by the command ConvexHull[pts] in the Wolfram Language package ComputationalGeometry` . Future versions of the Wolfram Language will support three-dimensional convex hulls. A makeshift package for computing three-dimensional convex hulls in the Wolfram Language has been written by Meeussen and Weisstein.In dimensions, the "gift wrapping" algorithm, which has complexity , where is the floor function, can be used (Skiena 1997, p. 352). In two and three dimensions, however, specialized algorithms exist with complexity (Skiena 1997, pp. 351-352). Yao (1981) has proved that any decision-tree..

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