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    Convex Hull

    Basic definition

    The convex hull of a set of points S is the intersection of all convex sets containing S.

    Detailed definition

    The convex hull of a set of points S in n dimensions is the intersection of all convex sets containing S. For N points p_1, ..., p_N, the convex hull C is then given by the expression C congruent { sum_(j = 1)^N λ_j p_j :λ_j>=0 for all j and sum_(j = 1)^N λ_j = 1}. Computing 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 ComputationalGeometryˋ . 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.

    Related terms

    Carathéodory's fundamental theorem | computational geometry | cross polytope | Delaunay triangulation | expansion | geometric span | Groemer packing | Groemer theorem | happy end problem | Radon's theorem | sausage conjecture | Sylvester's four-point problem | temperature | Voronoi diagram

    Educational grade level

    high school level

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