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Convex Hull

The convex hull of a set of points $S$ 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\equiv \left\{{\,\sum_{j=1}^N \lambda_jp_j : \lambda_j\geq ...
...or\ all\ } j
{\rm\ and\ } \sum_{j=1}^N \lambda_j=1}\right\}.

See also Carathéodory's Fundamental Theorem, Cross Polytope, Groemer Packing, Groemer Theorem, Sausage Conjecture, Sylvester's Four-Point Problem


Santaló, L. A. Integral Geometry and Geometric Probability. Reading, MA: Addison-Wesley, 1976.

© 1996-9 Eric W. Weisstein