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

References

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