Support function

In mathematics, the support function h_A of a non-empty closed convex set A in ${\displaystyle \mathbb {R} ^{n}}$ describes the (signed) distances of supporting hyperplanes of A from the origin. The support function is a convex function on ${\displaystyle \mathbb {R} ^{n}}$. Any non-empty closed convex set A is uniquely determined by h_A. Furthermore, the support function, as a function of the set A, is compatible with many natural geometric operations, like scaling, translation, rotation and Minkowski addition. Due to these properties, the support function is one of the most central basic concepts in convex geometry.