The convex body support function of a convex body 
is the function
 |
where 
is the Euclidean inner product. For a unit
vector 
, it gives the signed distance
from the origin to the supporting
hyperplane with outward normal vector 
. The function determines
uniquely and satisfies 
for every 
. For the unit ball,
, where 
is the Euclidean norm.
Convex body support functions add under Minkowski sum.
