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.
