Support function

File:Support function value.png

Value of support function for this surface (red = 0, blue=max value).

In mathematics, for an oriented regular surface, M, with a unit normal vector, N, defined everywhere on its surface, the support function $h:M\to \mathbb {R}$ is defined by

$h(\mathbf {x} )=\mathbf {x} \cdot N(\mathbf {x} )\quad \forall \mathbf {x}$ on the perimeter of M.

In other words, the support function of a set is an alternate representation of the set in terms of the position of all tangent planes that enclose the set. That is, $\mathbf {x} \cdot N(\mathbf {x} )$ defines a plane that intersects x with a normal N.

External links

• MathWorld on Support Function