Support function

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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.