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

$h(\mathbf {x} )=\mathbf {x} \cdot N(\mathbf {x} )$.

In other words, for any $\mathbf {x} \in M$, the support function $h(\mathbf {x} )$ gives the signed distance of the unique hyperplane that touches $M$ in $\mathbf {x}$. This hyperplane is also called the supporting hyperplane.

External links

• MathWorld on Support Function