Support Function

Let $M$ be an oriented Regular Surface in $\Bbb{R}^3$ with normal N. Then the support function of $M$ is the function $h:M\to\Bbb{R}$ defined by

$$h({\bf p})={\bf p}\cdot{\bf N}({\bf p}).$$

References

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, p. 293, 1993.