terminology needed regarding convex bodies

Question

Let $K$ be a convex body in $\mathbb{R}^n$. I'm looking for a term for a continuous function $f: \mathbb{R}^n \to \mathbb{R}$ that is zero on $\partial K$, negative on the interior of $K$, and positive on the exterior of $K$. Moreover, if the gradient of $f$ is defined at a point on $\partial K$, then it must be non-zero. Such a function always exists - e.g. the signed distance to $\partial K$, but for some $K$ a different function is easier to compute, or more convenient in some way. Obviously there are infinitely many such functions for a given $K$. Many convex bodies are canonically defined by a function like this (e.g. the unit ball), but many are not.