Imagine a subspace $S$ of our environment, denoted by $X$, is densely covered with icing sugar. Further we assume we can see the icing sugar but not the space $S$ itself. Now let $f:X\to \mathbb{R}$ be the function that assigns to each point in $X$ it’s distance to $S$ and let $g:X\to \mathbb{R}$ assign to each point the distance to a nearest grain of icing sugar. Then $S$ is the zero locus of $f$. Moreover $g$ can be as close to $f$ as we like, if we only spread the icing sugar densely enough. The icing sugar is also referred to as point-cloud data for $S$.