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
\(f \colon X \rightarrow {\mathbb{R}}\) be the function that
assigns to each point in \(X\) it’s distance to \(S\) and let
\(g \colon X \rightarrow {\mathbb{R}}\) 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 \(S\)*.