  We consider the problem of computing the distance between two
piecewise-linear bivariate functions $f$ and $g$ defined over a common domain
$M$. We focus on the distance induced by the $L_2$-norm, that is
$\|f-g\|_2=\sqrt{\iint_M (f-g)^2}$. If $f$ is defined by linear interpolation
over a triangulation of $M$ with $n$ triangles, while $g$ is defined over
another such triangulation, the obvious na\"ive algorithm requires
$\Theta(n^2)$ arithmetic operations to compute this distance. We show that it
is possible to compute it in $\O(n\log^4 n)$ arithmetic operations, by reducing
the problem to multi-point evaluation of a certain type of polynomials. We also
present an application to terrain matching.
