  It is well known that the Fourier--Bohr coefficients of regular model sets
exist and are uniformly converging, volume-averaged exponential sums. Several
proofs for this statement are known, all of which use fairly abstract
machinery. For instance, there is one proof that uses dynamical systems theory
and another one based on Meyer's theory of harmonious sets. Nevertheless, since
the coefficients can be defined in an elementary way, it would be nice to have
an alternative proof by similarly elementary means, which is to say by standard
estimates of exponential sums under an appropriate use of the Poisson summation
formula. Here, we present such a proof for the class of regular Euclidean model
sets, that is, model sets with Euclidean physical and internal spaces and
topologically regular windows with almost no boundary.
