  In this study we investigate the calibration of surface brightness--color
(SBC) relations based solely on eclipsing binary stars. We selected a sample of
35 detached eclipsing binaries with trigonometric parallaxes from Gaia DR1 or
Hipparcos, whose absolute dimensions are known with an accuracy better than 3%
and that lie within 0.3 kpc from the Sun. For the purpose of this study, we
used mostly homogeneous optical and near-infrared photometry based on the
Tycho-2 and 2MASS catalogs. We derived geometric angular diameters for all
stars in our sample with a precision better than 10%, and for 11 of them with a
precision better than 2%. The precision of individual angular diameters of the
eclipsing binary components is currently limited by the precision of the
geometric distances ($\sim$5% on average). However, by using a subsample of
systems with the best agreement between their geometric and photometric
distances, we derived the precise SBC relations based only on eclipsing binary
stars. These relations have precisions that are comparable to the best
available SBC relations based on interferometric angular diameters, and they
are fully consistent with them. With very precise Gaia parallaxes becoming
available in the near future, angular diameters with a precision better than 1%
will be abundant. At that point, the main uncertainty in the total error budget
of the SBC relations will come from transformations between different
photometric systems, disentangling of component magnitudes, and for hot OB
stars, the main uncertainty will come from the interstellar extinction
determination. We argue that all these issues can be overcome with modern
high-quality data and conclude that a precision better than 1% is entirely
feasible.
