  Aims: We present a comparison of the visual and NIR intensity profile of the
M0 giant gamma Sagittae to plane-parallel ATLAS 9 as well as to plane-parallel
& spherical PHOENIX model atmospheres. Methods: We use previously described
visual interferometric data obtained with the NPOI in July 2000. We apply the
recently developed technique of coherent integration, and thereby obtain
visibility data of more spectral channels and with higher precision than
before. In addition, we employ new measurements of the K-band diameter of gamma
Sagittae obtained with the instrument VINCI at the VLTI in 2002. Results: The
spherical PHOENIX model leads to a precise definition of the Rosseland angular
diameter and a consistent high-precision diameter value for our NPOI and
VLTI/VINCI data sets of Theta_Ross=6.06 pm 0.02 mas, with the Hipparcos
parallax corresponding to R_Ross=55 pm 4 R_sun, and with the bolometric flux
corresponding to an effective temperature T_eff=3805 pm 55 K. Our visual
visibility data close to the first minimum and in the second lobe constrain the
limb-darkening effect and are generally consistent with the model atmosphere
predictions. The visual closure phases exhibit a smooth transition between 0
and pi. Conclusions: The agreement between the NPOI and VINCI diameter values
increases the confidence in the model atmosphere predictions from optical to
NIR wavelengths as well as in the calibration and accuracy of both
interferometric facilities. The consistent night-by-night diameter values of
VINCI give additional confidence in the given uncertainties. The closure phases
suggest a slight deviation from circular symmetry, which may be due to surface
features, an asymmetric extended layer, or a faint unknown companion.
