  In the first paper of this series we use the publicly available code Gim2D to
model the r- and i-band images of all galaxies in a magnitude-limited sample of
roughly 1800 morphologically classified galaxies taken from the Sloan Digital
Sky Survey. The model is a concentric superposition of two components, each
with elliptical isophotes with constant flattening and position angle. The disk
luminosity profile is assumed exponential, while the bulge is assumed to have a
de Vaucouleurs or a Sersic profile. We find that the parameters returned by
Gim2D depend little on the waveband or bulge profile used; their formal
uncertainties are usually small. Nevertheless, for bright galaxies the measured
distribution of b/a, the apparent disk flattening, deviates strongly from the
expected uniform distribution, showing that the `disk' identified by the code
frequently corresponds to an intrinsically 3-dimensional structure rather than
to a true thin disk. We correct approximately for this systematic problem using
the observed statistics of the b/a distribution and estimate, as a function of
absolute magnitude, the mean fractions of galaxy light in disks and in `pure
bulge' systems (those with no detectable disk). For the brightest galaxies the
disk light fraction is about 10% and about 80% are `pure bulge' systems. For
faint galaxies most of the light is in disks and we do not detect a `pure
bulge' population. Averaging over the galaxy population as a whole, we find
that 54 \pm 2% of the local cosmic luminosity density at both r and i comes
from disks and 32 \pm 2% from `pure bulge' systems. The remaining 14 \pm 2%
comes from bulges in galaxies with detectable disks.
