  We model the projected b/a-log a distributions of CANDELS main sequence
star-forming galaxies, where a (b) is the semi-major (semi-minor) axis of the
galaxy images. We find that smaller-a galaxies are rounder at all stellar
masses M and redshifts, so we include a when analyzing b/a distributions.
Approximating intrinsic shapes of the galaxies as triaxial ellipsoids and
assuming a multivariate normal distribution of galaxy size and two shape
parameters, we construct their intrinsic shape and size distributions to obtain
the fractions of prolate, oblate and spheroidal galaxies in each redshift and
mass bin. We find that galaxies tend to be prolate at low m and high redshifts,
and oblate at high M and low redshifts, qualitatively consistent with van der
Wel et al. (2014), implying that galaxies tend to evolve from prolate to
oblate. These results are consistent with the predictions from simulations
(Ceverino et al. 2015, Tomassetti et al. 2016) that the transition from prolate
to oblate is caused by a compaction event at a characteristic mass range,
making the galaxy center baryon dominated. We give probabilities of a galaxy's
being prolate, oblate or spheroidal as a function of its M, redshift, projected
b/a and a, which can facilitate target selections of galaxies with specific
shapes at hight redshifts. We also give predicted optical depths of galaxies,
which are qualitatively consistent with the expected correlation that AV should
be higher for edge-on disk galaxies in each log a slice at low redshift and
high mass bins.
