  In surfaces with grainy features, the local roughness $w$ shows a crossover
at a characteristic length $r_c$, with roughness exponent changing from
$\alpha_1\approx 1$ to a smaller $\alpha_2$. The grain shape, the choice of $w$
or height-height correlation function (HHCF) $C$, and the procedure to
calculate root mean-square averages are shown to have remarkable effects on
$\alpha_1$. With grains of pyramidal shape, $\alpha_1$ can be as low as 0.71,
which is much lower than the previous prediction 0.85 for rounded grains. The
same crossover is observed in the HHCF, but with initial exponent
$\chi_1\approx 0.5$ for flat grains, while for some conical grains it may
increase to $\chi_1\approx 0.7$. The universality class of the growth process
determines the exponents $\alpha_2=\chi_2$ after the crossover, but has no
effect on the initial exponents $\alpha_1$ and $\chi_1$, supporting the
geometric interpretation of their values. For all grain shapes and different
definitions of surface roughness or HHCF, we still observe that the crossover
length $r_c$ is an accurate estimate of the grain size. The exponents obtained
in several recent experimental works on different materials are explained by
those models, with some surface images qualitatively similar to our model
films.
