  Based on the stellar orbit distribution derived from orbit-superposition
Schwarzschild models, we decompose each of 250 representative present-day
galaxies into four orbital components: cold with strong rotation, warm with
weak rotation, hot with dominant random motion and counter-rotating (CR). We
rebuild the surface brightness ($\Sigma$) of each orbital component and we
present in figures and tables a quantification of their morphologies using the
Sersic index \textit{n}, concentration $C =
\log{(\Sigma_{0.1R_e}/\Sigma_{R_e})}$ and intrinsic flattening
$q_{\mathrm{Re}}$ and $q_{\mathrm{Rmax}}$, with $R_e$ the half-light-radius and
$R_{\mathrm{max}}$ the CALIFA data coverage. We find that: (1) kinematic hotter
components are generally more concentrated and rounder than colder components,
and (2) all components become more concentrated and thicker/rounder in more
massive galaxies; they change from disk-like in low mass late-type galaxies to
bulge-like in high-mass early type galaxies. Our findings suggest that Sersic
\textit{n} is not a good discriminator between rotating bulges and non-rotating
bulges. The luminosity fraction of cold orbits $f_{\rm cold}$ is well
correlated with the photometrically-decomposed disk fraction $f_{\rm disk}$ as
$f_{\mathrm{cold}} = 0.14 + 0.23f_{\mathrm{\mathrm{disk}}}$. Similarly, the hot
orbit fraction $f_{\rm hot}$ is correlated with the bulge fraction $f_{\rm
bulge}$ as $f_{\mathrm{hot}} = 0.19 + 0.31f_{\mathrm{\mathrm{bulge}}}$. The
warm orbits mainly contribute to disks in low-mass late-type galaxies, and to
bulges in high-mass early-type galaxies. The cold, warm, and hot components
generally follow the same morphology ($\epsilon = 1-q_{\rm Rmax}$) versus
kinematics ($\sigma_z^2/\overline{V_{\mathrm{tot}}^2}$) relation as the thin
disk, thick disk/pseudo bulge, and classical bulge identified from cosmological
simulations.
