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.
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