GDit implements the mathematical model for gravity darkening in rotating stars presented by Espinosa Lara & Rieutord (2011).
The above figure shows a range of Roche equipotential surfaces corresponding to rotating stars at different fractions of the Keplerian angular velocity ω and inclination angle i. In the figure the colorscale indicates the Teff of the stellar surface: red is cooler and yellow is hotter.
The code allows one to calculate the gravity darkening coefficients CL and CT, which tell how both rotation and inclination alter the projected Teff and luminosity of the star. These are inspired by Georgy et al. (2014) but calculated in a manner consistent with Espinosa Lara & Rieutord (2011) for Roche equipotential surfaces. This is described in detail in MESA V.
CT and CL allow one to quickly determine the observational consquences of rotating stellar models with arbitrary orientation.