We analyse interferometric data obtained for Regulus with AMBER (Astronomical Multi-BEam combineR) at high spectral resolution (λ/δλ ≈ 12000) across the Brγ spectral line. The study of the photocentre displacement allows us to constrain a large number of stellar parameters -equatorial radius R eq , equatorial velocity V eq , inclination i, rotation-axis position angle P A rot , and flattening -with an estimation of gravity-darkening coefficient β using previously published theoretical results. We use the Simulation Code of Interferometric-observations for ROtators and CirCumstellar Objects (SCIROCCO), a semi-analytical algorithm dedicated to fast rotators. We chose Regulus because it is a very well-known edge-on star, for which an alternative approach is needed to check the previously published results. Our analysis showed that a significant degeneracy of solution is present. By confronting the results obtained by differential interferometry with those obtained by conventional long-base interferometry, we obtain similar results (within the uncertainties), thereby validating our approach, where V eq and i are found separately. From the photocentre displacement, we can independently deduce P A rot . We use two minimization methods to restrict observed stellar parameters via a fast rotator model: a non-stochastic method (χ 2 fit) and a stochastic one (Markov Chain Monte Carlo method), in order to check whether the correct global minimum is achieved particularly with respect to the degeneracies of the gravity darkening parameter β, where we demonstrate, using a quantitative analysis of parameters, that the estimate of β is easier for stars with an inclination angle of around 45 • .