  We analyse interferometric data obtained for Regulus with AMBER (Astronomical
Multi- BEam combineR) at high spectral resolution ($\lambda/\delta\lambda
\approx 12000$) across the Br$\gamma$ spectral line. The study of the
photocentre displacement allows us to constrain a large number of stellar
parameters -- equatorial radius $R_{\rm eq}$, equatorial velocity $V_{\rm eq}$,
inclination $i$, rotation-axis position angle $PA_{\rm rot}$, and flattening --
with an estimation of gravity-darkening coefficient $\beta$ 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 $PA_{rot}$. We
use two minimization methods to restrict observed stellar parameters via a fast
rotator model: a non-stochastic method ($\chi^2$ 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 $\beta$, where we demonstrate, using a quantitative
analysis of parameters, that the estimate of $\beta$ is easier for stars with
an inclination angle of around $45^\circ$.
