Interferometric observations have revealed that the rapid rotator Altair is a flattened star with a non-centrally symmetric intensity distribution. In this work we perform for the first time a physically consistent analysis of all interferometric data available so far, corresponding to three different interferometers operating in several spectral bands. These observations include new data (squared visibilities in the H and K bands from VLTI-VINCI) as well as previously published data (squared visibilities in the K band from PTI and squared visibilities, triple amplitudes, and closure phases in the visible between 520 nm and 850 nm from NPOI). To analyze these data we perform a χ2 minimization using an interferometry-oriented model for fast rotators, which includes Roche approximation, limb-darkening, and von Zeipel-like gravity-darkening. Thanks to the rich interferometric data set available and to this physical model, the main uniqueness problems were avoided. As a result, we show that the observations can only be explained if Altair has a gravity-darkening compatible with the expected value for hot stars, i.e., the von Zeipel effect (T_eff∝ g0.25).