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We observe the high-mass X-ray binary (HMXB) BP Cru using interferometry in the near-infrared K band with VLTI/GRAVITY. Continuum visibilities are at most partially resolved, consistent with the predicted size of the hypergiant. Differential visibility amplitude () and phase () signatures are observed across the He i and Brγ lines, the latter seen strongly in emission, unusual for the donor star’s spectral type. For a baseline m, the differential phase rms corresponds to an astrometric precision of . We generalize expressions for image centroid displacements and variances in the marginally resolved limit of interferometry to spectrally resolved data, and use them to derive model-independent properties of the emission such as its asymmetry, extension, and strong wavelength dependence. We propose geometric models based on an extended and distorted wind and/or a high-density gas stream, which has long been predicted to be present in this system. The observations show that optical interferometry is now able to resolve HMXBs at the spatial scale where accretion takes place, and therefore to probe the effects of the gravitational and radiation fields of the compact object on its environment. [ABSTRACT FROM AUTHOR]