  Azimuthally-sensitive femtoscopy for heavy-ion collisions at RHIC and LHC is
explored within the approach consisting of the hydrodynamics of perfect fluid
followed by statistical hadronization. It is found that for the RHIC initial
conditions the very same framework that reproduces the standard soft
observables (including the transverse-momentum spectra, the elliptic flow, and
the azimuthally-averaged HBT radii) leads to a proper description of the
azimuthally-sensitive femtoscopic observables - we find that the azimuthal
variation of the side and out HBT radii is very well reproduced for all
centralities, while the out-side correlation is somewhat too large for
non-central events. Concerning the dependence of the femtoscopic parameters on
kT we find that it is very well reproduced for the out and side radii, and
fairly well for the long radius. The model is then extrapolated for the LHC
energy. We predict the overall moderate growth of the HBT radii and the
decrease of their azimuthal oscillations. Such effects are naturally caused by
longer evolution times. In addition, we discuss in detail the space-time
patterns of particle emission. We show that they are quite complex and argue
that the overall shape seen by the femtoscopic methods cannot be easily
disentangled on the basis of simple-minded arguments.
