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We used an Isospin dependent Quantum Molecular Dynamics (IQMD) model tosimulate Au + Au collisions at beam energy $E_{beam}$ = 1.23$A$ GeV, whichcorresponds to center of mass energy $\sqrt{s_{NN}} = 2.4$ GeV. Firstly, weobtained reasonable rapidity and transverse mass spectra of $\pi^-$ and $\pi^+$as well as "apparent" temperature parameters in comparison with the HADES data.Then by calculating three-dimensional Hanbury Brown and Twiss (HBT) radius ofsame charged pion-pairs, we obtained the square difference of outward radiusand sideward radius, i.e. $R_{out}^{2}-R_{side}^{2}$, as well as the freeze-outvolume ($V_{fo}$), which were basically consistent with the trend of HADESexperimental results. The azimuthal dependence of the HBT radii was alsocalculated by a matrix method, and corrected by the rotation matrix. Inaddition, the eccentricities of the $xy$- and $zy$- planes of pion-pairemissions were also extracted for different pair transverse momentum andcollision centrality, which show that the $xy$-eccentricity increases with pairtransverse momentum as well as centrality but not for $zy$-eccentricity,indicating a more asymmetric transverse emission of particle-pairs with highertransverse momentum in off-central collisions.

Azimuthal-sensitive three-dimensional HBT radius in Au-Au collisions at $E_{beam} = 1.23$$A$ GeV by the IQMD model