  Some supernova (SN) explosions show evidence for interaction with
pre-existing non-spherically symmetric circumstellar medium (CSM) in their
light curves, spectral line profiles, and polarization signatures. To better
understand the connection with binary stars and to aid in the interpretation of
observations, we perform two-dimensional axisymmetric hydrodynamic simulations
where an expanding spherical SN ejecta initialized with realistic density and
velocity profiles collide with various aspherical CSM distributions. We
consider CSM in the form of a circumstellar disk, colliding wind shells in
binary stars with different orientations and distances from the SN progenitor,
and bipolar lobes representing a scaled down version of the Homunculus nebula
of $\eta$~Car. We study how our simulations map onto observables, including
approximate light curves, indicative spectral line profiles at late times, and
estimates of polarization signature. We find that the SN--CSM collision layer
is composed of normal and oblique shocks, reflected waves, and other
hydrodynamical phenomena that lead to acceleration and shear instabilities. As
a result, the total shock heating power fluctuates in time, although the
emerging light curve might be smooth if the shock interaction region is deeply
embedded in the SN envelope. SNe with circumstellar disks or bipolar lobes
exhibit late-time spectral line profiles symmetric with respect to the rest
velocity and relatively high polarization. In contrast, SNe with colliding wind
shells naturally lead to line profiles with asymmetric and time-evolving blue
and red wings and low polarization. Given the high frequency of binaries among
massive stars, interaction of SN ejecta with a pre-existing colliding wind
shell must occur and the observed signatures could be used to characterize the
binary companion.
