  We analyze the directional dependence of the gravitational wave (GW) emission
from 15 3D neutrino radiation hydrodynamic simulations of core-collapse
supernovae. Using spin weighted spherical harmonics, we develop a new analytic
technique to quantify the evolution of the distribution of GW emission over all
angles. We construct a physics-informed toy model that can be used to
approximate GW distributions for general ellipsoid-like systems, and use it to
provide closed form expressions for the distribution of GWs for different CCSN
phases. Using these toy models, we approximate the PNS dynamics during multiple
CCSN stages and obtain similar GW distributions to simulation outputs. When
considering all viewing angles, we apply this new technique to quantify the
evolution of preferred directions of GW emission. For nonrotating cases, this
dominant viewing angle drifts isotropically throughout the supernova, set by
the dynamical timescale of the protoneutron star. For rotating cases, during
core bounce and the following tens of ms, the strongest GW signal is observed
along the equator. During the accretion phase, comparable -- if not stronger --
GW amplitudes are generated along the axis of rotation, which can be enhanced
by the low T/|W| instability. We show two dominant factors influencing the
directionality of GW emission are the degree of initial rotation and explosion
morphology. Lastly, looking forward, we note the sensitive interplay between GW
detector site and supernova orientation, along with its effect on detecting
individual polarization modes.
