  We propose a ray-tracing method to estimate gravitational waves (GWs)
generated by anisotropic neutrino emission in supernova cores. To calculate the
gravitational waveforms, we derive analytic formulae in a useful form, which
are applicable also for three-dimensional computations. Pushed by evidence of
slow rotation prior to core-collapse, we focus on asphericities in neutrino
emission and matter motions outside the protoneutron star. Based on the
two-dimensional (2D) models, which mimic SASI-aided neutrino heating
explosions, we compute the neutrino anisotropies via the ray-tracing method in
a post-processing manner and calculate the resulting waveforms. With these
computations, it is found that the waveforms exhibit more variety in contrast
to the ones previously estimated by the ray-by-ray analysis (e.g., Kotake et
al. (2007)). In addition to a positively growing feature, which was predicted
to determine the total wave amplitudes predominantly, the waveforms are shown
to exhibit large negative growth for some epochs during the growth of SASI.
These features are found to stem from the excess of neutrino emission in
lateral directions, which can be precisely captured by the ray-tracing
calculation. Due to the negative contributions and the neutrino absorptions
appropriately taken into account by the ray-tracing method, the wave amplitudes
become more than one-order-of magnitude smaller than the previous estimation,
thus making their detections very hard for a galactic source.On the other hand,
it is pointed out that the GW spectrum from matter motions have its peak near
$\sim 100$ Hz, which could be characteristic for the SASI-induced supernova
explosions.(abridged)
