The construction of PP angle gathers from the saved angles to vertical during wavefield propagation may be technically difficult, but the physical principle is simple. For PP reflections, the incidence angle is equal to the reflection angle. Therefore, a simple summation of the source wavefield's angle to the vertical at an imaging point at a particular propagation time, with the receiver wavefield's angle to the vertical, is enough to determine opening angle. The result of the cross-correlation between the wavefields at that time can be placed into an angle gather at the resulting opening angle. Though we save only the angle to the vertical for each wavefield, this is simply a reference axis. Once the opening angle is determined, adding half of that opening angle to either the source or receiver wave's angle to the vertical will produce an angle which is perpendicular to dip angle at that (specular) reflection point.
For PS (or SP) angle gathers, the relation between the P incidence angle and the S reflection angle is more complicated, as shown in Rosales and Rickett (2001).