How to convert LOR data to Sinogram data for plane PET Modules?

Dear users,
I am working on image reconstruction of the plane PET module prototype. I get the LOR positions for coincidences on each detector. I have attached the geometric view of my detector geometry. What I have, is the coordinates of coincidence -1 (y1,z1) and coincidence-2 (y2,z2) positions and fixed detector spacing. The case seems a bit different to me compared to the ring PET case because I have to get the coincidence with oblige planes as well. It needs to include all LORs on the oblique planes in a trans-axial direction. Do you have any suggestions, references, resources, or experience to deal with this problem? Your help will be appreciated. (I want to record coincidences between each crystal with other and want to store them as sinogram data. )
XYZ_Plane