Plumbers often combine two 45° elbows (1/8 bends) or a 45° wye and an 1/8 bend to give them more freedom through rotation before gluing PVC pipes.
Often, this is necessary because the incoming pipe has a vertical angle (of 1/4" per foot) when viewed in elevation, the outgoing pipe has its own vertical angle (again of 1/4" per foot), and the plumber wants some horizontal angle between the two pipes (when viewed from above in plan).
For a single fitting, a previously answered question shows that the space of available angles forms a cone through rotation (New angle formed after rotating pipe).
What is the space of available vertical and horizontal angles between the two pipes? How could I visualize this? Can this be generalized to other combinations of angle fittings (1/4 bends, 1/8 bends, and 1/16 bends)?
