Two fittings, one obstruction, and a piece of pipe that has to land exactly. Give the offset and the fitting angle and this returns the travel, the run, and the length to actually cut once the take-off of both fittings is removed.
Notes
Travel, run and offset
Offset is how far the line shifts sideways. Travel is the length of the sloping pipe, centre to centre. Run is how far along the original direction you consume doing it. Travel equals offset divided by the sine of the angle — for 45 degrees that is offset times 1.414.
Why the take-off matters
Travel is centre to centre of the fittings. The pipe you cut is shorter by the take-off of each fitting — the distance from the fitting centre to the end of the socket. Forget it and every offset comes out long by an inch or more.
Rolling offsets
When the obstruction moves the line both sideways and up, the true offset is the diagonal of those two: the square root of the sum of their squares. The roll angle tells you how far round the vertical the whole offset is rotated.
What this does not do
It is pure geometry. It does not size pipe, check fall on drainage, or know which fittings your system allows.