A simple pipe offset jogs the run sideways in one plane; a rolling offset has to move the line in two planes at once — over and up together. The trick that tames it is finding the true offset first: treat the rise (vertical move) and the roll (horizontal move) as the sides of a box, and the true offset is that box’s diagonal, √(rise² + roll²). From there the rolling case is solved exactly like a simple one, with the right-triangle identities the pipe trades have always used: travel = offset ÷ sin(angle) for the center-to-center length of the diagonal piece, and run = offset ÷ tan(angle) for how far it advances along the original direction.
The fitting angle sets the multiplier the trade memorizes — at 45° the travel is the offset times the familiar 1.414, at 22.5° times 2.613, both simply 1/sin(angle). The last step from geometry to a saw cut is the take-out: each elbow’s center-to-face dimension eats into the diagonal, so the actual end-to-end pipe length is the travel minus one take-out per end. Take-outs vary by size, schedule, and manufacturer, which is why they come off the fitting data sheet or the bench rather than from a universal table.