Volume of intersection of two cylinders with radiuses r1 and r2, intersecting in 90° angle and offset in z-axis

35 Views Asked by At

I'm trying to calculate the volume on the intersection of two cylinders with radiuses r1 and r2. They intersect at an angle of 90° as described by the picture in 1. They also might have an offset in z-direction. I'm interested in the solution and where to find it. How the solution can be derived is most probably beyond my mathematical capabilities.

I've searched for a book with formulas for intersections of bodies but couldn't find it. I only found formulas for the Steinmetz solid where r1 = r2.

Also I thought of integrating the intersection curve from 1 but it's been some years since I've done that. How hard is that going to be?

As a last resort I would use a CAD-tool for it but a formula would be nicer.