I'm trying to come up with a method, given two convex hulls A & B, which overlap, to determine how far along a given axis vector (in a given direction) that I would have to translate B in order to avoid intersection with A. Consider the following two examples, presented visually:

![Before and After States](https://i.stack.imgur.com/GRpAm.png)

The goal is to determine *d*. I started my investigation thinking of the Separating Axis Theorem, and initially projected the two hulls onto the given axis and calculated the `d` necessary to prevent overlap on that axis, but that fails to find the minimum distance for cases like this: 

![Fault in Naive approach](https://i.stack.imgur.com/CryA4.png)

I'm starting to think that I want to be *more* like the SAT and project along the axes parallel to each face of the hulls, but it's not coming together in my head. Can anyone help me break this mental logjam?