What process should we use to find the maximum outline of an arbitrary object (closed, or open polysurface) relative to the Z-Axis ?

In the attached (random) example we want to create a cavity in the box such that the object slides in perfectly. To do so we need to find the widest possible perimeter about the Z-Axis.

(The red curve in the file is the XY intersection, to illustrate how not to do it)

Thoughts ?

Thermoform.3dm (112.2 KB)