I am trying to find a method similar to how “Proximity” finds the shortest distance between two curves, but for the maximum distance instead. Thank you

Quick and dirty but gives the desired result.

Someone with Python skill can deliver better solution, I guess.

This rather appears to me as the *maximum of all minimum distances* from the outer curve to the inner curve. Divide you outer curve in 500 points, Curve Closest Point to the inner curve, sort the distances, take the last element of the list.

Maximum distance would be the blue line.

That’s clearly not the longest distance between two curves without intersecting (which is a goal, I believe).

You found the longest among perpendiculars to two curves.

I’m going by the drawing from the OP, until informed otherwise.

I thought the same at the beginning but the ‘overlapping’ was a key phrase to me. Perpendiculars do not overlap.

Good plan but the blue line then doesn’t look possible. Looks more like the red line to me, eh?

Absolutely, this method should answer OP’s screenshot, which is not the same thing as the title of the thread.

I guess as always, clarification of the problem is required before moving on !

Another possibility, at least in terms of the screenshot. Create a mesh between the two curves and look for the point whose total distance from both curves is greatest. Is this any better? Who knows…

maximum distance.gh (10.5 KB)