Finding distance between two curves

I'd like to find the minimum distance between two curves that do not share the same support, i.e. the X-axis range is different for each curve.

Previous MATLAB answers referred to the case when at least partially the curves share the same support.

I'm looking for efficient way to do that, not by calculating the distance from each point on curve 1 to each point in curve 2 and then finding the minimum distance

Thanks so much for the help

Talmon