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I think some more optimal algorithms are used for measurements in this case (maybe not even actual distance measurments to the faces)

 

Using the NameValueMap is simple. You create an object and pass as an argument to MeasureTools.GetMinimumDistance method.

 

Please check Inventor Api for this method:

https://help.autodesk.com/view/INVNTOR/2018/ENU/?guid=GUID-240D2F92-2701-4D9D-BCE7-02759538E2FC

 

Here is a good article as well:

https://adndevblog.typepad.com/manufacturing/2014/01/vector-of-minimum-distance.html