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I have zero experience in this type of modelling API. But... I would recommend that you look in the utilities API if you have SolidWorks Professional or higher.
There is a power select method that would help you with this.
If you do not have Professional... then I would try to use entities in order to select or store data for selection later.
See this blog where they process edges and uses the IEdge and IEntity interface.
Set swEntity = swEdge
This would allow you to select the edge(s) as entity or give the entity a name and store that in a array for use to select later.
Meanwhile I will personally keep thinking about your question, I'm sure that someone have solved it in the past without adding a radius and analyse the mass. There is some quite impressive techniques and algorithms out there.
The power select link has a filter for concave vs. convex edges, which works great! "power select method "
Only, be sure to use the following preconditions to load the SolidWorks Utilities before you can use power select.
' 1. Add the SolidWorks Utilities as an add-in
' (in SolidWorks, click Tools > Add-Ins > SolidWorks Utilities).
' 2. Add the SolidWorks Utilities type library as a reference
' (in the IDE, click Tools > References > SolidWorks
' Utilities version type library).
' 3. The specified files exist.
' 4. C:\test\ exists.