Ultimate Tricky Mesh Question of the Week

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You could probably adapt (simplify) my mesh clipping code to solve this (click on my profile to access my code archive entries).

It may also be a good idea to have a hidden, proxy mesh attached to each entity - i.e. a single triangle that represents the outer edges. You could then chop one of the proxy meshes up, using the edges of all the other meshes that intersect with it.

Why do your 'things' have to comprise many triangles?

Is this for some kind of light effect?