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    $\begingroup$ I assume you're using 3D Delaunay meshes and they are convex, you have the convenient result that the intersection of two convex sets is also a convex set, so it would be the convex hull of the intersection points. You can already get the intersection points as per this answer using graphics and then just take the convex hull of those points $\endgroup$ Commented May 29, 2015 at 1:15