Alphashape calculated with points and triangles

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Hi there,
another alphaShape related question: If i do not only have a point cloud, but if i also have some triangulation of that point cloud, can the triangulation's surfaces be taken into account with some algorithm?
I just want to "roll" a sphere of given radius on the surface of the given triangulation and mark those faces and points, which are touched by any such movement of that sphere. (These marked entities do not neccessarily be postprozessed to give a closed surface. That may be the second step afterwards.)
Why is that different from a pointcloud's alphashape? If there is a boundary triangle, which's circumscribed circle is large, then it would be removed in a standard pointcloud's alphashape. In my wishlist, i need an algorithm which keeps this triangle as it i prescribed by the underlying triangulation.

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