Is there any way? Trivially, yes. Ok, maybe trivial is in the eyes of the writer. I can say this because I have written both 2d and 3d alpha shape codes from scratch, and they both start from a triangulation/tessellation.
You just look at the surface facets of the triangulation. Then any tetrahedron that would allow the alpha ball to penetrate into the shape so that an alpha sphere of radius alpha would touch the interior vertex, that tetrahedron gets deleted. Now just test every surface facet. Whenever you delete a tetrahedron from the list, just update the list of surface facets.
There is some bookkeeping in this of course, and you will need to figure out the test to determine if an alpha ball can penetrate the shape through that facet. Without looking at any of my code, the test would seem to take two parts, first by looking at the radius of the in-circle that fits inside the triangular facet.
So, is there a way to do this? Yes, as I said, it is straightforward. You will need to write some code, since I won't provide the code I wrote myself (many years ago, before MATLAB even had a 2-d alpha shape. Geez, roughly 23 years ago, since I've been retired almost that long. Time flies.)
