Alpha shape

If α = 0, then the alpha-shape associated with the finite point set is its ordinary convex hull.

The α-complex is also a subcomplex of the Čech complex, but computationally more efficient if the ambient space has dimension 2 or 3.

(In this later work, Edelsbrunner used the name "α-shape" to refer to the union of the cells in the α-complex, and instead called the related curvilinear shape an α-body.)

This technique can be employed to reconstruct a Fermi surface from the electronic Bloch spectral function evaluated at the Fermi level, as obtained from the Green's function in a generalised ab-initio study of the problem.

The Fermi surface is then defined as the set of reciprocal space points within the first Brillouin zone, where the signal is highest.