page_title: Alpha shape
section_title: Examples
hierarchical_section_title: Alpha shape / Examples
caption_attribution_description: English: Fermi surface of bulk silver: alpha-shape reconstruction from the electronic Bloch spectral function in the Korringa, Kohn and Rostoker multiple scattering framework for first-principles electronic structure calculations.
context_page_description: In computational geometry, an alpha shape, or α-shape, is a family of piecewise linear simple curves in the Euclidean plane associated with the shape of a finite set of points. They were first defined by Edelsbrunner, Kirkpatrick & Seidel. The alpha-shape associated with a set of points is a generalization of the concept of the convex hull, i.e. every convex hull is an alpha-shape but not every alpha shape is a convex hull.
context_section_description: 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 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. 
  The definition has the advantage of covering also cases of various forms of disorder.
caption: Fermi surface of bulk silver: alpha-shape reconstruction from KKR Bloch spectral function reconstruction
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