Illustration of the alpha shape theory and discrete-flow method used in CAST. A: Two-dimensional depiction of pocket atoms represented as disks of uniform radii. The blue lines show the Voronoi diagram for the pocket atoms. B: The seven bordering lines running through the atom centers represent the convex hull, which is triangulated into Delaunay triangles using information of the Voronoi diagram. The "alpha shape" or "dual complex" is defined by the shaded triangles and the black lines. Three "empty triangles" having at least one grey bordering line are shown. C: Two obtuse empty triangles (1, 3) are assigned to the obtuse triangle (2) by the discrete-flow method.