Overview of the algorithm. The solid body and circles indicate an all-atom and Cá atom representation, respectively. Open circles are virtual atoms determined by the algorithm. (1) Step 1: the protein structure is represented as Cá atoms. (2) Step 2: Cá atoms are Delaunay tessellated. The convex hull is determined at the same time. (3) Step 3: the environmental boundary (red solid lines) is determined from the Delaunay tessellation by peeling off the tetrahedra (triangles labeled as a, b, and c) with edge lengths larger than 30.0 Å (black dashed lines) starting from the convex hull. (4) Step 4: the protein boundary (blue and purple solid lines). The purple lines are overlapped with the environmental boundary and determined from the Delaunay tessellation by removing tetrahedra with circumscribed sphere radius larger than 7.5 Å. (5) Step 5–7: shape descriptors such as residue surface direction and geometric potential for each Cá atom position are computed and ligand binding sites and virtual atoms (open circle) are predicted.