Receptor site shape is described by a set of overlapping spheres of varied size (idea from UCSF Dock).
Spheres generated to be tangent to four receptor atoms and not to intersect other receptor atoms.
In two dimensions, a tangent circle should be generated for three circles:
In inversive geometry, this transforms into finding a line which is tangent to two circles (in 3D, a plane tangent to three spheres):
This is a simple problem of analytical geometry. So for each triplet of circles, a tangent circle can be generated analytically by this method:
However, for most triplets, the tangent circle will intersect other circles (in 3D, the tangent sphere will intersect with other receptor atoms). It turns out that in inversive space, the lines (planes) which are part of the convex hull correspond to tangent spheres which do not intersect with other parts of the receptor.