Defining and computing accessibility radius

In structural molecular biology software, the accessibility of an atom in a molecule to a ball representing solvent is either computed slowly by building a solventaccessible surface, or estimated quickly by counting neighboring atoms within some radius. We believe that techniques from computational geometry, notably retraction motion planning in Voronoi diagrams, can give a more direct measure that is faster than surface computation. We propose an O(n log n) time algorithm for computing the accessibility radii for sets of points in R, and extend this algorithm to sets of circles in R and sets of spheres in R. We provide results in R that approximates accessibility radii from the power diagram.