Decomposition and Construction of Molecular Skin Surfaces

Abstract

The skin surface is defined for a set of spheres as the boundary of their shrunken convex hull. It is a continuously smooth surface that can be decomposed as a set of quadratic patches. Each patch is a part of a sphere or hyperboloid inscribed in a polyhedron called the mixed cell. Starting from a finite set of spheres, representing the atoms of a molecule, the molecular skin surface can be constructed. There are various efficient algorithms to mesh the skin surface and discuss the mesh quality. However, little is known about the implementation of the skin surface decomposition which is the objective of this paper. First we describe a discrete framework and present algorithms constructing the shrunken convex hull. Secondly, we construct the skin as a collection of quadratic patches. The first step is to apply 3D-Delaunay algorithm to the centers of spheres. Then, for each Delaunay simplex, weighted Voronoi vertices are computed, the mixed cell is constructed and the coefficients of the quadratic equation of the patch are computed. Several illustrative examples are included.