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A computer algorithm is presented for calculating the part of the van der Waals surface of molecule that is accessible to solvent. The solvent molecule is modeled by a sphere. This sphere is, in effect, rolled over the molecule to generate a smooth outer-surface contour. This surface contour is made up of pieces of spheres and tori that join at circular arcs. The spheres, tori and arcs are defined by analytical expressions in terms of the atomic coordinates, van der Waals radii and the probe radius. The area of each surface piece may be calculated analytically and the surface may be displayed on either vector or raster computer-graphics systems. These methods are useful for studying the structure and interactions of proteins and nucleic acids.
Michael L. Connolly (1983) studied this question.