Questions of chemical reactivity can often be cast as questions of mol
ecular geometry. Common geometric models for proteins and other molecu
les are the space-filling diagram, the solvent accessible surface and
the molecular surface. In this paper we present a new approach to tria
ngulating the surface of a molecule under the three models, which is f
ast, robust, and results in topologically correct triangulations. Our
computations are based on a simplicial complex dual to the molecule mo
dels. All proposed algorithms are parallelizable.