The problem addressed in this paper consists in triangulating the van der Waals surface without computing the geometric intersections of its atoms. Recall that the van der Waals surface is useful in computational molecular biology and biochemistry to, for example, determine the volume occupied by a molecule, as well as other important geometric properties. Assuming that every atom is represented by a ball, this amounts to compute the surface of the union of a number of balls. The novelty of our method lies in avoiding the computation of surface-surface intersections (SSI) of two or more balls.