The representation and characterization of molecular surfaces are important in many areas of molecular modeling. Parametric representations of protein molecular surfaces are a compact way to describe a surface, and are useful for the evaluation of surface properties such as the normal vector, principal curvatures, and principal curvature directions. Simplified representations of molecular surfaces are useful for efficient rendering and for the display of large-scale surface features. Several techniques for representing surfaces by expansions of spherical harmonic functions have been reported, but these techniques require that the radius function is single valued, that is, each ray from an origin inside the surface intersects the surface at one and only one point. A new technique is described that removes this limitation and can be used to compute surface shape properties.