Exact analytical models represent a viable alternative for applications requiring geometric constructs with a level of surface perfection unachievable with traditional polynomial techniques. To avoid the limitations in shape complexity normally associated with traditional analytic models, a model based upon a topological transformation of a lofted surface was developed. The consequence is, if not an equation of all shapes, then, at least, an equation describing a great many arbitrarily complicated shapes. A full theoretical development of the model is presented along with a model-implementing FORTRAN source module and some example geometries. Keywords Computer graphics Lofted surface Superquadric Analytic surface model, Surface modelling Topological transformation.