In this paper, we present two closely related techniques, radius mapping, and direct function modification, that allow for the alteration of both the major geometry and surface features of implicit solids. The first technique, radius mapping, is applied to implicit functions generated by swept solid techniques. A more generalized technique, direct function modification, allows for the mapping of generalized function modifiers onto any implicit solid. Both the radius functions and the function modifiers can be either algebraic or non-algebraic in nature. Techniques for generating both algebraic and non-algebraic radius functions and function modifiers are given along with several examples of their use on both swept solids and implicit functions.