Abstract: Methods for the transformation of shapes in Computer Aided Design (CAD) applications applying a general function composition mechanism. This method allows the geometry of a shape expressed in terms of surface and curve functions and positions to be transformed by any generic function while maintaining the topography of the shape. Once the underlying geometry of the shape has been represented as a set of functions and positions, the functions and positions are composed with a transformation function to define new surface and curve functions. Once the new functions and positions have been created, the geometry of the transformed shape can be found by passing each point in the domain of each original geometry function through the new transformed function. This shape may then be displayed to the user, and the steps of this method repeated for refinement of the transformation function.