This paper presents two self-similar models that allow the control of curves and surfaces. The first model is based on IFS (Iterated Function Systems) theory and the second on subdivision curve and surface theory. Both of these methods employ the detail concept as in the wavelet transform and allow the multiresolution control of objects with control points at any resolution level. In the first model, the detail is inserted independently of control points, requiring it to be rotated when applying deformations. On the contrary, the second method describes details relative to control points, allowing free control point deformations. Modelling examples of curves and surfaces are presented, showing manipulation facilities of the models.