Freeform synthesized by means of perturbation functions are considered. A special feature of the free forms based on the scalar perturbation functions and the method of their visualization is that the time of geometrical processing and the amount of data required for visualization the surface do not depend on its geometry. The free forms based on the analytical perturbation functions have an advantage of spline representation of surfaces, that is, a high degree of smoothness, and an advantage of arbitrary form for a small number of perturbation functions.