Deforming a three-dimensional computer-generated model to cause a change of shape of the three-dimensional model includes representing a surface of the model using a surface representation initially comprised of an original surface definition, deriving smooth three-dimensional mapping functions where each mapping function defines a deformation to the surface and at least one mapping function is non-affine, constructing a composition of the mapping functions and the original surface definition where each mapping function is included in the composition in succession in accordance with the order of derivation, and applying the composition after each successive mapping function is included in the composition causing the surface of the three-dimensional model to be deformed while preserving the smoothness to the lowest degree of smoothness of the mapping functions.