1. A computer-implemented method for deforming a three-dimensional computer-generated model to cause a change of shape of the three-dimensional model, the method comprising: representing a surface of the three-dimensional model using a surface representation initially comprised of an original surface definition; deriving a plurality of smooth three-dimensional mapping functions, wherein each three-dimensional mapping function defines a deformation to the surface and at least one three-dimensional mapping function is non-affine; constructing a composition of the plurality of three-dimensional mapping functions and the original surface definition, wherein each three-dimensional mapping function is included in the composition in succession in accordance with an order in which the three-dimensional mapping functions were derived; and applying the composition after each successive three-dimensional mapping function is included in the composition causing the surface of the three-dimensional model to be deformed while preserving smoothness to a lowest degree of smoothness of the plurality of mapping functions.