Constructing computer aided design models from procedurally defined curve and surface lofts

The advantageous embodiments provide a computer implemented method, apparatus, and computer program product for constructing a computer aided design model. User input is received that contains a callback function and a required accuracy. The callback function prescribes a procedurally defined geometry and the required accuracy specifies the degree of accuracy needed for the computer aided design model. The callback function is sampled at a number of points to form sampled points and a candidate curve is constructed that approaches the sampled points. A determination is made as to whether the candidate curve meets the required accuracy.