Step length in forward differencing for curved surface display

Principles and basic algorithms for evaluating polynomial functions by Forward Differencing (FD) and Adaptive Forward Differencing (AFD) are presented. Both techniques are used nowadays in scanning/display algorithms for parameteric polynomial surfaces by generating and displaying a set of points. Constraints to be put on such a set of points are made explicit. One FD and two AFD surface-scanning/display algorithms presented in literature are evaluated in terms of these constraints. The FD algorithm is proved to be valid, but the AFD algorithms are shown to be incorrect. A valid AFD algorithm is presented.This research was partially done at the Faculty of Technical Mathematics and Informations of the Delft University of Technology, Delft, The Netherlands