A Generalization of cubic curves and their Bézier representations

In this paper, the relation between difference algorithms and the representation of parametric curves is studied in detail. It is shown that stationary difference algorithms could generate a class of curves, the so-called D-curves, that are suitable in free-form curve and surface modelling and design. The corresponding D-Bézier curves are also constructed and their properties studied. This generalizes our findings in the study of a simple three-term difference algorithm in which it has been concluded that a simple three-term difference algorithm could generate both conic curves, general monomial curves, and exponential spiral curves.