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- B e ́ zier 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.