ABSTRACT
To meet the needs of some practical applications, we first present, in this paper, a general definition of the recurrent curves and thereby create two sorts of recurrent curve, L-curve and W-curve. The main results obtained here are derivation formulae, envelope theorem, basis properties of the L-curve and convexity theorem of the W-curve. By revealing a simple duality relationship between the L-curve, W-curve and their characteristic vertices, we obtain an equivalent representation which allows us to consider L,W-curves as Bezier curves. Finally we give the recursive representations of several common curves.
