Visual continuity of piecewise parametric curves denotes the smoothness of the curve in terms of matching Taylor expansions (up to a certain order) of the component functions, at the knot points. Thus curves are called VCr continuous if the Taylor expansions up to terms of order r match. This allows more freedom than requiring parametric continuity of the components. Using the Bézier representation of the polygonal segments, Lasser give a representation for quartic and quintic curves that allows the specification of two design parameters per knot for quartics, and three for quintics. Provided certain inequalities are satisfied, the curves have the usual properties, such as variation diminishing and convex hull properties.

Designers of CAD software may find these representations useful, since they will allow additional freedom in terms of parameters to be specified by the user. Some examples show how varying the parameters affects the curve. The paper will also be useful to those interested in more general ideas of continuity than are represented by parametric continuity.