Basis Functions for Rational Continuity

The parametric or geometric continuity of a rational polynomial curve has often been obtained by requiring the homogeneous polynomial curve associated with the rational curve to possess parametric or geometric continuity, respectively. Recently this approach has been shown overly restrictive. We make use of the necessary and su cient conditions of rational parametric continuity for de ning basis functions for the homogeneous representation of a rational curve. These functions are represented in terms of shape parameters of rational continuity, which are introduced due to these exact conditions. The shape parameters may be varied globally, a ecting the entire curve, or modi ed locally thereby a ecting only a few segments. Moreover, the local parameters can be represented as continuous or discrete functions. Based on these properties, we introduce three classes of basis functions which can be used for the homogeneous representation of rational parametric curves.