GEOMETRIC CONTINUITY WITH INTERPOLATING BEZIER CURVES.

Abstract

The Bezier formulation for parametric curves has many qualities, among them the intuitive relationship between the shape of the control polygon and the shape of the curve, and the case of computation and subdivision. Other formulations, however, have become more popular because they offer local control, or because they are interpolating, or even more recently because they provide the added flexibility of shape parameters. We present here techniques to use the Bezier formulation to interpolate the two-dimensional points given by a user with cubic piecewise Bezier curves, while maintaining up to G**(**2**) continuity, and to interactively manipulate the bias and tension of each span, with geometric entities clearly related to the curve, while preserving the degree of geometric continuity prescribed by the user.