Variational design of smooth rational Bézier curves (Q1183532)

A fundamental idea of the rational Bézier and \(B\)-spline algorithms is to evaluate and manipulate the curves and surfaces by a small number of control points and weights. The authors describe an algorithm for determining the weights of a rational Bézier curve in a way as to achieve a smooth curve in the sense of an energy integral. Some examples of rational cubic curves are presented to illustrate the concept.