Symmetry—A Research Direction in Curve and Surface Modelling; Some Results and Applications

Many parametric curve and surface methods, including polynomial and spline, require sets of `parameter’ functions to be specified in addition to control-, or interpolation-point sets. It is shown here that symmetry is a powerful tool for the analysis of this class of curve function and can, for example, be applied to provide complete answers to fundamental questions such as: (i) if the control point set is held fixed, under what conditions do different sets of parameter functions determine the same curve?