Standardization of Rational Bézier Surfaces

The sufficient and necessary condition for the existence of linear Möbius transformations that can standardize the rational Bézier surfaces is given based on Möbius reparameterization theorem.To obtain the standard form of an arbitrary cubic rational Bézier surface,we then present a quadratic reparameterization algorithm to reparameterize the surface so that all the corner weights of the surface are equal to one. Examples are included to show the performance of the new method.