Rational Bezier patch differentiation using the rational forward difference operator

This paper introduces the rational forward difference operator for differential computation on a rational Bezier patch based on its control mesh. With this rational version of the forward difference operator, and by ignoring the appropriate dependent (on lower order derivatives) terms of various derivatives, the derivatives themselves have the same expressions as their polynomial counterparts; the curvature and torsion, and the first and second fundamental forms, all have very similar expressions as those equations from classical differential geometry. This new approach also allows straightforward generalization to higher dimensional rational Bezier patches, the special co-dimension 1 case of which is treated with the result of the first and second fundamental forms.