Comparison of Surface and Derivative Evaluation Methods for the Rendering of NURB Surfaces

Abstract

Three methods for evaluating the surface coordinates, first derivatives, and normal vectors of a NURB surface are compared. These methods include forward differencing, knot insertion, and a two-stage Cox-de Boor technique. The computational complexity of each of these techniques is analyzed and summarized. The use of Hermite functions is shown to yield a poor approximation for the shading functions of a NURB surface. An improved method for computing derivatives by knot insertion is presented. An efficient algorithm for computing the forward difference matrix and a method for using forward differencing to compute the first derivatives of a NURB surface are also presented.