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

William L. Luken, Fuhua Cheng

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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.

Original languageEnglish
Pages (from-to)153-178
Number of pages26
JournalACM Transactions on Graphics
Issue number2
StatePublished - Apr 1996


  • 1.3.3 [Computer Graphics]: Picture/Image Generation - display algorithms
  • 1.3.4 [Computer Graphics]: Graphics Utilities - software support

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design


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