Evaluation of NURBS surfaces: an overview based on runtime efficiency

Abstract

Dynamic tessellation of (trimmed) NURBS surfaces is an important topic for interactive rendering of complex models. Independently of the decomposition method used to approximate surfaces by polygons, an evaluation of the surface at many parametric pairs is required to generate meshes vertices. In this paper we give an overview of the most important evaluation algorithms and compare them regarding their runtime efficiency.

Three different representations and five algorithms for the evaluation of NURBS surfaces are compared: direct evaluation of NURBS surfaces, evaluation of their Bezier patches and evaluation of them in power basis representation. We add to the comparison two algorithms, based on the approximated computation of normal vectors. The deviation among the exact and the approximated normal vectors is measured. The obtained results are checked with partial comparisons that appear in the bibliography.