Research of whole fairing and approximation algorithm of NURBS curve

Abstract

With regard to the accuracy and smoothness of a set of discrete data points approximation, this paper gave a whole fairing and approximation algorithm of cubic Non-Uniform Rational B-Spline (NURBS) curve. The algorithm constructed an objective function composed of least square, sum of curvatures on discrete points and sum of curvature varieties on discrete points, obtained a series of the best control points, adjusted weights using nonlinear optimization method, set up an approximation approach to verify the fitting errors and constructed a calculation procedure. At last, this paper displayed and analyzed the obtained curve in UG NX 4.0.