Design of NURBS Surface with a B-Spline Line of Curvature

In order to satisfy the requirements of design for the products, an algorithm of design NURBS surfaces is proposed on constructing surfaces interpolating a line of curvature. Firstly, utilizing the mathematical expres- sion of isoparametric surface pencil with a given common line of curvature, as well as the formulae of both the derivatives and the products of B-splines, we provide an explicit expression of isoparametric surface pencil with a non-uniform B-spline common curve of curvature. Furthermore, the necessary condition to express the interpo- lating surface as NURBS form exactly is introduced, and two styles of the expression are given. Then, an exact NURBS expression of surface pencil with a given non-uniform B-spline plane curve of curvature and a formula for calculating the control points of the surface are derived. Finally, the effect of surface design is shown in the experimental results, which demonstrate the effectiveness of the proposed algorithm.