NURBS surface generation by control points

Abstract

A method on how to generate traditional quadrilateral NURBS surfaces, non-quadrilateral NURBS surfaces, such as triangle NURBS (Non-uniform Rational B-spline) surfaces and pentagon NURBS surfaces and their equidistant surfaces is presented. A NURBS surface is a bi-parameter surface, and the surface can be generated in accordance with its parameters. With the method given by this paper, if a series of values of the two parameters can be obtained in sequence, Surface Points and the Equidistant Surfaces Points based on these values of the two parameters can be obtained. These points can comprise a NURBS surface and its equidistant surface. Traditionally a NURBS surface is a quadrilateral surface. It is difficult to obtain a non-quadrilateral NURBS surface. A strategy is to generate non-quadrilateral surfaces by adjusting the NURBS surfaces' control points. The results show that the NURBS surface generation method is effective and the strategy to generate non-quadrilateral surfaces by adjusting the control points is feasible in some areas. What discussed in the paper can be used at computer graphics and numerical control areas.