Of Nurbs In The Study Of Certain Issues

From the eights, the method of Non Uniform Rational B-spline(NURBS) has become the most popular in design of curves and surfaces. It is used widely in CAD/CG and has become the standard of industry. Because of the advantages of NURBS curves and surfaces, it is important to research into NURBS.In this paper, the main work is about the modification of NURBS curves and surfaces. NURBS is one of the most popular method for designing complex curves and surfaces. After creating NURBS curves/surfaces, we often need to modify them to satisfy the user' s design requirements. By definition of NURBS curves/surfaces, there are three ways to. modify the shape: i) by changing knots vector; ii) by moving control points; iii) by changing the weights.This paper presents a unified approach that modifies the shape of NURBS surfaces by altering the weights and the location of the control points simultaneously. A homogeneous coordinate representation is introduced in this method. An algebraic procedure for modifying the shape of NURBS surface is presented, which can overcome shortcoming of geometry way. It is not only used for modification of one point on the surface, but also used for modifying one point of the surface by moving several control points. Furthermore it is used for the condition of modifying several points of surface.This paper is organized as follows: there is a briefing of the development of NURBS shape modification in the first chapter; the second introduces the fundamental knowledge of NURBS curves/surfaces; At presents, some people investigates shape modification of NURBS curves/surfaces based the method of fairing B-spline curves/surfaces, so the methods that fairs B-spline curves/surfaces are introduced in the third chapter; The forth presents several approaches of modifying NURBS curves. The method of modifying NURBS surfaces is presented in the last chapter.