B-spline curve smoothing through the node adjustment and basing on weight factor

In CAD system, parametric curves and surfaces are usually applied to interpolate, approximate and fit the giving data. Nevertheless, As error exists while measuring and calculating data, it is necessary to do fairing operations on the curves and surfaces obtained by these data, thus to get the aesthetic curves and surfaces. Fairing curves and surfaces is becoming one of the most important problems in the research of computer-aided design. B-spline curves or surfaces are commonly-used tools for shape design and data fitting. The problem of how to fair cubic planar B-spline curves is discussed in this paper. The shape of a B-spline curve is determined by its control polygon, therefore one can get the fair curve by vibrating its control points. In this thesis, the choice of site modification method is presented. First, find out the light is not in conformity with the rules of point type, each time a value point to modify. And then for each control vertex disturbance amplitude choose specific weight. Last, disturbance of the constrained control vertices on the basis of limited shape to the purpose of the light.