A New Kind Of Fairing Method For Parametric Cubic B-Spline Curves

Many results in fairing researches about curves and surfaces have been achieved in both theory and applications. Now, the methods are increasingly mature.As we know, any algorithm has its advantage and disadvantage. If two or more algorithms are combined to deal with the fairing of parametric cubic B-Spline curves, better fairing effect will be achieved,which is the main job of this thesis.The main idea is to use new fairing method integrating the merits of the method of selecting points and energy method and taking into account of curve's relative curvature, so that the two methods are able to foster strengths and circumvent weaknesses. The objective function not only reflects the curve's strain energy, but also reflects whether the curvature's change is uniform, thus making the fairing effectiveness of parametric cubic B-Spline curve better.The method of this thesis can not only modify the controlling points at a time that only have influences on bad points, but also make the curve's curvature vary relatively evenly and the curve have smaller strain energy. The experiments show that the method has quite good fairing effects on the curve.