Study On The New Algorithms For Fairing B-Spline Curves

The fairness of curves and surfaces has been widely studied in the field of CAGD due to its great theoretical and practical value. Considering some problems existing in fairing methods of B-spline curves, three new fairing algorithms are given in this paper in different view.1) Considering that traditional wavelet-base algorithm is a global fairing method which can not smooth the curve locally, based on the property of wavelet's time-frequency localization a wavelet-based local fairing algorithm for B-spline curves is presented in this paper. Some related problems such as selection of "bad points", controlling of error and handling of boundary constraints are discussed. The curves smoothed by this method not only have good fairness but also have less change in global shape.2) Considering that the "bad" points are often selected interactively in knot-removed fairing method and the process is of low automation, an automatically fairing algorithm for B-spline curves based on Genetic Algorithm is given in the paper. Knot-removal method and energy minimization method are combined in this algorithm. The main idea is: the knots which be removed are determined automatically by GA such that the resulted curve possesses the least energy on condition that deviation is within given tolerance. This method is not only automatically and objectively, but also condenses the data at the same time.3) In the view of signal, fairing algorithm for B-spline curves based on image smoothing skill is given. Using the reference of template method in the image processing, three fairness templates such as average template, power template and Gaussian template are designed for the fairing of B-spline curves. By these templates, B-spline curves can be faired within the given tolerance. The essence in both this new method and the wavelet-base method are low-pass filter in which the control points of B-spline curves are viewed as "signal". But the flexibility and adaptability of the new method is better and the computing speed is faster than that of wavelet-base method.Again, aiming at selection of knots in fitting B-spline curves, a method for determining the knots of B-spline curves based on Genetic Algorithm is presented. It ensures the least number of control points within the given tolerance. This is also an important problem in CAGD.Examples show that the methods presented in this paper are feasible and effective.