The Fairing Of Curves And Surfaces In Parameters

In CAGD, we often get some bad data-points which yield some errors compared with the true datapoints since the data-getting process is constrained by the level of technology or some other factors. These bad data-points sometimes generate some kinds of oscillations or some unwanted inflexions in the interpolated curves or surfaces, so we must do something to make them fairing. Normally, the fairing methods just move the data-point to one new located position by some equations. The new position is very likely beyond the limit of the data error, though it can make the curves or surfaces fairing in bad data-points.In this dissertation, the two very important curves in CAGD-the Bezier curves and the B-spline curves are first discussed in fairing with controlling parameters. The basic idea is to introduce the parameters based on the fairing of curves, which serve as controlling the distance between the bad data-point and its new position, i.e., the fairing of curves is carried out within the limit of the data error. Then we introduce the fairing of B-spline surfaces with controlling parameters based on the fairing of the B-spline curves. This dissertation contains four chapters. In the first two chapters, some basic properties and relevant calculation methods of Bezier curves, B-spline curves and surfaces are introduced. A method of fairing of Bezier curves with controlling parameters is presented in the third chapter which is illustrated with examples. Some novel methods of fairing of B-spline curves and surfaces with controlling parameters are worked out in the fourth chapter.