Study On The Fairing Algorithms For Curves And Surfaces And Their Computer Implementation

Fairing, one of the most important branches in Computer Aided Geometry Design, has attracted worldwide attention. Owing to the effects of system error and random error happened in the measuring process, the data obtained is far from being accurate. Applying the data without further treatment would inevitably result in the loss in the shape of the design, ripple, ruffle and indention. Therefore, a demand of fairing in the process of measuring data becomes necessary. And the revisable control points are also vital in assuring that no big warp happened in the original control points required by the designing officials. The process of fairing and the artistic design of curves and surfaces played an important role in design. This article focuses on fairing. The following is the discussion of the main procedure. The first part reviews the concepts and criteria of fairing, and discusses the theoretical development of CAGD fairing method and its application . The second part focuses on the discussion of the improved offset achieved with the method that applied to fairing the NURBS. The application of the method meets the needs of processing models, and deduces the math formula of unit normal vector of the NURBS, which significantly decreases the amounts of calculation. The third step talks about the preliminary study on the modification of the new C-Bézier curves. Fairing C-Bézier curves are satisfied by adjusting the shape of the parameterα on the basis of applying energy. Next no fairness appears in joining C-Bézier curves.The energy-method is used by adjusting the shape of the control points or the parameter λk and α kagain. This method satisfies with deviser. The fourth step is about the analysis of the disadvantage of the current finite element. Based on the demands of the curves and surfaces, the fairing criteria of finite element and the optimal models achieved on the criteria are offered. The geometric meanings of fairing are given for this model. The physical meanings of fairing are also discussed in this part. Furthermore, in order to obtain the optimal effects a new optimal calculation of genetic algorithm is proposed.