Theory Of Curve And Surface Fairing

The requirements of product抯 form especial fairness are expected in the computer-aided design of aircraft, automobile, watercraft and household appliances, etc. Therefore, the problem of fairing curve and surface becomes very important in CAD/CAM. In this paper, the theories and methods of fairing curve and surface are elaborately studied in the cooperation with GE company about fairness of curve and surface. It is aimed for the reduction of the swing caused by digitized data. ~ The method of knot removal and degree reduction is applied when dealing with curves in order to minimize the data. One method is presented when removing the knots. ~ Both the removal & reinsertion of knot and the elevation & reduction of degree are used to uniform a group of curves?parameters. ~ As we all know that C2 is required in the fairness of curve. According to the properties of B-spline, the knot removal is adopted to keep curve C2. )~ Combining with reality of engineering, the rule 揊airness of curve or surface should meet the requirement of manufacture 揳re presented after the deeper research of the rule of fairness. This rule will make the quantificational description one of the standard of fairness which provide the basis for the quantification of fairness. > Energy method and LSM are used in the fairness of curves which can be extended to the NURBS. > Piecewise energy method is adopted in the fairness of surfaces in order to minimize the data of energy method. The method in this paper can well meet the requirements of the project. The fairness is satisfactory by the even fluctuation of curvature and the small strain energy.