双三次曲面的等距面的光顺逼近

本文提出了一种用双三次参数曲面逼近双三次Bezier曲面的等距面的方法.通过对曲面片角点处扭矢量的调整,得到最佳平方逼近的光顺的等距面.

Faired Spline Approximation of Offset Surface of Bicubic Surface

In 1991 Ravani1] gave only an algorithm for obtaining offset surfaces of developable surface. In this paper, the authors present the algorithm for obtaining offset surfaces of bicubic surface which is one type of non-developable surface that is frequently employed in CAGD. Contrary to the engineering practice of considering approximation and fairing one at a time, the authors deal simultaneously with approximation and fairing to obtain offset surfaces of bicubic surface. through adjusting twist vectors at the patch corners, the interior shapes of the patches can be modified without altering the interpolating points of surface, thus improving fairness of surface is facilitated. Through optimizative computation the optimum Beier control network of offset surfaces are obtained, and then faired offset surfaces of bicubic surfaces are obtained. The offset surfaces designed by the authors possess Gaussian curvatures and mean curvatures that vary very slowly along two sets of orthogonal parametric curves, furthermore offset surfaces are G~1 continuous. In solving nonlinear equations, the least squares method and Quasi-Newton's method are used.