张量积等距曲面的样条逼近  

The Spline Approximation of Tensor Product Offset Surface

作　　者：陈雪娟[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005

出　　处：《厦门大学学报（自然科学版）》2007年第6期770-773,共4页Journal of Xiamen University：Natural Science

基　　金：国家自然科学基金(10571145);厦门大学985项目;集美大学科研基金(C506123)资助

摘　　要：在几何造型系统中,通常需要用低次有理参数曲线、曲面来逼近等距曲线、曲面.这篇文章主要研究张量积等距曲面的样条逼近.利用样条曲面和原曲面加权组合构造一个新的有理曲面,该曲面通过插值原曲面的等距曲面上的采样点,从而逼近等距曲面.此方法较为简单,逼近曲面的次数不会超过原曲面,逼近曲面能达到C2连续.由插值点决定控制点的个数和逼近所能达到的误差精度,而且可以通过调节权值使等距曲面达到最佳逼近.In the system of geometric modeling, we generally use rational parametric curves and surfaces with low degree to approximate offset curves and surfaces. In this paper, we consider the spline approximation of tensor product offset surfaces. The spline surface and the original surface are combined to generate a new rational surface by adding the weights. This approximating offset surface interpolates some sample nodes on the offset surface. The degree of the approximating surface can＇t exceed the original surface, and it is C^2-continue. The number of control points and approximation error depend on the choosing of interpolatory points,and we can get the best approximation by adjusting the weights.

关 键 词：等距曲面 样条曲面 逼近 误差 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] O241.5[自动化与计算机技术—计算机科学与技术]