基于一元对称幂基的等距曲面有理逼近算法

给出了基于一元对称幂基的等距曲面蒙面逼近新算法。利用一元对称幂基逼近张量积Bézier曲面u向曲线的等距曲线，得到一组等距逼近曲线，取固定的v值，得到一组数据点，用反算控制顶点的方法得到过这组数据点的v向曲线。对这两组曲线用蒙面算法得到逼近的有理等距曲面。该算法计算简单，将二元等距曲面有理逼近转化为一元曲线有理逼近，同时方便地解决了整体误差问题，随着对称幂基阶数的升高，可以得到较理想的逼近效果。

Rational Approximation of Offset Surface by Univariate S-Power Basis

A new algorithm for approximating offset surfaces by using univariate symmetric power basis is presented. It uses symmetric power basis to approximate u directional curves of tensor product Bézier surface, then it gets a set of offset approximating curves. From fixed v value of these curves, it will get a set of data points. The paper gets v directional approximating curves which get through these data points by anti algorithm of control points. Finally, rational approximating offset surface is got by using skinning surface algorithm. The algorithm is easy and solves the integral tolerance. Numerical examples show that it can achieve good effect with the raise of the S-power basis’ degree.