关于曲线拟合的广义Bezier方法

On the Generalized Bezier Scheme for Curve-Fitting

基于Kirov逼近定理,研究了一类带有附加导数条件的广义Bezier曲线拟合方法。该方法可以在每个型值点再给出导数条件,因此与通常的Bezier曲线拟合相比,有更多的自由度,但其拟合曲线的次数仅比Bezier曲线高一次。这一方法有助于CAGD领域的工程人员采用Bezier技术达到控制所设计曲线形状的目的。

A class of Generalized Bezier fitting curve with condition of tangent vectors is studied in this paper.The method is based on the Kirov approximation theorem.Using this method,it can specify the tangent vectors at every control point in advance.So,it can adjust the shape of fitting curve(Generalized Bezier curve)more freely according to the given tangent vectors.However,the degree of Generalized Bezier curve increases only one.It is helpful for the engineer who wants to control shape of curve by using Bezier scheme in CAGD.