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

Key words: Bezier(curve)surface, Hermite-Bezier scheme, Kirov theorem, surface-fitting, computer aided geometric design

摘要： 基于Kirov定理，研究带有附加导数条件的Bezier曲（线）面。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 曲面拟合相比，有更多的自由度，但其拟合曲面的次数仅比Bezier 曲面高一次。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面形状的目的。

关键词: Hermite-Bezier方法, Kirov定理, Bezier曲（线）面, 曲面拟合, 计算机辅助几何设计