De Casteljau algorithm and degree elevation of Bézier and NURBS curves/surfaces are two important techniques in computer aided geometric design. This paper presents the de Casteljau algorithm and degree elevation of toric surface patches, which include tensor product and triangular rational Bézier surfaces as special cases. Some representative examples of toric surface patches with common shapes are illustrated to verify these two algorithms. Moreover, the authors also apply the degree elevation of toric surface patches to isogeometric analysis. And two more examples show the effectiveness of proposed method.

中文翻译：

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De Casteljau算法和复曲面曲面贴片的度高

De Casteljau算法以及Bézier和NURBS曲线/曲面的度高是计算机辅助几何设计中的两项重要技术。本文介绍了de Casteljau算法和复曲面曲面片的度高，其中包括张量积和三角有理Bézier曲面作为特例。说明了具有共同形状的复曲面表面贴片的一些代表性示例，以验证这两种算法。此外，作者还将复曲面表面贴片的度高应用于等几何分析。另外两个例子说明了该方法的有效性。