基于（p，q）-整数的Bernstein型多项式的de Casteljau算法
A de Casteljau Algorithm for Bernstein type Polynomials based on (p,q)-integers
摘要：
本文提出了一种基于（p，q）-整数的（p，q）-Bernstein Bezier曲线的de Casteljau算法。研究了（p，q）-Bezier Bernstein函数升阶和降阶的性质.新曲线具有类似于q-Bezier曲线的一些性质。此外，我们还构造了矩形域（u，v）\in [0，1] \times [0，1]上的张量积曲面.我们还研究了de Casteljau算法和度评价性质的表面，这些推广在矩形域。进一步讨论了（p，q）-Bernstein Bezier曲线的一些基本性质.当参数p1 = p2 = 1时，我们得到了（u，v）\in [0，1] \times [0，1]的q-Bezier曲线和曲面。
英文摘要：
In this paper, a de Casteljau algorithm to compute (p,q)-Bernstein Bezier curves based on (p,q)-integers is introduced. We study the nature of degree elevation and degree reduction for (p,q)-Bezier Bernstein functions. The new curves have some properties similar to q-Bezier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u, v) \in [0, 1] \times [0, 1] depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. Furthermore, some fundamental properties for (p,q)-Bernstein Bezier curves are discussed. We get q-Bezier curves and surfaces for (u, v) \in [0, 1] \times [0, 1] when we set the parameter p1 = p2 = 1.
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