This paper proposes two novel families of non-stationary subdivision schemes with a shape parameter of hierarchically and efficiently generating mixed hyperbolic/trigonometric curves of order 3 and 4. An analysis of convergence and smoothness of the proposed schemes is established by using the asymptotic equivalence method. This paper also discusses the bivariate tensor-product subdivision scheme for the surface modeling on the regular meshes. The numerical results they produce are very encouraging. In this context, the performance of our algorithms has been exposed by considering examples, which illustrate how the shape parameter and the control points are assigned to reproduce such analytic curves and surfaces using tensor-product notion.

本文提出了两个新颖的非平稳细分方案系列，它们的形状参数可以分层并有效地生成阶数为3和4的混合双曲/三角曲线。 。本文还讨论了用于正则网格上的曲面建模的二元张量积乘积细分方案。他们产生的数值结果非常令人鼓舞。在这种情况下，我们通过考虑示例来展示我们算法的性能，这些示例说明了如何使用张量积概念指定形状参数和控制点以重现此类分析曲线和曲面。