The generation of curves and surfaces from given data is a well-known problem in Computer-Aided Design that can be approached using subdivision schemes. They are powerful tools that allow obtaining new data from the initial one by means of simple calculations. However, in some applications, the collected data are given with noise and most of schemes are not adequate to process them. In this paper, we present some new families of binary univariate linear subdivision schemes using weighted local polynomial regression. We study their properties, such as convergence, monotonicity, polynomial reproduction and approximation and denoising capabilities. For the convergence study, we develop some new theoretical results. Finally, some examples are presented to confirm the proven properties.

翻译：从给定数据生成曲线和曲面是计算机辅助设计中一个广为人知的问题，可通过细分格式加以解决。这类格式作为强大工具，能通过简单计算从初始数据中获取新数据。然而，在部分应用中，采集到的数据含有噪声，而大多数细分格式并不适用于处理此类数据。本文提出若干基于加权局部多项式回归的二元单变量线性细分格式新族系，研究其收敛性、单调性、多项式复现能力、逼近性能及去噪特性等性质。针对收敛性研究，我们开发了若干新的理论成果。最后通过示例验证了所证性质。