  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.

Numerical Analysis;Numerical Analysis