Moving least squares

Summary

Moving least squares builds a smooth function from scattered data in $\R^d$. At each point $x$ it fits a low-degree polynomial to the data by weighted least squares, with weights that favour data points close to $x$. The value of the reconstruction at $x$ is the value of this local fit at $x$. As $x$ moves, the weights and so the local polynomial change continuously, which gives a smooth global approximation. It is a basic tool of multivariate interpolation and approximation, of surface reconstruction from point clouds and of meshfree methods for differential equations.