MovingWeightedLeastSquares.jl

Overview

MovingWeightedLeastSquares.jl is a package that provides an implementation of the moving weighted least squares method. A short description of this method by Andy Nealen can be found here.

Let $\theta(d): \mathbb{R}^+ \rightarrow \mathbb{R}^+$ be a weighting function of the method. Very often the there will be an $\varepsilon \in \mathbb{R}$, such that $\forall \delta > \varepsilon: \theta(\delta) = 0$. Whenever we use $\varepsilon$ or EPS in this document, we mean the cutoff distance for the weighting function. An example of a good weighting function is $\theta(d) = \exp(d^2 / a^2)$, where $a$ is the average distance between sample input data.

Point data type is an alias to Vector{T} where {T <: Real}.

Interaction with this package is done mostly via structure MwlsObject and its subclasses MwlsKdObject, MwlsCllObject and MwlsNaiveObject. This interface is similar to the interface of "interpolations objects" from Interpolations.jl.

The difference between the subclasses is the solution of the range search problem. MwlsKdObject solves the range search problem by using a k-d tree created by Kristoffer Carlsson, see NearestNeighbors.jl. MwlsCllObject solves the range search problem by using a cell linked list, which is implemented in this package. MwlsNaiveObject solves the range search problem naively.

TL;DR: use anything but MwlsNaiveObject.

Installation

At the moment this package can be installed by manually cloning the package

Pkg.clone("https://github.com/vutunganh/MovingWeightedLeastSquares.jl")

The package has been merged to Julia's METADATA, but I haven't tried installing it that way (using Pkg.add) yet.