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  "body": "\n## Summary\n\nMoving least squares builds a smooth function from scattered data in $\\R^d$.\nAt each point $x$ it fits a low-degree polynomial to the data by [[weighted least squares|H5CGZHBR58]], with weights that favour data points close to $x$.\nThe value of the reconstruction at $x$ is the value of this local fit at $x$.\nAs $x$ moves, the weights and so the local polynomial change continuously, which gives a smooth global approximation.\nIt is a basic tool of [[multivariate interpolation|BM703GV34G]] and approximation, of surface reconstruction from point clouds and of meshfree methods for differential equations.\n\n## Explanations\n\n### L1 human\n\nTo estimate a value at a point, look at the data near that point.\nFit a simple model such as a plane by least squares, and read off the model at that point.\nDo this afresh at every point, always giving more weight to nearby data.\nBecause the weights change gradually from point to point, the estimates fit together into a smooth surface.\nIf the model is just a constant, the fit is a weighted average of the data, as in [[inverse distance weighting|QHN67MSH8S]].\nThe [[definition|9HWTPQHHZK]] gives the formula.\n",
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