Provably good moving least squares

We analyze a moving least squares algorithm for reconstructing a surface from point cloud data. Our algorithm defines an implicit function I whose zero set U is the reconstructed surface. We prove that I is a good approximation to the signed distance function of the sampled surface F and that U is geometrically close to and homeomorphic to F. Our proof requires sampling conditions similar to e-sampling, used in Delaunay reconstruction algorithms.

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