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Provably good moving least squaresIn SODA '05: Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms (2005), pp. 1008-1017.
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Notes for this articleThis paper describes a variation of Moving Least Square. The require global $\epsilon$ sampling (lower bounded by the smallest local feature size).
They show that, for a point $x$, the sign of the signed distance is correct, if $x$ is not very close to the surface. This is quite interesting.
Also, because they do not allow point arbitrary close to the surface, the implicit function can be reduced to use LOCAL neighbors instead of the entire point set. Which is helpful in time-complexity.
Though I am not sure whether the global $\epsilon$ sampling can be replaced by normal $\epsilon$ sampling, or $(\epsilon,\delta)$ sampling.
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