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Interpolating and approximating implicit surfaces from polygon soup
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Registration of point cloud data from a geometric optimization perspective
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Natural neighbor coordinates of points on a surface
Computational Geometry: Theory and Applications
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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 ε-sampling, used in Delaunay reconstruction algorithms.