Provably good moving least squares

Ravikrishna Kolluri
2008 ACM Transactions on Algorithms  
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 -sampling, used in Delaunay reconstruction algorithms.
doi:10.1145/1361192.1361195 fatcat:hmu6e3wi5bhsnbmquvycotkh2m