An analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented. In particular, theorems are proved concerning the smoothness of interpolants and the description of m.l.s. processes as projection methods. Some properties of compositions of the m.l.s. projector, with projectors associated with finiteelement schemes, are also considered. The analys...

The radial basis function interpolant is known to be the best approximation to a set of scattered data when the error is measured in the native space norm. The approximate moving least squares method, on the other hand, was recently proposed as an efficient approximation method that avoids the solution of the system of linear equations associated with the radial basis function interpolant. In t...

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Image morphing has received much attention in recent years. It has proven to be a powerful tool for visual effects in film and television, depicting the fluid transformation of one digital image into another. In this paper, we present a novel approach for image morphing based on moving least squares. A sketching interface is proposed for quickly and easily specifying the feature correspondences...

We describe two experiments recently conducted with the approximate moving least squares (MLS) approximation method. On the one hand, the NFFT library of Kunis, Potts, and Steidl is coupled with the approximate MLS method to obtain a fast and accurate multivariate approximation method. The second experiment uses approximate MLS approximation in combination with a multilevel approximation algori...

We describe a new method for surface reconstruction based on unorganized point clouds without normals. We also present a new algorithm for refining the inital triangulation. The output of the method is a refined triangular mesh with points on the moving least squares surface of the original point cloud.