We introduce moving least squares approximation as an approximation scheme on the sphere. We prove error estimates and approximation orders. Finally, we show certain numerical results. x1. Introduction Recently, approximation on the sphere has become important because of its obvious applications to Meteorology, Oceanography and Geoscience and Geo-engineering in general. Over the last years seve...

The paper shows that the SPH boundary handling of Akinci et al. [AIA∗12] suffers from perceivable issues in planar regions due to deviations in the computed boundary normals and due to erroneous oscillations in the distance computation of fluid particles to the boundary. In order to resolve these issues, we propose a novel boundary handling that combines the SPH concept with Moving Least Square...

We present a 3d deformation method based on Moving Least Squares that extends the work by Schaefer et al. [Schaefer et al. 2006] to the 3d setting. The user controls the deformation by manipulating a set of point handles. Locally, the deformation takes the form of either a rigid transformation or optionally a similarity transformation, and tends to preserve local features. Our derivation of the...

Modern simulation and measurement methods tend to produce meshfree data sets if modeling of processes or objects with free surfaces or boundaries is desired. In Computational Fluid Dynamics (CFD), such data sets are described by particle-based vector fields. This paper presents a summary of a selection of methods for the extraction of geometric features of such point-based vector fields while p...

A general method for near-best approximations to functionals on Rd, using scattered-data information is discussed. The method is actually the moving least-squares method, presented by the Backus-Gilbert approach. It is shown that the method works very well for interpolation, smoothing and derivatives’ approximations. For the interpolation problem this approach gives Mclain’s method. The method ...

boundary integral equations (bie) are reformulations of boundary value problems for partial differential equations. there is a plethora of research on numerical methods for all types of these equations such as solving by discretization which includes numerical integration. in this paper, the neumann problem is reformulated to a bie, and then moving least squares as a meshless method is describe...

Data obtained by scanning 3D models typically contains missing pieces and holes. These can be caused due to scanning artifacts or artifacts in the surface due to wear and tear. We provide a method based on the Moving Least Squares projection to fill holes in triangular meshes obtained during the process of surface reconstruction . Our method can be applied to holes with non-planar geometry as w...

The Moving Least Squares method (MLS) provides an approximation û of a function u based solely on values u(xj) of u on scattered ”meshless” nodes xj . Derivatives of u are usually approximated by derivatives of û. In contrast to this, we directly estimate derivatives of u from the data, without any detour via derivatives of û. This is a generalized Moving Least Squares technique, and we prove t...

Based on sampling likelihood and feature intensity, in this paper, a feature-preserving denoising algorithm for point-sampled surfaces is proposed. In terms of moving least squares surface, the sampling likelihood for each point on point-sampled surfaces is computed, which measures the probability that a 3D point is located on the sampled surface. Based on the normal tensor voting, the feature ...

In this paper, we analyze the weight functions used in implicit moving least squares (IMLS) methods to construct implicit surfaces that interpolate or approximate polygon soup. We found that one method that presented an analytic solution to the integrated moving least squares method has issues with degeneracies because they changed the weight functions to decrease too slowly. We derive bounds f...