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.

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...

The numerical implementation of the truly Meshless Local Petrov-Galerkin (MLPG) type weakforms of the displacement and traction boundary integral equations is presented, for solids undergoing small deformations. In the accompanying part I of this paper, the general MLPG/BIE weak-forms were presented [Atluri, Han and Shen (2003)]. The MLPG weak forms provide the most general basis for the numeri...

a r t i c l e i n f o This paper presents a shock detection technique based on Moving Least Squares reproducing kernel approximations. The multiresolution properties of these kinds of approximations allow us to define a wavelet function to act as a smoothness indicator. This MLS sensor is used to detect the shock waves. When the MLS sensor is used in a finite volume framework in combination wit...

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...