In this paper we report some recent advances regarding applications using the method of finite spheres; a truly meshfree numerical technique developed for the solution of boundary value problems on geometrically complex domains. First, we present the development of a preprocessor for the generation of nodal points on twodimensional computational domains. Then, the development of a specialized v...

By combining the well known moving least squares approximation method and the theory of approximate approximations due to Maz’ya and Schmidt we are able to present an approximate moving least squares method which inherits the simplicity of Shepard’s method along with the accuracy of higher-order moving least squares approximations. In this paper we focus our interest on practical implementation...

We present a formulation for achieving “as rigid as possible” deformations of 3D models using a Moving Least Squares (MLS) approach. This research was inspired by the work of Schaefer et al.[25] which describes an approach solving a 2D version of the same problem. Our main contribution is showing how the problem may be efficiently handled in 3D for both point and line segment constraints. Our p...

While digital panoramic photography taken along travelling routes is very popular, digital panoramic strip maps are virtually nonexistent. In this article, we explore the characteristics of panoramic strip maps and provide an interactive method for their digital creation, focusing on the challenge of straightening curved routes. The resulting software Terrain Bender implements a geometric defor...

We introduce a distance measure for use in scattered data approximation. Reconstruction from sparse, non-uniformly distributed data should utilize application-specific knowledge to produce highquality results. Our distance measure is considering the specific problem of computing reconstructions from sparse observational paleoceanography data, where it is possible to consider certain problem-spe...

A multiscale meshfree particle method is developed, which includes recent advances in SPH and other meshfree research efforts. Key features will include linear consistency, stability, and both local and global conservation properties. In addition, through the incorporation of Reproducing Kernal Particle Method(RKPM), standard moving least squares (MLS) enhancement and wavelet techniques, the me...

Meshless methods have been extensively popularized in literature in recent years, due to their flexibility in solving boundary value problems. The meshless local Petrov-Galerkin(MLPG) method for solving the bending problem of the thin plate is presented and discussed in the present paper. The method uses the moving least-squares approximation to interpolate the solution variables, and employs a...

We present a new method for point cloud denoising. We introduce a robust smoothing operator Q(r) = r + t∗n∗, inspired in moving least squares and M-estimators robust statistics theory. Our algorithm can be seen as a generalization and improvement of the Fleishman et al algorithm for mesh denoising.

This work presents a method for deforming meshes in a shape-sensible way using Moving Least Squares (MLS) optimization. This work explains how an approach for deforming space [10] can be transformed into a skeleton-guided deformation scheme, where more sensitivity to the mesh geometry is achieved. Given a mesh and its skeleton, for each joint a minimization problem is solved subject to position...

Craniofacial reconstruction aims at estimating the facial outlook associated to an unknown specimen. Craniofacial reconstruction is generally based on the statistical tissue thickness on anthropometric landmarks. However, the features points alone are not enough for realistic reconstruction. So, in our paper, we take advantage of a reference facial model, through measuring the differences betwe...