In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent...

Moving least squares (MLS) surfaces representation directly defines smooth surfaces from point cloud data, on which the differential geometric properties of point set can be conveniently estimated. Nowadays, the MLS surfaces have been widely applied in the processing and rendering of point-sampled models and increasingly adopted as the standard definition of point set surfaces. We classify the ...

A successful approach in triangulating point set surfaces is to apply operations, like a projection operator for advancing front algorithms, directly to Moving-Least Squares (MLS) surfaces. The MLS method naturally handles noisy input data and is especially useful for point clouds derived from real-world solids. Unfortunately, MLS is computationally extensive and complex. We present a novel pro...

Owing to the meshless and local characteristics, moving least squares (MLS) methods have been used extensively to approximate the unknown function of partial differential equation initial boundary value problem. In this paper, based on matrix analysis, a sufficient and necessary condition for the existence of inverse of coefficient matrix used in MLS methods is developed firstly. Then in the li...

Moving-Least Squares (MLS) surfaces are a popular way to define a smooth manifold surface from a set of unorganized points without normals. In this paper we present a formulation of MLS surfaces that sheds light on shortcomings of the original technique proposed by Levin, which is based on a two-step minimization procedure. We show that there are cases intrinsic to the geometry of the underlyin...

This paper presents a novel craniofacial reconstruction algorithm based on moving least squares deformation. The 3D skull mesh model is obtained with Marching Cube Algorithm, which extract the iso-surface from a complete head CT slice datum. The holes detected in the 3D skull model can be repaired with different methods after the holes are clarifed . Then, the craniofacial is reconstructed usin...

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...

Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth-out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicit...

A particular meshless method, named meshless local Petrov–Galerkin is investigated. To treat the essential boundary condition problem, an alternative approach is proposed. The basic idea is to merge the best features of two different methods of shape function generation: the moving least squares (MLS) and the radial basis functions with polynomial terms (RBFp). Whereas the MLS has lower computa...