This paper focuses on the reconstruction of surfaces of revolution. We propose a method for estimating those surfaces from point clouds. We are more particularly dealing with data coming from one unique laser scanner acquisition; indeed, our approach extensively uses the range image topology. It makes originally use of geometric properties of surfaces of revolution. We firstly get an approximat...

In this paper, we propose an approach for diagnostics and prognostics of damaged aircraft structures, by combing high-performance fatigue mechanics with filtering theories. Fast & accurate deterministic analyses of fatigue crack propagations are carried out, by using the Finite Element Alternating Method (FEAM) for computing SIFs, and by using the newly developed Moving Least Squares (MLS) law ...

Given finite subset J ⊂ IR, and a point λ ∈ IR, we study in this paper the possible convergence, as h→ 0, of the coefficients in least-squares approximation to f(·+hλ) from the space spanned by (f(·+ hj)j∈J . We invoke the ‘least solution of the polynomial interpolation problem’ to show that the coefficient do converge for a generic J and λ, provided that the underlying function f is sufficient...

Nonlinear stochastic optimal control problems are fundamental in control theory. A general class of such problems can be reduced to computing the principal eigenfunction of a linear operator. Here, we describe a new method for finding this eigenfunction using a moving least-squares function approximation. We use efficient iterative solvers that do not require matrix factorization, thereby allow...

We construct and analyze a least-squares procedure for approximately solving the initial-value problem for the linearized equations of coupled sound and heat flow, in a bounded domain Í2 in Ä , with homogeneous Dirichlet boundary conditions. The method is based on Crank-Nicolson time differencing. To approximately solve the resulting system of boundary value problems at each time step, a least-...

In this paper we focus on two methods for multivariate approximation problems with non-uniformly distributed noisy data. The new approach proposed here is an iterated approximate moving least-squares method. We compare our method to ridge regression which filters out noise by using a smoothing parameter. Our goal is to find an optimal number of iterations for the iterative method and an optimal...

A non-compactly supported cubic radial basis function implementation of the MLPG method for beam problems is presented. The evaluation of the derivatives of the shape functions obtained from the radial basis function interpolation is much simpler than the evaluation of the moving least squares shape function derivatives. The radial basis MLPG yields results as accurate or better than those obta...

In this study, we propose to approximate the a− n relation as well as the da/dn−∆K relation, in fatigue crack propagation, by using the Moving Least Squares (MLS) method. This simple approach can avoid the internal inconsistencies caused by the celebrated Paris’ power law approximation of the da/dn−∆K relation, as well as the error caused by a simple numerical differentiation of the noisy data ...

Meshless methods based on the local Petrov-Galerkin approach are proposed for solution of steady and transient heat conduction problem in a continuously nonhomogeneous anisotropic medium. Fundamental solution of the governing partial differential equations and the Heaviside step function are used as the test functions in the local weak form. It is leading to derive local boundary integral equat...

IN a recent article, Geary [1972] discussed the merit of taking first differences to deal with the problems that trends in data present in regression analysis. Geary gave examples of situations where this procedure leads to highly inefficient estimates of the regression coefficients. The first difference transforma­ tion has also been suggested as an appropriate way of dealing with multicolline...