Shape preserving surface reconstruction using locally anisotropic radial basis function interpolants

Casciola, Giulio; Lazzaro, Damiana; Montefusco, Laura; Morigi, Serena

doi:10.1016/j.camwa.2006.04.002

Cited by 46 publications

(28 citation statements)

References 13 publications

(20 reference statements)

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“…In this field, fitting with anisotropic directionally dependent covariances is a popular method for ore grade estimation; see Chiles and Delfiner [4]. From the approximation theory community, Cascioli et al [2,3] have demonstrated numerically the effectiveness of local anisotropic RBF fitting, and also that the condition of the matrix solution process is improved.…”

Section: Introductionmentioning

confidence: 99%

Error bounds for anisotropic RBF interpolation

Beatson¹,

Davydov²,

Levesley³

2010

Journal of Approximation Theory

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We present error bounds for the interpolation with anisotropically transformed radial basis functions for both a function and its partial derivatives. The bounds rely on a growth function and do not contain unknown constants. For polyharmonic basic functions in , we show that the anisotropic estimates predict a significant improvement of the approximation error if both the target function and the placement of the centers are anisotropic, and this improvement is confirmed numerically

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Section: Introductionmentioning

confidence: 99%

Error bounds for anisotropic RBF interpolation

Beatson¹,

Davydov²,

Levesley³

2010

Journal of Approximation Theory

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“…However, interpolation of data with anisotropic distribution of data sites in the domain requires special consideration. To this end, anisotropic radial basis functions (ARBFs) have been introduced and used in practice [8,9,2]; they are also known as elliptic basis functions as they have hyper-ellipsoidal level surfaces.…”

mentioning

confidence: 99%

Multilevel Sparse Kernel-Based Interpolation

Georgoulis¹,

Levesley²,

Subhan³

2013

SIAM J. Sci. Comput.

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A multilevel kernel-based interpolation method, suitable for moderately high-dimensional function interpolation problems, is proposed. The method, termed multilevel sparse kernelbased interpolation (MLSKI, for short), uses both level-wise and direction-wise multilevel decomposition of structured (or mildly unstructured) interpolation data sites in conjunction with the application of kernel-based interpolants with different scaling in each direction. The multilevel interpolation algorithm is based on a hierarchical decomposition of the data sites, whereby at each level the detail is added to the interpolant by interpolating the resulting residual of the previous level. On each level, anisotropic radial basis functions are used for solving a number of small interpolation problems, which are subsequently linearly combined to produce the interpolant. MLSKI can be viewed as an extension of d-boolean interpolation (which is closely related to ideas in sparse grid and hyperbolic crosses literature) to kernel-based functions, within the hierarchical multilevel framework to achieve accelerated convergence. Numerical experiments suggest that the new algorithm is numerically stable and efficient for the reconstruction of large data in R d × R, for d = 2, 3, 4, with tens or even hundreds of thousands data points. Also, MLSKI appears to be generally superior over classical radial basis function methods in terms of complexity, run time and convergence at least for large data sets.

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“…As already introduced in Section 1, RBF applications recur in many different areas of science and engineering: neural networks in computer graphics (surface reconstruction), solution of partial differential equations, and mesh morphing in image analysis of deformations . RBF mesh morphing has been used for several applications, from FSI coupling to genetic and evolutionary optimizations and advanced modeling …”

Section: Mathematical Backgroundmentioning

confidence: 99%

A balanced load mapping method based on radial basis functions and fuzzy sets

Biancolini

Chiappa

Giorgetti

et al. 2018

Numerical Meth Engineering

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A common issue in multiphysics analysis regards a reliable way for loose couplings, because the same object is modeled using different mesh refinements, each one suited for a proper field of physics. Output data originating from a simulation environment are transferred as input data to a different model to run a new analysis. It is strongly desirable that such information transfers in a conservative way in terms of general balance. This paper faces the problem of pressure mapping between widely dissimilar meshes. The proposed procedure yields two steps: pressure interpolation by means of radial basis functions and fuzzy subset correction. The first step is pointwise interpolation that exploits a series of basis functions. The second step applies to the outcome of the first one to reestablish load balance between the two models through the introduction of a smooth correction field. Practical tests from the aeronautical field allow validating the method.

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Shape preserving surface reconstruction using locally anisotropic radial basis function interpolants

Cited by 46 publications

References 13 publications

Error bounds for anisotropic RBF interpolation

Error bounds for anisotropic RBF interpolation

Multilevel Sparse Kernel-Based Interpolation

A balanced load mapping method based on radial basis functions and fuzzy sets

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