Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

Crivellaro, Alberto; Perotto, Simona; Zonca, Stefano

doi:10.1016/j.apnum.2016.11.003

Cited by 16 publications

(10 citation statements)

References 13 publications

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“…We note that the withed approach in (16) entails stronger assumptions compared with (17). In particular, problem (17) only requires  to be full rank, whereas (16) necessitatesŴ +  to be full rank. As a result, condition ĉ ≥ N has to be added for the weighted approach, while such a condition is not required for the other approach.…”

Section: Pod For Sidw Shape Morphingmentioning

confidence: 99%

“…The second column provides the number of control points employed for morphing the original structure, being understood that ≡  when dealing with the IDW approach. The third column gathers the CPU time required by the offline phase of Algorithm 3 to construct the response matrix, to extract the POD basis, whose cardinality is furnished in the fourth column, and to assemble matrices  T (Ŵ + ) TŴ +  and  T (Ŵ + ) T in (16). The fifth column summarizes the CPU time required to perform the shape morphing via (3) and (6) in the case of the basic IDW and SIDW interpolations, respectively; for the POD variants, this coincides with the CPU time demanded by the online phase, ie, by the resolution of system (16) and by the computation of the linear combination  ( * ).…”

Section: Structural Deformation Of a Wingmentioning

confidence: 99%

“…The third column gathers the CPU time required by the offline phase of Algorithm 3 to construct the response matrix, to extract the POD basis, whose cardinality is furnished in the fourth column, and to assemble matrices  T (Ŵ + ) TŴ +  and  T (Ŵ + ) T in (16). The fifth column summarizes the CPU time required to perform the shape morphing via (3) and (6) in the case of the basic IDW and SIDW interpolations, respectively; for the POD variants, this coincides with the CPU time demanded by the online phase, ie, by the resolution of system (16) and by the computation of the linear combination  ( * ). Finally, the last column investigates the accuracy of the provided deformation by collecting the value of the L 2 (Ω h )-norm of the relative error between the computationally cheaper deformations and the reference IDW shape.…”

Section: Structural Deformation Of a Wingmentioning

confidence: 99%

“…These techniques have been recently applied to parametrized partial differential equations (PPDEs). For instance, shape morphing techniques based on free-form deformation (FFD) 8 and radial basis functions (RBF) interpolation 9 have been successfully applied to PPDEs, [10][11][12] shape optimization problems, [13][14][15] reconstruction of scattered geometrical data, 16 mesh motion and interface coupling for FSI problems, [17][18][19] interpolation between nonconforming meshes, 20 and sensitivity analysis studies in complex geometrical configurations. 21 In this paper, we focus on a different approach, the inverse distance weighting (IDW) interpolation that relies on the inverse of a weighted sum of distances between mesh nodes, where some of which will be chosen as control points.…”

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confidence: 99%

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A POD‐selective inverse distance weighting method for fast parametrized shape morphing

Ballarin

D'Amario

Perotto

et al. 2018

Numerical Meth Engineering

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Summary Efficient shape morphing techniques play a crucial role in the approximation of partial differential equations defined in parametrized domains, such as for fluid‐structure interaction or shape optimization problems. In this paper, we focus on inverse distance weighting (IDW) interpolation techniques, where a reference domain is morphed into a deformed one via the displacement of a set of control points. We aim at reducing the computational burden characterizing a standard IDW approach without significantly compromising the accuracy. To this aim, first we propose an improvement of IDW based on a geometric criterion that automatically selects a subset of the original set of control points. Then, we combine this new approach with a dimensionality reduction technique based on a proper orthogonal decomposition of the set of admissible displacements. This choice further reduces computational costs. We verify the performances of the new IDW techniques on several tests by investigating the trade‐off reached in terms of accuracy and efficiency.

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Section: Pod For Sidw Shape Morphingmentioning

confidence: 99%

Section: Structural Deformation Of a Wingmentioning

confidence: 99%

Section: Structural Deformation Of a Wingmentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

A POD‐selective inverse distance weighting method for fast parametrized shape morphing

Ballarin

D'Amario

Perotto

et al. 2018

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…For instance, RBF, thin plate spline, and compactly supported positive definite function [2,10,11]. Crivellaro et al [5] applied RBFs to reconstruct 3D scattered data. To achieve this, they proposed new algorithms involving an adaptive multi-level interpolating approach based on implicit surface representation and least square approximation to filter the noisy data.…”

Section: Introductionmentioning

confidence: 99%

Construction of new cubic Bézier-like triangular patches with application in scattered data interpolation

et al. 2020

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This paper discusses the functional scattered data interpolation to interpolate the general scattered data. Compared with the previous works, we construct a new cubic Bézier-like triangular basis function controlled by three shape parameters. This is an advantage compared with the existing schemes since it gives more flexibility for the shape design in geometric modeling. By choosing some suitable value of the parameters, this new triangular basis is reduced to the cubic Ball and cubic Bézier triangular patches, respectively. In order to apply the proposed bases to general scattered data, firstly the data is triangulated using Delaunay triangulation. Then the sufficient condition for C 1 continuity using cubic precision method on each adjacent triangle is implemented. Finally, the interpolation scheme is constructed based on a convex combination between three local schemes of the cubic Bézier-like triangular patches. The detail comparison in terms of maximum error and coefficient of determination r 2 with some existing meshfree methods i.e. radial basis function (RBF) such as linear, thin plate spline (TPS), Gaussian, and multiquadric are presented. From graphical results, the proposed scheme gives more visually pleasing interpolating surfaces compared with all RBF methods. Based on error analysis, for all four functions, the proposed scheme is better than RBFs except for data from the third function. Overall, the proposed scheme gives r 2 value between 0.99920443 and 0.99999994. This is very good for surface fitting for a large scattered data set.

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A 3D Geometry Service Platform Based on Point-Cloud Towards Curved Plate Forming

Cai,

Dong,

et al. 2024

Lecture Notes on Data Engineering and Communications Technologies

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Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

Cited by 16 publications

References 13 publications

A POD‐selective inverse distance weighting method for fast parametrized shape morphing

A POD‐selective inverse distance weighting method for fast parametrized shape morphing

Construction of new cubic Bézier-like triangular patches with application in scattered data interpolation

A 3D Geometry Service Platform Based on Point-Cloud Towards Curved Plate Forming

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