Patchwork B-spline refinement

Engleitner, Nora; Jüttler, Bert

doi:10.1016/j.cad.2017.05.021

Cited by 14 publications

(10 citation statements)

References 29 publications

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“…There are many other definitions of B-splines over meshes with local refinements, such as PHT-splines [11], PB-splines [12] and LR B-splines [13]. A discusssion of the differences and similarities of HB-splines, THB-splines, T-splines, AST-splines and LR B-splines can be found in [14].…”

Section: Overview Of Locally Refined Spline Methodsmentioning

confidence: 99%

Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes

Patrizi

Dokken

2020

Computer Aided Geometric Design

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The focus on locally refined spline spaces has grown rapidly in recent years due to the need in Isogeoemtric analysis (IgA) of spline spaces with local adaptivity: a property not offered by the strict regular structure of tensor product B-spline spaces. However, this flexibility sometimes results in collections of B-splines spanning the space that are not linearly independent. In this paper we address the minimal number of B-splines that can form a linear dependence relation for Minimal Support B-splines (MS B-splines) and for Locally Refined B-splines (LR B-splines) on LR-meshes. We show that the minimal number is six for MS Bsplines and eight for LR B-splines. Further results are established to help detecting collections of B-splines that are linearly independent.

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Section: Overview Of Locally Refined Spline Methodsmentioning

confidence: 99%

Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes

Patrizi

Dokken

2020

Computer Aided Geometric Design

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“…In the field of geodesy, the regression B-spline approximation, as introduced by Reference [20], allows great flexibility to model raw TLS observations: no predetermined geometric primitives, such as circles, planes or cylinders, restrict the fitting [21]. Other strategies exist, such as penalized splines [22] or patches splines [23]. They seem less suitable for applications with noisy and scattered observations from TLS PC: please refer to Reference [24] for a short review of the different methods); 2.…”

Section: Introductionmentioning

confidence: 99%

Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load

2020

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The choice of an appropriate metric is mandatory to perform deformation analysis between two point clouds (PC)—the distance has to be trustworthy and, simultaneously, robust against measurement noise, which may be correlated and heteroscedastic. The Hausdorff distance (HD) or its averaged derivation (AHD) are widely used to compute local distances between two PC and are implemented in nearly all commercial software. Unfortunately, they are affected by measurement noise, particularly when correlations are present. In this contribution, we focus on terrestrial laser scanner (TLS) observations and assess the impact of neglecting correlations on the distance computation when a mathematical approximation is performed. The results of the simulations are extended to real observations from a bridge under load. Highly accurate laser tracker (LT) measurements were available for this experiment: they allow the comparison of the HD and AHD between two raw PC or between their mathematical approximations regarding reference values. Based on these results, we determine which distance is better suited in the case of heteroscedastic and correlated TLS observations for local deformation analysis. Finally, we set up a novel bootstrap testing procedure for this distance when the PC are approximated with B-spline surfaces.

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“…The constantly increasing demand for higher precision in simulations and reverse engineering processes requires the possibility to apply adaptive local refinement strategies, in order to reduce the approximation error while keeping the computational costs low. This request for adaptivity, triggered the interest in new formulations of B-splines and NURBS, still based on local tensor structures [12,23,9,5,13,10,11]. All these new classes of functions are defined on locally refined meshes, in which T-vertices in the interior of the domain are allowed, the so-called T-meshes.…”

Section: Introductionmentioning

confidence: 99%

Adaptive refinement with locally linearly independent LR B-splines: Theory and applications

Patrizi,

Manni,

Pelosi

et al. 2020

Preprint

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Patchwork B-spline refinement

Cited by 14 publications

References 29 publications

Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes

Linear dependence of bivariate Minimal Support and Locally Refined B-splines over LR-meshes

Deformation Analysis Using B-Spline Surface with Correlated Terrestrial Laser Scanner Observations—A Bridge Under Load

Adaptive refinement with locally linearly independent LR B-splines: Theory and applications

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