Polynomial splines over hierarchical T-meshes

Deng, Jiansong; Chen, Falai; Li, Xin; Hu, Changqi; Tong, Weihua; Yang, Zhouwang; Feng, Yong

doi:10.1016/j.gmod.2008.03.001

Cited by 281 publications

(182 citation statements)

References 13 publications

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“…cubic splines over hierarchical T-meshes with reduced C 1 regularity, no refinement propagation is observed -see for example the original papers [2,12] or their recent application for the numerical solution of partial differential equations [9,14]. Despite a proper local refinement behavior in this case, the reduced regularity leads to a higher number of degrees of freedom to achieve a certain given accuracy.…”

Section: Neverthelessmentioning

confidence: 99%

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THB-splines: The truncated basis for hierarchical splines

Giannelli

Jüttler

Speleers

2012

Computer Aided Geometric Design

426

402

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The construction of classical hierarchical B-splines can be suitably modified in order to define locally supported basis functions that form a partition of unity. We will show that this property can be obtained by reducing the support of basis functions defined on coarse grids, according to finer levels in the hierarchy of splines. This truncation not only decreases the overlapping of supports related to basis functions arising from different hierarchical levels, but it also improves the numerical properties of the corresponding hierarchical basis -which is denoted as truncated hierarchical B-spline (THB-spline) basis. Several computed examples will illustrate the adaptive approximation behavior obtained by using a refinement algorithm based on THB-splines.

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Section: Neverthelessmentioning

confidence: 99%

“…T-splines [17,18] and PHT-splines [2] are defined over T-meshes, where T-junctions between axis aligned segments are allowed. The T-spline framework has already shown its potential as a powerful modeling tool for advanced computer aided geometric design problems.…”

Section: Introductionmentioning

confidence: 99%

THB-splines: The truncated basis for hierarchical splines

Giannelli

Jüttler

Speleers

2012

Computer Aided Geometric Design

426

402

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“…The polynomial splines introduced in [7] are related to B-splines of reduced continuity over hierarchical T-meshes. Local refinement is an appealing property of the PHT-splines, which makes their use suitable for fitting arbitrary domains.…”

Section: Polynomial Splines Over Hierarchical T-meshes (Pht Splines)mentioning

confidence: 99%

“…For a linear mapping between the parameter space and the physical space, the control points of the initial mesh (ℓ = 1) are set as the locations of the Greville Abscissae, while the control points at level ℓ > 1 can be computed using the geometric information of the basis functions [7]. The geometric information is determined by the location of the basis vertex in the physical space and the values of the derivatives of the mapping evaluated at the basis vertex.…”

Section: Computing the Control Pointsmentioning

confidence: 99%

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Volumetric parametrization from a level set boundary representation with PHT-splines

Chan

Anitescu

Rabczuk

2017

Computer-Aided Design

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A challenge in isogeometric analysis is constructing analysis-suitable volumetric meshes which can accurately represent the geometry of a given physical domain. In this paper, we propose a method to derive a splinebased representation of a domain of interest from voxel-based data. We show an efficient way to obtain a boundary representation of the domain by a level-set function. Then, we use the geometric information from the boundary (the normal vectors and curvature) to construct a matching C 1 representation with hierarchical cubic splines. The approximation is done by a single template and linear transformations (scaling, translations and rotations) without the need for solving an optimization problem. We illustrate our method with several examples in two and three dimensions, and show good performance on some standard benchmark test problems.

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Isogeometric Analysis: Representation of Geometry

Haberleitner

Jüttler

Scott

et al. 2017

Encyclopedia of Computational Mechanics Second Edition

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This chapter provides a review of analysis‐suitable geometric descriptions and approaches commonly used in the context of isogeometric analysis (IGA). A primary focus is on NURBS (nonuniform rational B‐splines), T‐splines, and hierarchical B‐splines. The integration of analysis‐suitable geometry and IGA using Bézier extraction is covered, as well as several emerging approaches to isogeometric mesh generation, adaptivity, and domain parameterization.

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Polynomial splines over hierarchical T-meshes

Cited by 281 publications

References 13 publications

THB-splines: The truncated basis for hierarchical splines

THB-splines: The truncated basis for hierarchical splines

Volumetric parametrization from a level set boundary representation with PHT-splines

Isogeometric Analysis: Representation of Geometry

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