Planar domain parameterization with THB-splines

Falini, Antonella; Ṡ́peh, Jaka; Jüttler, Bert

doi:10.1016/j.cagd.2015.03.014

Cited by 58 publications

(53 citation statements)

References 31 publications

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“…The optimal control points and weights of the reparameterized surface are then obtained using a variational harmonic metric. The idea of using harmonic mappings to determine a planar parametrization is also explored in [9].…”

Section: Introductionmentioning

confidence: 99%

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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Section: Introductionmentioning

confidence: 99%

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

Chan

Anitescu

Rabczuk

2017

Computer-Aided Design

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“…[36,37]. The proposed linear direct method was recently used in a similar way in [5,9] to parameterize (multi-patch) domains. The novelty of our approach is the use of specific linear constraints to ensure that the resulting multi-patch parameterization F is AS-G 1 .…”

Section: Problem Statement and Outlinementioning

confidence: 99%

“…Therefore, we simplify these constraints to linear ones by first computing the linear gluing data α ( ) , α ( ) , β ( ) and β ( ) by means of the initial multi-patch parameterization F and the relations (6)- (9). Consider an interface Γ ( , ) .…”

Section: As-gmentioning

confidence: 99%

“…The functionals F L and F U (the so-called parametric length functional and the uniformity functional, cf. [5,9]) are used to obtain parameterizations F of good quality, and are controlled by the non-negative weights λ L and λ U , respectively. The regularity condition (d) is nonlinear and cannot be guaranteed directly by our method.…”

Section: Problem Statement and Outlinementioning

confidence: 99%

“…Several existing methods allow such a parameterization of single patches, e.g. [9,10,11,13,28]. If only the boundary of a multi-patch domain is given, the recent method [5] is able to generate a suitable multi-patch parameterization.…”

Section: Introductionmentioning

confidence: 99%

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Construction of analysis-suitableG1planar multi-patch parameterizations

Kapl

Sangalli

Takacs

2018

Computer-Aided Design

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Isogeometric analysis allows to define shape functions of global C 1 continuity (or of higher continuity) over multi-patch geometries. The construction of such C 1 -smooth isogeometric functions is a non-trivial task and requires particular multi-patch parameterizations, so-called analysis-suitable G 1 (in short, AS-G 1 ) parameterizations, to ensure that the resulting C 1 isogeometric spaces possess optimal approximation properties, cf. [7]. In this work, we show through examples that it is possible to construct AS-G 1 multi-patch parameterizations of planar domains, given their boundary. More precisely, given a generic multi-patch geometry, we generate an AS-G 1 multi-patch parameterization possessing the same boundary, the same vertices and the same first derivatives at the vertices, and which is as close as possible to this initial geometry. Our algorithm is based on a quadratic optimization problem with linear side constraints. Numerical tests also confirm that C 1 isogeometric spaces over AS-G 1 multi-patch parameterized domains converge optimally under mesh refinement, while for generic parameterizations the convergence order is severely reduced.

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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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Planar domain parameterization with THB-splines

Cited by 58 publications

References 31 publications

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

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

Construction of analysis-suitableG1planar multi-patch parameterizations

Isogeometric Analysis: Representation of Geometry

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