Generalized B-splines as a tool in isogeometric analysis

Manni, Carla; Pelosi, Francesca; Sampoli, Maria Lucia

doi:10.1016/j.cma.2010.10.010

Cited by 76 publications

(70 citation statements)

References 22 publications

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“…NURBS typically involve the explicit characterization of non-uniform knot vectors with double knots. A drawback of NURBS is their rational form, which leads to complicated expressions for related integrals and derivatives [7]. Furthermore, the NURBS formulation depends on additional weight parameters, which have no intuitive interpretation.…”

Section: Continuous Closed Surfacesmentioning

confidence: 99%

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Smooth shapes with spherical topology: Beyond traditional modeling, efficient deformation, and interaction

2017

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Existing shape models with spherical topology are typically designed either in the discrete domain using interpolating polygon meshes or in the continuous domain using smooth but non-interpolating schemes such as subdivision or NURBS. Both polygon models and subdivision methods require a large number of parameters to model smooth surfaces. NURBS need fewer parameters but have a complicated rational expression and non-uniform shifts in their formulation. We present a new method to construct deformable closed surfaces, which includes exact spheres, by combining the best of two worlds: a smooth, interpolating model with a continuously varying tangent plane and well-defined curvature at every point on the surface.Our formulation is considerably simpler than NURBS and requires fewer parameters than polygon meshes. We demonstrate the generality of our method with applications including intuitive user-interactive shape modeling, continuous surface deformation, shape morphing, reconstruction of shapes from parameterized point clouds, and fast iterative shape optimization for image segmentation. Comparisons with discrete methods and non-interpolating approaches highlight the advantages of our framework.

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Section: Continuous Closed Surfacesmentioning

confidence: 99%

“…Parametric NURBS surfaces are based on polynomial B-splines and are defined by a set of control points which allow local shape control [3,[5][6][7][8]. The main reason for using rational NURBS instead of (non-rational) polynomial Bsplines is that NURBS are able to exactly reproduce conic sections [9].…”

Section: Continuous Closed Surfacesmentioning

confidence: 99%

Smooth shapes with spherical topology: Beyond traditional modeling, efficient deformation, and interaction

2017

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“…6.3. Example 3: analysis of a problem in solid mechanics based on NURPS splines This example aims to illustrate our conversion strategy in the presence of local refinements, by solving a classical problem in solid mechanics [4,9,13]. We consider an infinite plate with a circular hole of radius R, subject to an inplane uniform tension T x in x-direction, see Fig.…”

Section: Example 2: Nurps Approximation Of a Nurbs Domainmentioning

confidence: 99%

“…Proposition 7. Let G be a quadratic NURBS map as in (13). Let T be an admissible triangulation of Ω 0 with a given PS refinement.…”

Section: In Both Cases T Satisfies (H1)mentioning

confidence: 99%

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From NURBS to NURPS geometries

Speleers

Manni

Pelosi

2013

Computer Methods in Applied Mechanics and Engineering

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Quadratic Powell-Sabin splines and their rational extension, the socalled NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a Bspline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic NURBS representation into a NURPS representation, suitable for the analysis.Keywords : Powell-Sabin splines, NURBS, NURPS, isogeometric analysis. AbstractQuadratic Powell-Sabin splines and their rational extension, the so-called NURPS surfaces, are an interesting alternative for classical tensor-product NURBS in the context of isogeometric analysis, because they allow the use of local refinements while retaining a B-spline like representation and exact description of conic sections. In this paper we present a simple and effective strategy to convert a given planar geometry defined by a quadratic NURBS representation into a NURPS representation, suitable for the analysis.

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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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Generalized B-splines as a tool in isogeometric analysis

Cited by 76 publications

References 22 publications

Smooth shapes with spherical topology: Beyond traditional modeling, efficient deformation, and interaction

Smooth shapes with spherical topology: Beyond traditional modeling, efficient deformation, and interaction

From NURBS to NURPS geometries

Isogeometric Analysis: Representation of Geometry

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