Geometric Modeling with Splines

Cohen, Elaine; Riesenfeld, Richard F.; Elber, Gershon

doi:10.1201/9781439864203

Cited by 207 publications

(138 citation statements)

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“…(cf., e.g., [7]). Hence, for weighted splines on consecutive grid levels, with a sparse matrix S. As is well known, the grid transfer matrix S is all that is needed for implementing a standard finite element multigrid scheme.…”

Section: Methodsmentioning

confidence: 99%

Introduction to the Web-method and its applications

2005

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The Web-method is a meshless finite element technique which uses weighted extended B-splines (Web-splines) on a tensor product grid as basis functions. It combines the computational advantages of B-splines and standard mesh-based elements. In particular, degree and smoothness can be chosen arbitrarily without substantially increasing the dimension. Hence, accurate approximations are obtained with relatively few parameters. Moreover, the regular grid is well suited for hierarchical refinement and multigrid techniques. This article should serve as an introduction to finite element approximation with B-splines. We first review the construction of Web-bases and discuss their basic properties. Then we illustrate the performance of Ritz-Galerkin schemes for a model problem and applications in linear elasticity. Finally, we discuss several implementation aspects.

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Section: Methodsmentioning

confidence: 99%

Introduction to the Web-method and its applications

2005

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“…Manipulating control meshes offers a straightforward interface which supports interactive shape deformations. This approach has been extensively employed in spline-based modeling [CRE01] and can be naturally extended to subdivision surfaces. Collections of control mesh vertices, edges, and faces are re-positioned so as to induce modifications of the resulting limit surface.…”

Section: Surface Modeling Toolsmentioning

confidence: 99%

A survey of subdivision-based tools for surface modeling

Boier-Martin¹,

Zorin²,

Bernardini³

2005

Geometric and Algorithmic Aspects Of Computer-Aided Design and Manufacturing

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Abstract. Subdivision surfaces have emerged as a powerful representation for surface modeling and design. They address important limitations of traditional spline-based methods, such as the ability to handle arbitrary topologies and to support multiscale editing operations. In this paper we survey existing subdivision-based modeling methods with emphasis on interactive tools for styling and decoration of 3D models.

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“…The connectivity between the key points can be linear or higher order. The higher order connectivity can be achieved using interpolation models like Hermitte cubic, Spline curves, Bezier curves (Laurent, 1994;Spath, 1995;Cohen 2001), which are the most common and successfully used techniques for smoothing curves in the systems. Aim of the high order interpolation techniques is to reduce the amount of input points required to describe a smooth shape.…”

Section: Wwwintechopencommentioning

confidence: 99%

Segmentation Techniques of Anatomical Structures with Application in Radiotherapy Treatment Planning

Zimeras¹

2012

Modern Practices in Radiation Therapy

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Geometric Modeling with Splines

Cited by 207 publications

References 0 publications

Introduction to the Web-method and its applications

Introduction to the Web-method and its applications

A survey of subdivision-based tools for surface modeling

Segmentation Techniques of Anatomical Structures with Application in Radiotherapy Treatment Planning

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