Journal ArticleDOI
Polynomial splines over locally refined box-partitions
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TLDR
This work addresses progressive local refinement of splines defined on axes parallel box-partitions and corresponding box-meshes in any space dimension and obtains a collection of hierarchically scaled B-splines that forms a nonnegative partition of unity and spans the complete piecewise polynomial space on the mesh when the mesh construction follows certain simple rules.About:
This article is published in Computer Aided Geometric Design.The article was published on 2013-03-01. It has received 358 citations till now. The article focuses on the topics: Box spline & Spline (mathematics).read more
Citations
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Book Chapter
Areal surface texture parameters on surface
Luca Pagani,Paul J. Scott +1 more
TL;DR: An approach that approximates a generic mesh based on locally refined (LR) Bspline based on a generic form surface to handle undercuts is proposed and will be compared with the discrete method implemented in standard software packages.
Journal ArticleDOI
Stabilization of spline bases by extension
TL;DR: In this paper , a method to stabilize bases with local supports by means of extension is presented, which generalizes the known approach for tensor product B-splines to a much broader class of functions, which includes hierarchical and weighted variants of polynomial, trigonometric, and exponential splines, but also box splines and other function spaces of interest with a local basis.
Proceedings ArticleDOI
Hierarchical Box Splines.
TL;DR: This paper takes the application of quartic smooth hierarchical box Splines in surface fitting as an example to demonstrate the adaptivity and flexibility of hierarchical box splines.
Journal ArticleDOI
LR B-splines to approximate bathymetry datasets: An improved statistical criterion to judge the goodness of fit
TL;DR: In this paper , a statistical information criterion based on the t-distribution is introduced to judge the goodness of fit of the surface approximation for remote sensing data with outliers, which can be used to select the most adequate refinement strategy of the LR B-splines.
Journal ArticleDOI
Evaluation Algorithm of PHT-Spline Surfaces
TL;DR: A de Boor like algorithm to evaluate PHT-splines provided that only the information about the control coefficients and the hierarchical mesh structure is given, which takes about the same order of computational costs while requires much less amount of memory compared with the Bézier representations.
References
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Journal ArticleDOI
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement
TL;DR: In this article, the concept of isogeometric analysis is proposed and the basis functions generated from NURBS (Non-Uniform Rational B-Splines) are employed to construct an exact geometric model.
Book
Isogeometric Analysis: Toward Integration of CAD and FEA
TL;DR: Providing a systematic approach to the topic, the authors begin with a tutorial introducing the foundations of Isogeometric Analysis, before advancing to a comprehensive coverage of the most recent developments in the technique.
Journal ArticleDOI
Isogeometric analysis using T-splines
Yuri Bazilevs,Victor M. Calo,J. A. Cottrell,John A. Evans,Thomas J. R. Hughes,S. Lipton,Michael A. Scott,Thomas W. Sederberg +7 more
TL;DR: T-splines, a generalization of NURBS enabling local refinement, have been explored as a basis for isogeometric analysis in this paper, and they have shown good results on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases.
Proceedings ArticleDOI
T-splines and T-NURCCs
TL;DR: A generalization of non-uniform B-spline surfaces called T-splines, which are C2 (in the absence of multiple knots), and T-NURCCs (Non-Uniform Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T- Splines and Catm Mull-Clark surfaces, which can handle any NURBS or CatmULL-Clark model as special cases.
Journal ArticleDOI
Hierarchical B-spline refinement
TL;DR: This work presents a method of localizing the effect of refinement through the use of overlays, which are hierarchically controlled subdivisions, and introduces two editing techniques that are effective when using overlays.