Journal ArticleDOI
Polynomial splines over locally refined box-partitions
Reads0
Chats0
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
More filters
Journal ArticleDOI
Digital Twin: Values, Challenges and Enablers From a Modeling Perspective
TL;DR: This work reviews the recent status of methodologies and techniques related to the construction of digital twins mostly from a modeling perspective to provide a detailed coverage of the current challenges and enabling technologies along with recommendations and reflections for various stakeholders.
BookDOI
Mathematical Methods for Curves and Surfaces
TL;DR: A construction of rational isotropic curves with a prescribed tangent field which leads to the description of all rational minimal surfaces is presented.
Journal ArticleDOI
Mathematical analysis of variational isogeometric methods
TL;DR: This review paper collects several results that form part of the theoretical foundation of isogeometric methods, and analyses variational techniques for the numerical resolution of PDEs based on splines or NURBS and provides optimal approximation and error estimates in several cases of interest.
Journal ArticleDOI
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models
Dominik Schillinger,Martin Ruess +1 more
TL;DR: This review article provides a concise introduction to the basics of the finite cell method, and summarizes recent developments of the technology, with particular emphasis on the research topics in which the author has been actively involved.
Journal ArticleDOI
Isogeometric analysis using LR B-splines
TL;DR: This paper proposes local refinement strategies for adaptive isogeometric analysis using LR B-splines and investigates its performance by doing numerical tests on well known benchmark cases.
References
More filters
Journal ArticleDOI
T-spline simplification and local refinement
Thomas W. Sederberg,David L. Cardon,G. Thomas Finnigan,Nicholas S. North,Jianmin Zheng,Tom Lyche +5 more
TL;DR: An algorithm for eliminating superfluous control points, producing a T-spline, which can remove substantially more control points than competing methods such as B- Spline wavelet decomposition is presented.
Journal ArticleDOI
A hierarchical approach to adaptive local refinement in isogeometric analysis
TL;DR: The theoretical properties of the spline space are investigated to ensure fundamental properties like linear independence and partition of unity and concepts well-established in finite element analysis are used to fully integrate hierarchical spline spaces into the isogeometric setting.
Journal ArticleDOI
Local refinement of analysis-suitable T-splines
TL;DR: A local refinement algorithm for analysis-suitable T-splines which does not produce excessive propagation of control points is developed and its use as an adaptive framework for isogeometric analysis is demonstrated.
Journal ArticleDOI
Polynomial splines over hierarchical T-meshes
TL;DR: A new type of splines-polynomial splines over hierarchical T-meshes (called PHT-splines) to model geometric objects which have the same important properties as B-spline do, such as nonnegativity, local support and partition of unity.
Journal ArticleDOI
Linear independence of the T-spline blending functions associated with some particular T-meshes
TL;DR: Based on the local refinement algorithm addressed in Sederberg et al. (2004) [17], the linear independence of the bi-cubic T-spline blending functions corresponding to particular T-meshes is analyzed.