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Volumetric T-Spline Modeling
Published in Yongjie Jessica Zhang, Geometric Modeling and Mesh Generation from Scanned Images, 2018
As reviewed in Section 7.1, there are three types of T-splines depending on whether their basis functions or their weighted basis functions satisfy a partition of unity, including standard, semi-standard and non-standard T-splines. T-splines support local refinement and provide a lot of flexibility for modeling. On the other hand, they are also limited due to several open problems. For example, how to characterize T-mesh configurations for a standard, semi-standard, or non-standard T-spline and how to calculate the associated weights for a semi-standard T-spline are still open problems.
STEP-NC compliant data model for freeform surface manufacturing based on T-spline
Published in International Journal of Computer Integrated Manufacturing, 2019
Yazui Liu, Gang Zhao, Oleksandr Zavalnyi, Wenlei Xiao
In 2003, T-spline is proposed to solve the drawbacks of NURBS essentially (Sederberg et al. 2003, 2004). T-spline can realise local refinement to create special features without introducing redundant control points. In addition to this, T-spline can be used for merging and trimming NURBS into a watertight surface without gaps. Hence, T-spline is an ideal geometric modelling tool for freeform surface and it is necessary to introduce T-spline into STEP-NC for freeform surface manufacturing.
Adaptive BEM for elliptic PDE systems, part I: abstract framework, for weakly-singular integral equations
Published in Applicable Analysis, 2022
Gregor Gantner, Dirk Praetorius
The aim of the present work is to develop such an abstract framework also for BEM, which is mathematically much more demanding than FEM. In ongoing research [12], we aim to show that this framework covers, besides standard discretizations with piecewise polynomials, also IGABEM with hierarchical splines resp. T-splines.