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Abstract
Analysis-suitable T-splines are a topological-restricted subset of T-splines, which are optimized to meet the needs both for design and analysis (Li and Scott Models Methods Appl Sci 24:1141–1164, 2014; Li et al. Comput Aided Geom Design 29:63–76, 2012; Scott et al. Comput Methods Appl Mech Eng 213–216, 2012). The paper independently derives a class of bi-degree $(d_{1}, d_{2})$ T-splines for which no perpendicular T-junction extensions intersect, and provides a new proof for the linearly independence of the blending functions. We also prove that the sum of the basis functions is one for an analysis-suitable T-spline if the T-mesh is admissible based on a recursive relation.
Keywords
T-splines
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Analysis-suitable T-splines
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Linear independence
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Partition of unity
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Isogeometric analysis
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Jingjing Zhang, Xin Li.
On the Linear Independence and Partition of Unity of Arbitrary Degree Analysis-Suitable T-splines.
Communications in Mathematics and Statistics, 2015, 3(3): 353-364 DOI:10.1007/s40304-015-0064-z
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Funding
NSF of China(ID0EPDAE5)
SRF for ROCS SE(ID0EAGAE6)
NBRPC(ID0EPIAE7)