On the Linear Independence and Partition of Unity of Arbitrary Degree Analysis-Suitable T-splines
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 (d1, d2) 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.
Publication Source (Journal or Book title)
Communications in Mathematics and Statistics
Zhang, J., & Li, X. (2015). On the Linear Independence and Partition of Unity of Arbitrary Degree Analysis-Suitable T-splines. Communications in Mathematics and Statistics, 3 (3), 353-364. https://doi.org/10.1007/s40304-015-0064-z