On the Linear Independence and Partition of Unity of Arbitrary Degree Analysis-Suitable T-splines

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.