When different locally refined spline methods generate the same knotline T-mesh, the resulting spline spaces and the numerical properties of the corresponding collection of B-splines can vary significantly. In [1], a formula is presented for calculating the dimension of a spline space over a box-partition. This formula can be used to determine the maximal dimension of the spline space over knotline T-meshes produced by T-splines, Truncated Hierarchical B-splines (THB), and Locally Refined B-splines (LRB). LRB can be defined over the knotline T-meshes generated by T-splines and, in most cases, over those defined by THB. However, the knotline T-meshes of T-splines and THB are not compatible and cannot be reused interchangeably. For each method, we will examine how the collection of B-splines fills the maximal spline space over the knotline T-mesh. Specifically, we will consider whether there are too few B-splines or too many (resulting in linear dependence). In general, LRB splines most consistently fill the maximal spline space, outperforming both T-splines and THB in this regard. When the maximal spline space is not fully filled, it becomes easy to misjudge the approximation power of the B-spline collection. Both LRB and T-splines sometimes run the risk of introducing too many B-splines, leading to linear dependence. The methods achieve partition of unity in different ways: • T-splines use rational scaling. • LRB applies positive-weight scaling of B-splines. • THB employs truncation, decomposing truncated B-splines into a sum of scaled B-splines at finer refinement levels. Among these approaches, THB generally results in smaller scaling values compared to LRB over the same knotline T-mesh. Consequently, THB exhibits higher condition numbers for mass and stiffness matrices, especially as the polynomial degree increases. This talk will further explore how each method addresses its respective challenges: • LRB: Monitoring refinements or imposing refinement restrictions ensures that the spline space of the knotline T-mesh is exactly filled and avoid linear dependence. • THB: Avoiding diagonal refinements helps mitigate scaling issues but results in a spline space of larger dimension. • T-splines: The subclass of Analysis-Suitable T-splines (ASTS) was introduced to prevent linear dependence. REFERENCES [1] T. Dokken, T. Lyche, K.F. Pettersen, Polynomial splines over locally refined box-partitions, CAGD (2013) 30: 331 1–356.