A general method computes dimensions of spline spaces on arbitrary rectilinear partitions by reducing the problem to rank of constructible conformality matrices, and proves Schumaker's lower bound is attained for partitions with disjoint truncated l-edges.
On the dimension of spline spaces on planar T-meshes,
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A recursive dimensional formula for bi-degree (d,d) highest-smoothness splines on hierarchical T-meshes is derived via conformality vector spaces, with a mesh modification strategy for stability and equivalence to lower-degree spaces on CVR graphs.
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Dimension Calculation for Spline Spaces over Rectilinear Partitions via Smoothing Cofactor Method
A general method computes dimensions of spline spaces on arbitrary rectilinear partitions by reducing the problem to rank of constructible conformality matrices, and proves Schumaker's lower bound is attained for partitions with disjoint truncated l-edges.
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Dimension of Bi-degree $(d,d)$ Spline Spaces with the Highest Order of Smoothness over Hierarchical T-Meshes
A recursive dimensional formula for bi-degree (d,d) highest-smoothness splines on hierarchical T-meshes is derived via conformality vector spaces, with a mesh modification strategy for stability and equivalence to lower-degree spaces on CVR graphs.