ACM SIGGRAPH 2003 Papers
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
Dimensions of spline spaces over T-meshes
Journal of Computational and Applied Mathematics
Polynomial splines over hierarchical T-meshes
Graphical Models
On the instability in the dimension of splines spaces over T-meshes
Computer Aided Geometric Design
Adaptive isogeometric analysis using rational PHT-splines
Computer-Aided Design
Hierarchical bases of spline spaces with highest order smoothness over hierarchical T-subdivisions
Computer Aided Geometric Design
Dimensions and bases of hierarchical tensor-product splines
Journal of Computational and Applied Mathematics
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This paper discusses the dimension of spline spaces S(m,n,m-1,n-1,T) over a certain type of hierarchical T-mesh. The key step is to establish a bijection between the spline space S(m,n,m-1,n-1,T) and a univariate spline space defined in terms of the l-edges of the extended T-mesh with respect to bi-degree (m,n). We decompose the univariate spline space into an isomorphic direct sum using the theory of short exact sequences from homological algebra. Using this decomposition, we can obtain a formula for the dimension of the spline space S(m,n,m-1,n-1,T) over the required type of hierarchical T-mesh. We also construct a set of basis functions for the spline space.