Hierarchical B-spline refinement
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
ACM SIGGRAPH 2003 Papers
T-spline simplification and local refinement
ACM SIGGRAPH 2004 Papers
Polynomial splines over hierarchical T-meshes
Graphical Models
Isogeometric Analysis: Toward Integration of CAD and FEA
Isogeometric Analysis: Toward Integration of CAD and FEA
Sharp asymptotics of the L p approximation error for interpolation on block partitions
Numerische Mathematik
Spline spaces on TR-meshes with hanging vertices
Numerische Mathematik
On the instability in the dimension of splines spaces over T-meshes
Computer Aided Geometric Design
Approximation power of polynomial splines on T-meshes
Computer Aided Geometric Design
Conformal solid T-spline construction from boundary T-spline representations
Computational Mechanics
Computer Aided Geometric Design
Dimensions and bases of hierarchical tensor-product splines
Journal of Computational and Applied Mathematics
Isogeometric methods for computational electromagnetics: B-spline and T-spline discretizations
Journal of Computational Physics
Computer Aided Geometric Design
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We address progressive local refinement of splines defined on axes parallel box-partitions and corresponding box-meshes in any space dimension. The refinement is specified by a sequence of mesh-rectangles (axes parallel hyperrectangles) in the mesh defining the spline spaces. In the 2-variate case a mesh-rectangle is a knotline segment. When starting from a tensor-mesh this refinement process builds what we denote an LR-mesh, a special instance of a box-mesh. On the LR-mesh we obtain a collection of hierarchically scaled B-splines, denoted LR B-splines, that forms a nonnegative partition of unity and spans the complete piecewise polynomial space on the mesh when the mesh construction follows certain simple rules. The dimensionality of the spline space can be determined using some recent dimension formulas.