# THB-splines: The truncated basis for hierarchical splines

@article{Giannelli2012THBsplinesTT, title={THB-splines: The truncated basis for hierarchical splines}, author={Carlotta Giannelli and Bert J{\"u}ttler and Hendrik Speleers}, journal={Comput. Aided Geom. Des.}, year={2012}, volume={29}, pages={485-498} }

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## References

SHOWING 1-10 OF 20 REFERENCES

### Multiresolution Surface Reconstruction for Hierarchical B-splines

- Computer ScienceGraphics Interface
- 1998

The resulting hierarchical surface accurately and economically reproduces the original mesh, is free from excessive undulations in the intermediate levels and produces a multiresolution representation suitable for animation and interactive modelling.

### Interpolating and approximating scattered 3D-data with hierarchical tensor product B-splines

- Mathematics
- 2010

In this note we describe surface reconstruction algorithms based on optimization techniques. The input are scattered 3D-data with specified topology. The surfaces constructed are tensor product…

### Isogeometric analysis using polynomial splines over hierarchical T-meshes for two-dimensional elastic solids

- Computer Science
- 2011

### Bases and dimensions of bivariate hierarchical tensor-product splines

- MathematicsJ. Comput. Appl. Math.
- 2013

### T-splines and T-NURCCs

- Computer ScienceACM Trans. Graph.
- 2003

A generalization of non-uniform B-spline surfaces called T-splines, which are C2 (in the absence of multiple knots), and T-NURCCs (Non-Uniform Rational Catmull-Clark Surfaces with T-junctions) are a superset of both T- Splines and Catm Mull-Clark surfaces, which can handle any NURBS or CatmULL-Clark model as special cases.

### A hierarchical approach to adaptive local refinement in isogeometric analysis

- Computer Science, Mathematics
- 2011