Approximation power of polynomial splines on T-meshes

Authors:
Larry L. Schumaker;Lujun Wang
Affiliations:
Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States;Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States
Venue:
Computer Aided Geometric Design
Year:
2012

Citing 11
Cited 3

T-splines and T-NURCCs

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T-spline simplification and local refinement

ACM SIGGRAPH 2004 Papers
Dimensions of spline spaces over T-meshes

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Surface modeling with polynomial splines over hierarchical T-meshes

The Visual Computer: International Journal of Computer Graphics
Polynomial splines over hierarchical T-meshes

Graphical Models
Error bounds for polynomial tensor product interpolation

Computing - Geometric Modelling, Dagstuhl 2008
Polynomial splines over general T-meshes

The Visual Computer: International Journal of Computer Graphics - Special Issue: CAD/Graphics 2009
Hierarchical Spline Approximation of the Signed Distance Function

SMI '10 Proceedings of the 2010 Shape Modeling International Conference
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
Adaptive finite element methods for elliptic equations over hierarchical T-meshes

Journal of Computational and Applied Mathematics

On Hermite interpolation with polynomial splines on T-meshes

Journal of Computational and Applied Mathematics
Polynomial splines over locally refined box-partitions

Computer Aided Geometric Design
Iterative refinement of hierarchical T-meshes for bases of spline spaces with highest order smoothness

Computer-Aided Design

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Abstract

Polynomial spline spaces defined on T-meshes are useful tools for both surface modeling and the finite element method. Here the approximation power of such spline spaces is established. The approach uses Bernstein-Bezier methods to get precise conditions on the geometry of the meshes which lead to local and stable bases.