SMI 2012: Short On the problem of instability in the dimension of a spline space over a T-mesh

Authors:
Dmitry Berdinsky;Min-Jae Oh;Tae-Wan Kim;Bernard Mourrain
Affiliations:
Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea;Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea;Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul 151-744, Republic of Korea and Research Institute of Marine Systems Engineering, Seoul National University, ...;GALAAD, INRIA Méditerranée, BP 93, 06902 Sophia Antipolis, France
Venue:
Computers and Graphics
Year:
2012

Citing 4
Cited 1

Surface modeling with polynomial splines over hierarchical T-meshes

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

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Polynomial splines over general T-meshes

The Visual Computer: International Journal of Computer Graphics - Special Issue: CAD/Graphics 2009
On the instability in the dimension of splines spaces over T-meshes

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

In this paper, we discuss the problem of instability in the dimension of a spline space over a T-mesh. For bivariate spline spaces S(5,5,3,3) and S(4,4,2,2), the instability in the dimension is shown over certain types of T-meshes. This result could be considered as an attempt to answer the question of how large the polynomial degree (m,m') should be relative to the smoothness (r,r') to make the dimension of a spline space stable. We show in particular that the bound m=2r+1 and m'=2r'+1 are optimal.