On the problem of instability in the dimension of a spline space over a T-mesh

Berdinsky Dmitry 1 Oh Min-Jae 1 Kim Taewan 1, 2 Bernard Mourrain 3
3 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis, CNRS - Centre National de la Recherche Scientifique : UMR6621
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+1and m′ ≥2r′ +1are optimal.
Document type :
Journal articles
Computers and Graphics, Elsevier, 2012, 36 (5), pp.507-513. <10.1016/j.cag.2012.03.005>


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Berdinsky Dmitry, Oh Min-Jae, Kim Taewan, Bernard Mourrain. On the problem of instability in the dimension of a spline space over a T-mesh. Computers and Graphics, Elsevier, 2012, 36 (5), pp.507-513. <10.1016/j.cag.2012.03.005>. <hal-00742505>

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