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Article Dans Une Revue Computers and Graphics Année : 2012

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

Résumé

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.
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Dates et versions

hal-00742505 , version 1 (16-10-2012)

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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, 2012, 36 (5), pp.507-513. ⟨10.1016/j.cag.2012.03.005⟩. ⟨hal-00742505⟩
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