Geodesic
Subdivision Scheme of Quartic Bivariate Splines on a Four-Directional Mesh
El Bachir Ameur1 ; Domingo Barrera Rosillo2 ; Driss Sbibih3
1 Université Moulay Ismail, Faculté des sciences et Techniques, Département d'Informatique, 52000 Errachdia, Maroc
2 Departamento de Matemática Aplicada, Faculdad de Ciencias, Universidad de Granada, Campus Universitario de Fuentenueva s/n, 18071, Granada, Spain
3 Université Mohammed I, Ecole Supérieure de Technologie, Laboratoire MATSI, Oujda, Maroc
ESAIM. Proceedings, Tome 20 (2007), pp. 16-28.

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In this paper we give a new definition of minimally and quasi-minimally supported quartic bivariate B-splines associated with the four-directional mesh of the plane, introduced in [7,19], which is convenient to show that theses B-splines satisfy the refinement equation and we determine the associated matrix mask, we prove that the family of these B-splines is stable and the associated subdivision scheme converges. These results can be extended to various cases in the spline space of class and degree 4k+4, but in these cases the supports of the masks are larger.
DOI : 10.1051/proc:072002

El Bachir Ameur 1 ; Domingo Barrera Rosillo 2 ; Driss Sbibih 3

1 Université Moulay Ismail, Faculté des sciences et Techniques, Département d'Informatique, 52000 Errachdia, Maroc
2 Departamento de Matemática Aplicada, Faculdad de Ciencias, Universidad de Granada, Campus Universitario de Fuentenueva s/n, 18071, Granada, Spain
3 Université Mohammed I, Ecole Supérieure de Technologie, Laboratoire MATSI, Oujda, Maroc 
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     title = {Subdivision {Scheme} of {Quartic} {Bivariate} {Splines} on a {Four-Directional} {Mesh}},
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El Bachir Ameur; Domingo Barrera Rosillo; Driss Sbibih. Subdivision Scheme of Quartic Bivariate Splines on a Four-Directional Mesh. ESAIM. Proceedings, Tome 20 (2007), pp. 16-28. doi : 10.1051/proc:072002. http://geodesic.mathdoc.fr/articles/10.1051/proc:072002/

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