Existence and construction of Δ1-splines of class Ck on a three-directional mesh

Numerical Algorithms

Volumn 26, Issue 1, 2001, Pages 21-48

  Mazroui, A ^a   Sbibih, D ^a  

^a FACULTÉ DES SCIENCES   (Morocco)

Author keywords

*1 splines; 1 splines; B splines

Indexed keywords

EID: 0035607646     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1016644429740     Document Type: Article

References (13)

1. C.K. Chui, Multivariate Splines, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 54 (SIAM, Philadelphia, PA, 1988).
2. C.K. Chui, Vertex splines and their applications to interpolation of discrete data, in: Computation of Curves and Surfaces, eds. W. Dahmen et al. (Kluwer, Dordrecht, 1990).
3. C.K. Chui and He Tian-Xiao, Computation of minimal and quasi-minimal supported bivariate splines, J. Comput. Math. 8(2) (1990) 108-117.
4. C. de Boor, K. Höllig and S. Riemenschneider, Box-Splines, Applied Mathematical Sciences, Vol. 98 (Springer, New York, 1993).
5. X. Guillet, Interpolation by new families of B-splines on uniform meshes of the plane, in: Surface Fitting and Multiresolution Methods, eds. A. Le Méhauté, C. Rabut and L.L. Schumaker (Vanderbilt Univ. Press, Nashville/London, 1997) pp. 183-190.
6. k on a three-directional mesh, submitted.
7. C.A. Micchelli, Mathematical Aspects of Geometric Modeling, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 65 (SIAM, Philadelphia, PA, 1995).
8. J. Riordan, Combinatorial Identities, Wiley Series in Probability and Mathematical Statistics (Wiley, New York, 1989).
9. P. Sablonnière, Quasi-interpolants associated with H-splines on a three-direction mesh, J. Comput. Appl. Math. 66 (1996) 433-442.
10. P. Sablonnière, New families of B-splines on uniform mesh of the plane, in: Program on Spline Functions and the Theory of Wavelets, ed. S. Dubuc, Proceedings and Lecture Notes, Vol. 17 (University of Montreal, 1998) pp. 67-78.
11. P. Sablonnièrea and D. Sbibih, B-splines à supports hexagonaux sur un réseau tridirectionnel régulier du plan, C. R. Acad. Sci. Paris Serie I 319 (1994) 277-282.
12. P. Sablonnière and D. Sbibih, Some families of splines with hexagonal support on a three-direction mesh, in: Mathematical Methods for Curves and Surfaces, eds. M. Daehlen, T. Lyche and L.L. Schumaker (Vanderbilt Univ. Press, Nashville, 1995) pp. 467-475.
13. D. Sbibih, B-splines et quasi-interpolants sur un réseau tridirectionnel uniforme du plan, Thèse d'habilitation, Université d'Oujda, Maroc (1995).