A Family of Spline Quasi-Interpolants on the Sphere |
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Authors: | O Nouisser D Sbibih Paul Sablonnière |
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Institution: | (1) Département de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed I, Oujda, Maroc;(2) INSA, 20 avenue des Buttes de Coesmes, CS 14315, 35043 Rennes Cédex, France |
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Abstract: | In this paper, we construct a local quasi-interpolant Q for fitting a function f defined on the sphere S. We first map the surface S onto a rectangular domain and next, by using the tensor product of polynomial splines and 2 -periodic trigonometric splines, we give the expression of Qf. The use of trigonometric splines is necessary to enforce some boundary conditions which are useful to ensure the C
2 continuity of the associated surface. Finally, we prove that Q realizes an accuracy of optimal order. |
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Keywords: | tensor products polynomial splines trigonometric splines quasi-interpolants |
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