C
k
-B-splines with Square Support on a Three-Direction Mesh of the Plane |
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Authors: | A Mazroui D Sbibih A Tijini |
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Institution: | (1) Département de Mathématiques et Informatique, Faculté des Sciences, Université Mohammed I, Oujda, Morocco |
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Abstract: | Let be the uniform triangulation generated by the usual three-directional mesh of the plane and let 1 be the unit square consisting of two triangles of . We study the space of piecewise polynomial functions in C
k
(R
2) with support 1 having a sufficiently high degree n, which are symmetrical with respect to the first diagonal of 1. Such splines are called 1-splines. We first compute the dimension of this space in function of n and k. Then, for any fixed k0, we prove the existence of 1-splines of class C
k
and minimal degree. These splines are not unique. Finally, we describe an algorithm computing the Bernstein–Bézier coefficients of these splines, and we give an example. |
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Keywords: | B-splines 1-splines" target="_blank">gif" alt="Sgr" align="BASELINE" BORDER="0">1-splines minimal degree |
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