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Carreaux de Bézier–Serendip

Abstract : We introduce reduced quadrilateral patches, the so called “Bézier–Serendip” patches. After some reminders about standard Bézier patches, we propose a method for constructing those reduced patches. The corresponding Bernstein polynomials are written by means of linear combinations of the standard Bernstein polynomials. We give a full description of the patches of degrees 2, 3, 4 and 5. Since degree 5, the location of the control points is no longer symmetric and to remedy this problem, we propose adding a number of control points, which results in extended Bézier–Serendip patches. Those reduced patches are in the Bézier framework what the Serendipity elements are in the finite-element framework.
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Submitted on : Wednesday, February 11, 2015 - 11:35:48 AM
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Paul-Louis George, Houman Borouchaki. Carreaux de Bézier–Serendip. Comptes Rendus Mathématique, Elsevier Masson, 2015, 353 (2), pp.179-184. ⟨10.1016/j.crma.2014.11.017⟩. ⟨hal-01115518⟩



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