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A New Class of Curves of Rational B-Spline Type
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  • Mohamed ALLAOUI,
  • Jamal ADETOLA,
  • Wilfrid HOUEDANOU,
  • Aurélien GOUDJO
Département de Sciences économiques, Université de Comores, Comores

Corresponding Author:allamath9@gmail.com

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Université Nationale des Sciences, Technologie, Ingénierie et Mathématiques (UNSTIM), Bénin
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Universite d'Abomey-Calavi
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Aurélien GOUDJO
Université d'Abomey-Calavi
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A new class of rational parametrization has been developed and it was used to generate a new family of rational k functions B-splines which depends on an index α ∈ ]−∞ , 0[ ∪ ]1 , +∞[. This family of functions verifies, among other things, the properties of positivity, of partition of the unit and, for a given degree k, constitutes a true basis approximation of continuous functions. We loose, however, the regularity classical optimal linked to the multiplicity of nodes, which we recover in the asymptotic case, when α → ∞. The associated B-splines curves verify the traditional properties particularly that of a convex hull and we see a certain “conjugated symmetry” related to α. The case of open knot vectors without an inner node leads to a new family of rational Bezier curves that will be separately, object of in-depth analysis.