A RATIONAL PARAMETRIZATION OF BÉZIER LIKE CURVES

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AuteurHOUEDANOU, KOFFI WILFRID
AuteurALLAOUI, MOHAMED
AuteurGOUDJO, AURELIEN
AuteurADETOLA, JAMAL
Date d'ajout2026-06-02T16:06:57Z
Date de disponibilite2026-06-02T16:06:57Z
Date de publication2022
ResumeIn this paper, we construct a family of Bernstein functions using a class of rational parametrizations. The new family of rational Bernstein basis on an index α ∈ ( − ∞ , 0 ) U ( 1 , + ∞ ) , and for a given degree k ∈ N ∗ , these basis functions are rationals with a numerator and a denominator each of polynomials of degree k. All of the classical properties as positivity, partition of unity hold for these rational Bernstein bases. They constitute approximation basis functions for spaces of continuous functions. The Bézier curves obtained satisfy the classical properties. We have the classical computational algorithms like the de Casteljau algorithm and the algorithm of subdivision with the similar accuracy. Given a degree k and a control polygon points, all of these algorithms converge to the same Bézier curve as the classical case. That means the Bézier curve is independent of the index α. The classical polynomial Bernstein basis seems to be an asymptotic case of our new class of rational Bernstein basis.
DOI10.17654/0972111822003
Autre identifiantBECDB-12541
URIhttps://dspace.uac.bj/handle/123456789/10820
Languefr
Fait partie deFar East Journal of Dynamical Systems
Sujetrational Bernstein functions
Sujetfunctions approximation
SujetBézier curves
Sujetde Casteljau algorithm
TitreA RATIONAL PARAMETRIZATION OF BÉZIER LIKE CURVES
TypeArticle

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