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Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bezier curves

dc.contributor.authorBhrawy, A. H.
dc.contributor.authorDoha, E. H.
dc.contributor.authorSaker, M. A.
dc.contributor.authorBaleanu, Dumitru
dc.date.accessioned2017-04-24T08:24:03Z
dc.date.available2017-04-24T08:24:03Z
dc.date.issued2016
dc.departmentÇankaya Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bilgisayar Bölümüen_US
dc.description.abstractThis paper reports new modified Jacobi polynomials (MJPs). We derive the basis transformation between MJPs and Bernstein polynomials and vice versa. This transformation is merging the perfect Least-square performance of the new polynomials together with the geometrical insight of Bernstein polynomials. The MJPs with indexes corresponding to the number of endpoints constraints are the natural basis functions for Least-square approximation of Bezier curves. Using MJPs leads us to deal with the constrained Jacobi polynomials and the unconstrained Jacobi polynomials as orthogonal polynomials. The MJPs are automatically satisfying the homogeneous boundary conditions. Thereby, the main advantage of using MJPs, in multi-degree reduction of Bezier curves on computer aided geometric design (CAGD), is that the constraints in CAGD are also satisfied and that decreases the steps of multi-degree reduction algorithm. Several numerical results for the multi-degree reduction of Bezier curves on CAGD are given.en_US
dc.description.publishedMonth8
dc.identifier.citationBhrawy, A.H...et al. (2016). Modified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bezier curves. Journal of Computational and Applied Mathematics, 302, 369-384. http://dx.doi.org/10.1016/j.cam.2016.01.009en_US
dc.identifier.doi10.1016/j.cam.2016.01.009
dc.identifier.endpage384en_US
dc.identifier.issn0377-0427
dc.identifier.startpage369en_US
dc.identifier.urihttp://hdl.handle.net/20.500.12416/1571
dc.identifier.volume302en_US
dc.language.isoenen_US
dc.publisherElsevier Science BVen_US
dc.relation.ispartofJournal of Computational and Applied Mathematicsen_US
dc.rightsinfo:eu-repo/semantics/closedAccessen_US
dc.subjectBasis Transformationen_US
dc.subjectModified Jacobi Polynomialsen_US
dc.subjectBernstein Polynomialsen_US
dc.subjectGalerkin Orthogonal Polynomialsen_US
dc.subjectMultiple Degree Reduction Of Bezier Curvesen_US
dc.titleModified Jacobi-Bernstein basis transformation and its application to multi-degree reduction of Bezier curvestr_TR
dc.titleModified Jacobi-Bernstein Basis Transformation and Its Application To Multi-Degree Reduction of Bezier Curvesen_US
dc.typeArticleen_US
dspace.entity.typePublication

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