Generalized Bezier Curves Based on Lupaş q-Analogue of the Bernstein Operator

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dc.contributor.advisor	Kara, Mustafa
dc.contributor.author	Atamert, Mehmet Salih
dc.date.accessioned	2021-09-01T11:13:45Z
dc.date.available	2021-09-01T11:13:45Z
dc.date.issued	2019
dc.date.submitted	2019
dc.identifier.citation	Atamert, Mehmet Salih. (2019). Generalized Bezier Curves Based on Lupaş q-Analogue of the Bernstein Operator. Thesis (M.S.), Eastern Mediterranean University, Institute of Graduate Studies and Research, Dept. of Mathematics, Famagusta: North Cyprus.	en_US
dc.identifier.uri	http://hdl.handle.net/11129/5087
dc.description	Master of Science in Mathematics. Thesis (M.S.)--Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics, 2019. Supervisor: Assist. Prof. Dr. Mustafa Kara.	en_US
dc.description.abstract	In this thesis, we study the Bezier curves and their properties. Bezier curves are one of the most important curves in Computer-Aided Geometric Design (CAGD). Bernstein functions are the basis of the Bezier curves. Therefore, we investigate the Lupaş 𝑞��- analogue of Bernstein functions, their properties and corresponding Lupaş 𝑞��-Bezier curves and their useful properties. Finally, we have studied the de Casteljau algorithms of Lupaş 𝑞��-Bezier curve and the upgrade procedure. Keywords: Bernstein polynomials, Bezier curve, de Casteljau algorithms, degree elevation, Lupaş 𝑞��-Bezier curve, Lupaş 𝑞��-Bezier surface, Lupaş q-analogue of Bernstein operator	en_US
dc.description.abstract	ÖZ Bu tezde Bezier eğrilerilerini ve bu ozellikleri inceliyoruz. Bezier eğrileri, Bilgisayar Destekli Geometrik Tasarım'daki (CAGD) en önemli eğrilerden biridir. Bernstein fonksiyonları Bezier eğrilerinin temelidir. Bu nedenle, Bernstein fonksiyonlarının Lupaş q-analogunu, özelliklerini ve bunlara karşılık gelen Lupaş q-Bezier eğrilerini ve yararlı özelliklerini araştırıyoruz. Son olarak, Lupaş q-Bezier eğrisinin de Casteljau algoritmalarını ve yükseltme prosedürünü inceledik. Anahtar kelimeler: Bernstein polinomları, Bezier egrileri, de Casteljau algoritması, derece yükseltme, Lupas 𝑞��-Bezier egrileri, Lupaş 𝑞��-Bezier yüzeyi, Lupaş 𝑞��-analogue of Bernstein operatoru	en_US
dc.language.iso	eng	en_US
dc.publisher	Eastern Mediterranean University (EMU) - Doğu Akdeniz Üniversitesi (DAÜ)	en_US
dc.rights	info:eu-repo/semantics/openAccess	en_US
dc.subject	Mathematics	en_US
dc.subject	Bernstein polynomials	en_US
dc.subject	Bezier curve	en_US
dc.subject	de Casteljau algorithms	en_US
dc.subject	degree elevation	en_US
dc.subject	Lupaş	en_US
dc.title	Generalized Bezier Curves Based on Lupaş q-Analogue of the Bernstein Operator	en_US
dc.type	masterThesis	en_US
dc.contributor.department	Eastern Mediterranean University, Faculty of Arts and Sciences, Dept. of Mathematics	en_US