{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T19:14:24Z","timestamp":1776280464676,"version":"3.50.1"},"reference-count":28,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,2,1]],"date-time":"2025-02-01T00:00:00Z","timestamp":1738368000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study presents a generalized approach to B\u00e9zier curves and surfaces by utilizing the blending (\u03b1,\u03bb,s)-Bernstein basis. The (\u03b1,\u03bb,s)-Bernstein basis introduces shape parameters \u03b1, \u03bb, and s, which allow for more flexibility and control over the curve\u2019s shape compared to the classical Bernstein basis. The paper explores the properties of these generalized curves and surfaces, demonstrating their ability to maintain essential geometric characteristics, such as convex hull containment and endpoint interpolation, while providing enhanced control over the shape. This work aims to contribute to the fields of computer-aided geometric design and related applications by offering a robust tool for curve and surface modeling.<\/jats:p>","DOI":"10.3390\/sym17020219","type":"journal-article","created":{"date-parts":[[2025,2,3]],"date-time":"2025-02-03T05:36:32Z","timestamp":1738560992000},"page":"219","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["B\u00e9zier Curves and Surfaces with the Blending (\u03b1, \u03bb, s)-Bernstein Basis"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8718-4268","authenticated-orcid":false,"given":"\u0130lhan","family":"Karak\u0131l\u0131\u00e7","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Dokuz Eyl\u00fcl University, 35390 \u0130zmir, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0407-0271","authenticated-orcid":false,"given":"Sedef","family":"Karak\u0131l\u0131\u00e7","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Dokuz Eyl\u00fcl University, 35390 \u0130zmir, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9308-4084","authenticated-orcid":false,"given":"G\u00fclter","family":"Budak\u00e7\u0131","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Dokuz Eyl\u00fcl University, 35390 \u0130zmir, T\u00fcrkiye"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4135-2091","authenticated-orcid":false,"given":"Faruk","family":"\u00d6zger","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Igd\u0131r University, 76000 Igd\u0131r, T\u00fcrkiye"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,1]]},"reference":[{"key":"ref_1","first-page":"29","article-title":"Curves used in highway design and B\u00e9zier curves","volume":"52","author":"Ayar","year":"2022","journal-title":"Novi. 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