{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:49:46Z","timestamp":1740156586293,"version":"3.37.3"},"reference-count":14,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,3,13]],"date-time":"2013-03-13T00:00:00Z","timestamp":1363132800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Numerical Analysis"],"published-print":{"date-parts":[[2013,3,13]]},"abstract":"<jats:p>A parametric equation for a modified B\u00e9zier curve is proposed for curve fitting applications. The proposed equation contains shaping parameters to adjust the shape of the fitted curve. This flexibility of shape control is expected to produce a curve which is capable of following any sets of discrete data points. A Differential Evolution (DE) optimization based technique is proposed to find the optimum value of these shaping parameters. The optimality of the fitted curve is defined in terms of some proposed cost parameters. These parameters are defined based on sum of squares errors. Numerical results are presented highlighting the effectiveness of the proposed curves compared with conventional B\u00e9zier curves. From the obtained\nresults, it is observed that the proposed method produces a curve that fits the data points more accurately.<\/jats:p>","DOI":"10.1155\/2013\/858279","type":"journal-article","created":{"date-parts":[[2013,3,13]],"date-time":"2013-03-13T22:44:01Z","timestamp":1363214641000},"page":"1-8","source":"Crossref","is-referenced-by-count":10,"title":["Modified B\u00e9zier Curves with Shape-Preserving Characteristics Using Differential Evolution Optimization Algorithm"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7295-2102","authenticated-orcid":true,"given":"Mohammad Asif","family":"Zaman","sequence":"first","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6325-0790","authenticated-orcid":true,"given":"Shuvro","family":"Chowdhury","sequence":"additional","affiliation":[{"name":"Department of Electrical and Electronic Engineering, Bangladesh University of Engineering and Technology, Dhaka, 1000, Bangladesh"}]}],"member":"311","reference":[{"key":"1"},{"issue":"3","key":"2","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1002\/(SICI)1099-0887(199603)12:3<197::AID-CNM972>3.0.CO;2-Q","volume":"12","year":"1996","journal-title":"Communications in Numerical Methods in Engineering"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1002\/nme.3167"},{"issue":"6","key":"4","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1631\/jzus.2005.A0497","volume":"6","year":"2005","journal-title":"Journal of Zhejiang University Science A"},{"issue":"1","key":"5","first-page":"124","volume":"6","year":"2005","journal-title":"Journal of Zhejiang University Science"},{"key":"6","series-title":"Lecture Notes in Computer Science","volume-title":"An improved shape descriptor using bezier curves","volume":"3776","year":"2005"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1134\/S0965542506110042"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1007\/s00009-010-0094-4"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1080\/00207160701821715"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8396(03)00003-7"},{"issue":"1","key":"12","first-page":"116","volume":"6","year":"2005","journal-title":"Journal of Zhejiang University Science"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-006-0111-y"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008202821328"},{"year":"2005","key":"15"}],"container-title":["Advances in Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/858279.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/858279.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/archive\/2013\/858279.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T15:54:15Z","timestamp":1607615655000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/ana\/2013\/858279\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3,13]]},"references-count":14,"alternative-id":["858279","858279"],"URL":"https:\/\/doi.org\/10.1155\/2013\/858279","relation":{},"ISSN":["1687-9562","1687-9570"],"issn-type":[{"type":"print","value":"1687-9562"},{"type":"electronic","value":"1687-9570"}],"subject":[],"published":{"date-parts":[[2013,3,13]]}}}