{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T12:39:45Z","timestamp":1771677585413,"version":"3.50.1"},"reference-count":31,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T00:00:00Z","timestamp":1625443200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T00:00:00Z","timestamp":1625443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s10851-021-01046-y","type":"journal-article","created":{"date-parts":[[2021,7,5]],"date-time":"2021-07-05T15:03:37Z","timestamp":1625497417000},"page":"1118-1142","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Construction of Generalized Hybrid Trigonometric B\u00e9zier Surfaces with Shape Parameters and Their Applications"],"prefix":"10.1007","volume":"63","author":[{"given":"Samia","family":"Bibi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0491-1528","authenticated-orcid":false,"given":"Muhammad","family":"Abbas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7869-0345","authenticated-orcid":false,"given":"Md Yushalify","family":"Misro","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0316-1585","authenticated-orcid":false,"given":"Abdul","family":"Majeed","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tahir","family":"Nazir","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,7,5]]},"reference":[{"key":"1046_CR1","first-page":"1","volume":"12","author":"MC Yip-Hoi","year":"2011","unstructured":"Yip-Hoi, M.C.: Teaching surface modeling to CAD\/CAM technologists. Am. Soc. Eng. Educ. 12, 1\u201322 (2011)","journal-title":"Am. Soc. Eng. Educ."},{"key":"1046_CR2","volume-title":"Curves and Surfaces for CAGD. A Practical Guide","author":"G Farin","year":"2002","unstructured":"Farin, G.: Curves and Surfaces for CAGD. A Practical Guide, 5th edn. Academic Press, San Diego (2002)","edition":"5"},{"issue":"2","key":"1046_CR3","first-page":"321","volume":"27","author":"R Schmidt","year":"2008","unstructured":"Schmidt, R., Singh, K.: Sketch-based procedural surface modeling and compositing. Eurographics 27(2), 321\u2013330 (2008)","journal-title":"Eurographics"},{"key":"1046_CR4","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/j.cagd.2017.05.002","volume":"55","author":"T Varady","year":"2017","unstructured":"Varady, T., Salvi, E., Kovacs, I.: Enhancement of a multi-sided B\u00e9zier surface representation. Comput. Aided Geom. Des. 55, 69\u201383 (2017)","journal-title":"Comput. Aided Geom. Des."},{"key":"1046_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cagd.2018.03.020","volume":"62","author":"I Kovacs","year":"2018","unstructured":"Kovacs, I., Varady, T.: P-B\u00e9zier and P-B-spline curves - new representations with proximity control. Comput. Aided Geom. Des. 62, 1\u201320 (2018)","journal-title":"Comput. Aided Geom. Des."},{"key":"1046_CR6","doi-asserted-by":"publisher","first-page":"545","DOI":"10.3390\/sym10110545","volume":"10","author":"G Hu","year":"2018","unstructured":"Hu, G., Bo, C., Wu, J., Wei, G., Hou, F.: Modeling of free-form complex curves using SG-B\u00e9zier curves with constraints of geometric continuities. Symmetry 10, 545\u2013567 (2018)","journal-title":"Symmetry"},{"key":"1046_CR7","doi-asserted-by":"crossref","first-page":"10183","DOI":"10.1016\/j.amc.2013.03.110","volume":"219","author":"U Bashir","year":"2013","unstructured":"Bashir, U., Abbas, M., Ali, J.M.: The $$G^{2}$$ and $$C^{2}$$ rational quadratic trigonometric B\u00e9zier curve with two shape parameters with applications. Appl. Math. Comput. 219, 10183\u201310197 (2013)","journal-title":"Appl. Math. Comput."},{"key":"1046_CR8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.amc.2013.07.073","volume":"223","author":"X Qin","year":"2013","unstructured":"Qin, X., Hu, G., Zhang, N., Shen, X., Yang, Y.: A novel extension to the polynomial basis functions describing B\u00e9zier curve and surfaces of degree $$n$$ with the multiple shape parameters. Appl. Math. Comput. 223, 1\u201316 (2013)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"1046_CR9","doi-asserted-by":"publisher","first-page":"165779","DOI":"10.1109\/ACCESS.2019.2953496","volume":"7","author":"S BiBi","year":"2019","unstructured":"BiBi, S., Abbas, M., Misro, M.Y., Hu, G.: A novel approach of hybrid trigonometric B\u00e9zier curve to the modeling of symmetric revolutionary curves and symmetric rotation surfaces. IEEE Access 7(1), 165779\u2013165792 (2019)","journal-title":"IEEE Access"},{"key":"1046_CR10","doi-asserted-by":"publisher","first-page":"967","DOI":"10.3390\/math8060967","volume":"8","author":"S BiBi","year":"2020","unstructured":"BiBi, S., Abbas, M., Miura, T.K., Misro, Y.M.: Geometric modelling of novel Generalized hybrid trigonometric B\u00e9zier-like curve with shape parameters and its applications. Mathematics 8, 967 (2020)","journal-title":"Mathematics"},{"issue":"8","key":"1046_CR11","doi-asserted-by":"publisher","first-page":"8625","DOI":"10.3934\/math.2021501","volume":"6","author":"S BiBi","year":"2021","unstructured":"BiBi, S., Misro, Y.M., Abbas, M.: Smooth path planning via cubic GHT-B\u00e9zier spiral curves based on shortest distance, bending energy and curvature variation energy. AIMS Math. 6(8), 8625\u20138641 (2021)","journal-title":"AIMS Math."},{"issue":"5","key":"1046_CR12","doi-asserted-by":"publisher","first-page":"825","DOI":"10.17576\/jsm-2017-4605-17","volume":"46","author":"MY Misro","year":"2017","unstructured":"Misro, M.Y., Ramli, A., Ali, J.M.: Quintic Trigonometric B\u00e9zier curve with two shape parameters. Sains Malaysiana. 46(5), 825\u2013831 (2017)","journal-title":"Sains Malaysiana."},{"key":"1046_CR13","doi-asserted-by":"crossref","unstructured":"Ismail, N.H.M., Misro, M.Y.: Surface construction using continuous trigonometric B\u00e9zier curve. In AIP Conference Proceedings (Vol. 2266, No. 1, p. 040012). AIP Publishing LLC (2020)","DOI":"10.1063\/5.0018101"},{"key":"1046_CR14","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1016\/j.advengsoft.2017.07.009","volume":"114","author":"G Hu","year":"2017","unstructured":"Hu, G., Cao, H., Qin, X., Wang, X.: Geometric design and continuity conditions of developable $$\\lambda $$-B\u00e9zier surfaces. Adv. Eng. Software 114, 235\u2013245 (2017)","journal-title":"Adv. Eng. Software"},{"key":"1046_CR15","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1016\/j.advengsoft.2018.09.002","volume":"125","author":"G Hu","year":"2018","unstructured":"Hu, G., Wu, J., Qin, X.: A novel extension of the B\u00e9zier model and its applications to surface modeling. Adv. Eng. Software 125, 27\u201354 (2018)","journal-title":"Adv. Eng. Software"},{"key":"1046_CR16","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1016\/j.advengsoft.2018.03.003","volume":"121","author":"G Hu","year":"2018","unstructured":"Hu, G., Junli, W., Xinqiang, Q.: A new approach in designing of local controlled developable H-B\u00e9zier surfaces. Adv. Eng. Software 121, 26\u201338 (2018)","journal-title":"Adv. Eng. Software"},{"issue":"1","key":"1046_CR17","doi-asserted-by":"publisher","first-page":"115","DOI":"10.1186\/s13660-017-1390-3","volume":"2017","author":"G Hu","year":"2017","unstructured":"Hu, G., Bo, C.C., Qin, X.Q.: Continuity conditions for Q-B\u00e9zier curves of degree $$n$$. J. Inequal. Appl. 2017(1), 115 (2017)","journal-title":"J. Inequal. Appl."},{"key":"1046_CR18","doi-asserted-by":"publisher","first-page":"4036434","DOI":"10.1155\/2020\/4036434","volume":"2020","author":"S Maqsood","year":"2020","unstructured":"Maqsood, S., Abbas, M., Hu, G., Ramli, A.L.A., Miura, K.T.: A novel generalization of trigonometric B\u00e9zier curve with shape parameters and its applications. Math. Probl Eng. 2020, 4036434 (2020)","journal-title":"Math. Probl Eng."},{"key":"1046_CR19","doi-asserted-by":"publisher","first-page":"728","DOI":"10.1016\/j.apm.2017.01.043","volume":"45","author":"G Hu","year":"2017","unstructured":"Hu, G., Cao, H., Zhang, S., Wei, G.: Developable B\u00e9zier-like surfaces with multiple shape parameters and its continuity conditions. Appl. Math. Modell. 45, 728\u2013747 (2017)","journal-title":"Appl. Math. Modell."},{"key":"1046_CR20","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1016\/j.cam.2017.02.044","volume":"329","author":"YC Li","year":"2016","unstructured":"Li, Y.C., Zhu, G.C.: $$G^{1}$$ continuity of four pieces of developable surfaces with B\u00e9zier boundaries. J. Comput. Appl. Math. 329, 164\u2013172 (2016)","journal-title":"J. Comput. Appl. Math."},{"issue":"2","key":"1046_CR21","first-page":"1","volume":"5","author":"G Hu","year":"2017","unstructured":"Hu, G., Cao, H., Qin, X., Wang, X.: Geometric design and continuity conditions of developable $$\\lambda $$-Bezier surfaces. Adv. Eng. Software 5(2), 1\u201311 (2017)","journal-title":"Adv. Eng. Software"},{"key":"1046_CR22","first-page":"266","volume":"194\u2013211","author":"G Hu","year":"2015","unstructured":"Hu, G., Qin, X., Ji, X., Wei, G., Zhang, S.: The construction of $$\\lambda \\mu $$-B-spline curves and its application to rotational surfaces. Appl. Math. Comput. 194\u2013211, 266 (2015)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"1046_CR23","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1186\/s13660-017-1524-7","volume":"2017","author":"G Hu","year":"2017","unstructured":"Hu, G., Cao, H., Wang, X., Qin, X.: $$G^{2}$$ continuity conditions for generalized B\u00e9zier-like surfaces with multiple shape parameters. J. Inequal. Appl. 2017(1), 248 (2017)","journal-title":"J. Inequal. Appl."},{"key":"1046_CR24","doi-asserted-by":"crossref","unstructured":"Bashir, U., Abbas, M., Mohid, N.H.A., Ali, J.M.: A Class of quasi-quintic trigonometric B\u00e9zier curve with two shape parameters. Sci. Asia. 39S, 1\u201315 (2013)","DOI":"10.2306\/scienceasia1513-1874.2013.39S.011"},{"issue":"1","key":"1046_CR25","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1016\/S0167-8396(01)00011-5","volume":"18","author":"E Mainer","year":"2001","unstructured":"Mainer, E.: Shape preserving alternatives to the rational B\u00e9zier model. Comput. Aided Geom. Des. 18(1), 37\u201360 (2001)","journal-title":"Comput. Aided Geom. Des."},{"issue":"5","key":"1046_CR26","first-page":"838","volume":"22","author":"Z Liu","year":"2010","unstructured":"Liu, Z., Chen, X., Jiang, P.: A class of generalized B\u00e9zier curves and surfaces with multiple shape parameters. J. Comput. Aided Des. Comput. Graph. 22(5), 838\u2013844 (2010)","journal-title":"J. Comput. Aided Des. Comput. Graph."},{"key":"1046_CR27","doi-asserted-by":"crossref","unstructured":"Han, X., Ma, Y.C., Huang. X.L. : A novel generalization of curve and surface. J. Comput. Appl. Math. 217, 180\u2013193 (2008)","DOI":"10.1016\/j.cam.2007.06.027"},{"key":"1046_CR28","volume-title":"Computer Aided Geometric Design and NURBS","author":"FZ Shi","year":"2001","unstructured":"Shi, F.Z.: Computer Aided Geometric Design and NURBS. China Higher Education Press, Beijing (2001)"},{"key":"1046_CR29","doi-asserted-by":"crossref","first-page":"125215","DOI":"10.1016\/j.amc.2020.125215","volume":"378","author":"G Hu","year":"2020","unstructured":"Hu, G., Bo, C.C., Wei, G., Qin, X.Q.: Shape adjustable generalized B\u00e9zier surfaces: construction and its geometric continuity conditions. Appl. Math. Comput. 378, 125215 (2020)","journal-title":"Appl. Math. Comput."},{"key":"1046_CR30","doi-asserted-by":"publisher","first-page":"1205","DOI":"10.3390\/sym12081205","volume":"12","author":"M Ammad","year":"2020","unstructured":"Ammad, M., Misro, M.Y.: Construction of local shape adjustable surfaces using quintic trigonometric B\u00e9zier curve. Symmetry 12, 1205 (2020)","journal-title":"Symmetry"},{"issue":"3","key":"1046_CR31","doi-asserted-by":"publisher","first-page":"283","DOI":"10.3390\/math9030283","volume":"9","author":"M Ammad","year":"2021","unstructured":"Ammad, M., Misro, M.Y., Abbas, M., Majeed, A.: Generalized developable cubic trigonometric B\u00e9zier surfaces. Mathematics 9(3), 283 (2021)","journal-title":"Mathematics"}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-021-01046-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10851-021-01046-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-021-01046-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,5]],"date-time":"2023-11-05T17:31:11Z","timestamp":1699205471000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10851-021-01046-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,7,5]]},"references-count":31,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["1046"],"URL":"https:\/\/doi.org\/10.1007\/s10851-021-01046-y","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,7,5]]},"assertion":[{"value":"29 September 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 June 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 July 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}