{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,19]],"date-time":"2025-05-19T14:26:40Z","timestamp":1747664800961,"version":"3.40.5"},"reference-count":20,"publisher":"Wiley","license":[{"start":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T00:00:00Z","timestamp":1564617600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2019,8,1]]},"abstract":"<jats:p>The problem of building a smooth surface containing given points or curves is actual due to development of industry and computer technology. Previously used for those purposes, shells of zero Gaussian curvature and minimal surfaces based on isotropic analytic curves are restricted in their consumer properties. To expand the possibilities regarding the shaping of surfaces we propose the method of constructing surfaces based on isotropic fractional-rational curves. The surfaces are built using flat isothermal and orthogonal grids and on the basis of the Weierstrass method. In the latter case, the surfaces are minimal. Examples of surfaces that were built according to the proposed method are given.<\/jats:p>","DOI":"10.1155\/2019\/5072676","type":"journal-article","created":{"date-parts":[[2019,8,1]],"date-time":"2019-08-01T19:31:16Z","timestamp":1564687876000},"page":"1-13","source":"Crossref","is-referenced-by-count":5,"title":["Surfaces Modelling Using Isotropic Fractional-Rational Curves"],"prefix":"10.1155","volume":"2019","author":[{"given":"Igor V.","family":"Andrianov","sequence":"first","affiliation":[{"name":"Institute of General Mechanics, RWTH Aachen University, Aachen 52056, Germany"}]},{"given":"Nataliia M.","family":"Ausheva","sequence":"additional","affiliation":[{"name":"Department of Design Automation of Energy Processes and Systems, National Technical University of Ukraine \u201cIgor Sikorsky Kyiv Polytechnic Institute\u201d, Kyiv 03056, Ukraine"}]},{"given":"Yuliia B.","family":"Olevska","sequence":"additional","affiliation":[{"name":"Mathematic Department, National Technical University \u201cDnipro Polytechnic\u201d, Dnipro 49005, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3824-1013","authenticated-orcid":true,"given":"Viktor I.","family":"Olevskyi","sequence":"additional","affiliation":[{"name":"Mathematic Department, Ukrainian State University of Chemical Technology, Dnipro 49005, Ukraine"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1177\/0266351117696577"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1155\/2013\/285165"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.7546\/jgsp-50-2018-57-69"},{"volume":"1773","journal-title":"AIP Conference Proceedings","year":"2016","key":"4"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1007\/BF00769121"},{"volume":"1","year":"1921","key":"6"},{"issue":"4","key":"9","first-page":"30","volume":"39","year":"2008","journal-title":"Tavria State Agrotechnological University"},{"year":"1963","key":"10"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/823809"},{"issue":"10","key":"12","first-page":"3","year":"1999","journal-title":"University of Belgrade Publications of Electrotechnical Faculty. 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