{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T22:48:26Z","timestamp":1773442106060,"version":"3.50.1"},"reference-count":17,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"name":"Fujian Provincial Natural Science Foundation of China","award":["2012J01013"],"award-info":[{"award-number":["2012J01013"]}]},{"name":"Fujian Provincial Natural Science Foundation of China","award":["ZC2012022"],"award-info":[{"award-number":["ZC2012022"]}]},{"name":"Panjinlong Discipline Construction Foundation of Jimei University, China","award":["2012J01013"],"award-info":[{"award-number":["2012J01013"]}]},{"name":"Panjinlong Discipline Construction Foundation of Jimei University, China","award":["ZC2012022"],"award-info":[{"award-number":["ZC2012022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>This paper proposes a definition of generalized offsets for curves and surfaces, which have the variable offset distance and direction, by using the local coordinate system. Based on this definition, some analytic properties and theorems of generalized offsets are put forward. The regularity and the topological property of generalized offsets are simply given by representing the generalized offset as the standard offset. Some examples are provided as well to show the applications of generalized offsets. The conclusions in this paper can be taken as the foundation for further study on extending the standard offset.<\/jats:p>","DOI":"10.1155\/2014\/124240","type":"journal-article","created":{"date-parts":[[2014,5,21]],"date-time":"2014-05-21T21:05:35Z","timestamp":1400706335000},"page":"1-13","source":"Crossref","is-referenced-by-count":6,"title":["Properties of Generalized Offset Curves and Surfaces"],"prefix":"10.1155","volume":"2014","author":[{"given":"Xuejuan","family":"Chen","sequence":"first","affiliation":[{"name":"School of Science, Jimei University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qun","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mathematical Science, Xiamen University, Xiamen 361005, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"18","doi-asserted-by":"publisher","DOI":"10.1007\/s00170-009-2164-y"},{"key":"10","first-page":"109","volume":"151","year":"2010","journal-title":"Nonlinear Computational Geometry"},{"key":"12","volume-title":"General tool offset curves and surfaces","year":"1992"},{"key":"15","first-page":"55","volume":"5","year":"1997","journal-title":"Neural Parallel and Scientific Computations"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-4049(98)00028-0"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/S0895-7177(97)00188-X"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1007\/s002090050004"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/618148"},{"key":"3","volume-title":"General tool offset curves and surfaces","year":"1992"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(90)90024-L"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8396(90)90023-K"},{"issue":"3","key":"9","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1016\/0167-8396(86)90039-7","volume":"3","year":"1986","journal-title":"Computer Aided Geometric Design"},{"key":"11","year":"1959"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s00025-009-0407-8"},{"key":"2","series-title":"Research Notes in Mathematics","year":"1982"},{"key":"13","year":"1988"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/S0010-4485(98)00066-9"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/124240.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/124240.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/124240.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T13:37:02Z","timestamp":1498138622000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/124240\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":17,"alternative-id":["124240","124240"],"URL":"https:\/\/doi.org\/10.1155\/2014\/124240","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014]]}}}