{"title":"About the geometry of the Cassini oval, its non-convexity degree and $\\varepsilon$-offset layer","authors":"O. Kuvshinov","doi":"10.35634/2226-3594-2022-60-03","DOIUrl":null,"url":null,"abstract":"The paper studies the geometry of a closed nonconvex smooth simply connected curve on a plane — of the Cassini oval, as well as the geometry of the $\\varepsilon$-layer around the set whose boundary is the Cassini oval. Various analytical representations of the $\\varepsilon$-layer boundary are formed, and special points of this boundary are described. The measure of nonconvexity $\\alpha$ of a simply connected set whose boundary is the Cassini oval is determined, and the angular characteristic of nonconvexity of its $\\varepsilon$-neighborhood is defined.","PeriodicalId":42053,"journal":{"name":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","volume":"13 1","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Instituta Matematiki i Informatiki-Udmurtskogo Gosudarstvennogo Universiteta","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.35634/2226-3594-2022-60-03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The paper studies the geometry of a closed nonconvex smooth simply connected curve on a plane — of the Cassini oval, as well as the geometry of the $\varepsilon$-layer around the set whose boundary is the Cassini oval. Various analytical representations of the $\varepsilon$-layer boundary are formed, and special points of this boundary are described. The measure of nonconvexity $\alpha$ of a simply connected set whose boundary is the Cassini oval is determined, and the angular characteristic of nonconvexity of its $\varepsilon$-neighborhood is defined.