Geodesic
About the geometry of the Cassini oval, its non-convexity degree and $\varepsilon$-offset layer
Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 60 (2022), pp. 34-57

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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.
Keywords: Cassini oval, $\varepsilon$-offset layer, non-convex set, approximation calculation.
Mots-clés : $\alpha$-sets 
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     author = {O. A. Kuvshinov},
     title = {About the geometry of the {Cassini} oval, its non-convexity degree and $\varepsilon$-offset layer},
     journal = {Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta},
     pages = {34--57},
     publisher = {mathdoc},
     volume = {60},
     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/IIMI_2022_60_a2/}
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O. A. Kuvshinov. About the geometry of the Cassini oval, its non-convexity degree and $\varepsilon$-offset layer. Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta, Tome 60 (2022), pp. 34-57. http://geodesic.mathdoc.fr/item/IIMI_2022_60_a2/