Geodesic
Visibility curves for ovals
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 13-35

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For $C^1$-smooth strictly convex oval, the class of visibility curves is introduced. The equivalence of four definitions of this class of curves is proved, and the possible types of the shortest curves of visibility are studied. Several exstremal problems for the curve of visibility of the circle are solved. 
@article{ZNSL_1997_246_a1,
     author = {M. L. Egorov and V. A. Zalgaller},
     title = {Visibility curves for ovals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--35},
     publisher = {mathdoc},
     volume = {246},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a1/}
}
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M. L. Egorov; V. A. Zalgaller. Visibility curves for ovals. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 2, Tome 246 (1997), pp. 13-35. http://geodesic.mathdoc.fr/item/ZNSL_1997_246_a1/