Geodesic
Right Triple Convexity
Journal of convex analysis, Tome 23 (2016) no. 4, pp. 1219-1246
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A set M in Rd is rt-convex if every pair of its points is included in a 3-point subset {x,y,z} of M such that the triangle with the corners x, y and z has a right angle at y. We characterize rt-convex sets, and for 2-connected polygonally connected sets, for 3-connected sets, for geometric graphs, and for finite sets. 
@article{JCA_2016_23_4_JCA_2016_23_4_a10,
     author = {L. Yuan and T. Zamfirescu},
     title = {Right {Triple} {Convexity}},
     journal = {Journal of convex analysis},
     pages = {1219--1246},
     year = {2016},
     volume = {23},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2016_23_4_JCA_2016_23_4_a10/}
}
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L. Yuan; T. Zamfirescu. Right Triple Convexity. Journal of convex analysis, Tome 23 (2016) no. 4, pp. 1219-1246. http://geodesic.mathdoc.fr/item/JCA_2016_23_4_JCA_2016_23_4_a10/