Geodesic
Computation of the longest segment of a given direction in a simplex
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 147-152 
M. V. Nevskii. Computation of the longest segment of a given direction in a simplex. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 2, pp. 147-152. http://geodesic.mathdoc.fr/item/FPM_2013_18_2_a10/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $S$ be a nondegenerate simplex in $\mathbb R^n$ and let $v$ be a nonzero $n$-dimensional vector. We give the computational formulas for the length and endpoints of the longest segment in $S$ parallel to $v$.

[1] Nevskii M. V., “Ob odnom svoistve $n$-mernogo simpleksa”, Mat. zametki, 87:4 (2010), 580–593 | DOI | MR | Zbl

[2] Nevskii M. V., Geometricheskie otsenki v polinomialnoi interpolyatsii, YarGU, Yaroslavl, 2012

[3] Nevskii M., “Properties of axial diameters of a simplex”, Discrete Comput. Geom., 46:2 (2011), 301–312 | DOI | MR | Zbl

[4] Scott P. R., “Lattices and convex sets in space”, Quart. J. Math. Oxford, 36:3 (1985), 359–362 | DOI | MR | Zbl

[5] Scott P. R., “Properties of axial diameters”, Bull. Austral. Math. Soc., 39:3 (1989), 329–333 | DOI | MR | Zbl