Geodesic
From standard monomial theory to semi-toric degenerations via Newton--Okounkov
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 78 (2017) no. 2, pp. 331-356

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The Hodge algebra structures on the homogeneous coordinate rings of Grassmann varieties provide semi-toric degenerations of these varieties. In this paper we construct these semi-toric degenerations using quasi-valuations and triangulations of Newton–Okounkov bodies. 
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     author = {X. Fang and P. Littelmann},
     title = {From standard monomial theory to semi-toric degenerations via {Newton--Okounkov}},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
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X. Fang; P. Littelmann. From standard monomial theory to semi-toric degenerations via Newton--Okounkov. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 78 (2017) no. 2, pp. 331-356. http://geodesic.mathdoc.fr/item/MMO_2017_78_2_a6/