Geodesic
Directional Rational Approximations with Some Applications to Algebraic Geometry
Informatics and Automation, Birational geometry: Linear systems and finitely generated algebras, Tome 240 (2003), pp. 73-81.

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We discuss the existence and order of accuracy of directional rational approximations of points in $\mathbb R^n$. As an application, we provide a simplified version of the lemma on Diophantine approximation. We also prove a generalization of the Rationality Theorem of log-MMP on the basis of a newer geometric approach. 
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A. A. Borisov; V. V. Shokurov. Directional Rational Approximations with Some Applications to Algebraic Geometry. Informatics and Automation, Birational geometry: Linear systems and finitely generated algebras, Tome 240 (2003), pp. 73-81. http://geodesic.mathdoc.fr/item/TRSPY_2003_240_a4/

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