Geodesic
On preserving the orientation of triangle under quasi-isometric mapping
Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 21 (2018) no. 2, pp. 5-12 Cet article a éte moissonné depuis la source Math-Net.Ru

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In the article the sufcient sign of preserving the orientation of a triangle under quasi-isometric mapping is formulated and proved. The received result can be considered as synthesis of the Alfors' theorem on preserving the orientation of the exact triangle under quasiconformal mapping. The result is formulated for the arbitrariest triangle. It is shown that for an equilateral triangle, assessment characteristics of mapping are weaker than in the specifed theorem. The proof is based on application of the concept of distance between families of points, discussed by us earlier.
Mots-clés : orientation of triangle, triangulation
Keywords: quasiisometrique mapping, triangle nondegeneracy, meshes, computer modeling. 
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A. Yu. Igumnov. On preserving the orientation of triangle under quasi-isometric mapping. Matematičeskaâ fizika i kompʹûternoe modelirovanie, Tome 21 (2018) no. 2, pp. 5-12. http://geodesic.mathdoc.fr/item/VVGUM_2018_21_2_a0/

[1] L. Alfors, Lectures on Quasiconformal Mappings, Mir Publ., Moscow, 1969, 154 pp.

[2] A. V. Boluchevskaya, “Preserving the Orientation of a Simplex by Quasi-Isometric Mapping”, zv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 13:2, no. 1 (2013), 20–23 | Zbl

[3] A. Yu. Igumnov, “Metrization in Space Families of Points in $\mathbb{R}^n$ and Adjoining Questions”, Science Journal of Volgograd State University. Mathematics. Physics, 37:6 (2016), 40–54 | MR

[4] V. A. Klyachin, “On Homomorphisms Preserving Triangulation”, Zapiski seminara “Sverkhmedlennye protsessy”, 2009, no. 4, 169–182, VolSU Publ., Volgograd

[5] V. A. Klyachin, N. A. Chebanenko, “About Linear Prototypes of the Continuous Mappings Preserving Orientation of Simplexes”, Science Journal of Volgograd State University. Mathematics. Physics, 22:3 (2014), 56–60

[6] V. M. Miklyukov, Introduction to Non-Smooth Analysis, VolSU Publ., Volgograd, 2008, 424 pp.

[7] V. M. Miklyukov, “Some of the Problems Arising in the Problem of Triangulation Boundary Layer”, Zapiski seminara “Sverkhmedlennye protsessy”, 2006, no. 1, 154–162, VolSU Publ., Volgograd

[8] M. F. Prokhorova, “Criterions of Homeomorphism in the Theory of Grid Generation”, Zhurn. vychisl. mat. i mat. fiz., 52:5 (2012), 878–88 | Zbl

[9] M. F. Prokhorova, “Problems of Homeomorphism Arising in the Theory of Grid Generation”, Tr. IMM UrO RAN, 14:1 (2008), 112–129 | MR