Igumnov A.Yu. On Preserving the Orientation of Triangle under Quasi-Isometric Mapping
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https://doi.org/10.15688/mpcm.jvolsu.2018.2.1
Alexander Yuryevich Igumnov
Candidate of Physical and Marhematical Sciences, Lecturer, Department
of Economic Theory, Mathematics and Information Systems,
Volzhsky Institute of Economics, Pedagogy and Law
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Sovetskaya St., 6, 404111 Volzhsky, Russian Federation
Abstract. In the article the sufficient 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 specified theorem. The proof is based on application of the concept of distance between families of points, discussed by us earlier.
Key words: orientation of triangle, quasiisometrique mapping, triangle nondegeneracy, meshes, triangulation, computer modeling.
On Preserving the Orientation of Triangle under Quasi-Isometric Mapping by Igumnov A.Yu. is licensed under a Creative Commons Attribution 4.0 International License.
Citation in English: Mathematical Physics and Computer Simulation. Vol. 21 No. 2 2018, pp. 5-12
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