Igumnov A.Y. About degree of nondegeneracy of a tetrahedron

https://doi.org/10.15688/mpcm.jvolsu.2019.4.1

Alexander Y. Igumnov
Candidate of Physical and Marhematical Sciences,
Lecturer of Department of the Economic Theory, Mathematics and Information Systems,
Volzhsky Institute of Economics, Pedagogy and Law
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ul. Sovetskaja, 6, 404111 Volzhsky, Russian Federation

Abstract. In work characteristic is offered nondegeneracies of a simplex, defined through ρ-distance between classes orthogonally equivalent families of points (numbered sets of tops of a simplex). This characteristic it can be used, in particular, for drawing up criteria of quality of a grid. In work the problem of calculation is investigated ρ-distances from the set tetrahedron (a 4-vertex simplex) to a set degenerate tetrahedrons. It is shown that this the task comes down to calculation of ρ-distance from this tetrahedron to families of points (on the plane) some three classes. For the correct 4-vertex tetrahedron the ρ-distance is calculated obviously.

Key words: Nondegeneracy of a tetrahedron, nondegeneracy of a triangle, triangulation, orientation saving, quality of a grid, generation of a grid, computer simulation, quasiisometric mappings.

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About degree of nondegeneracy of a tetrahedron by Igumnov A.Y. is licensed under a Creative Commons Attribution 4.0 International License.

 

Citation in EnglishMathematical Physics and Computer Simulation. Vol. 22 No. 4 2019, pp. 5-29

 

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