Geodesic
The mapping of integer sets and Euclidean approximations
Numerical methods and programming, Tome 8 (2007) no. 1, pp. 10-19.

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The development of discrete models for representations of nonconvex parts of $R^3$ space and the solution of routing problems with a metric that approximates the Euclidean metric on these models continue to remain fundamental in the fields of robotics, geoinformatics, computer vision, and designing of VLSI. The paper deals with a lattice-cellular model. The main attention is paid to the mapping of the integer sets $Z^2$, $Z^3$, $Z^4$ onto itself, the construction of a lattice fan under a given accuracy of metric approximation, the decomposition of equidistant graphs, and the combined application of lattice and polyhedral models for a software system of metric-topological constructions.
Keywords: Euclidean metric аpproximation , prime edges, metric neighborhood, lattice fan, topological processor.
Mots-clés : fan triangulation, equidistant graph 
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     author = {G. G. Ryabov and V. A. Serov},
     title = {The mapping of integer sets and {Euclidean} approximations},
     journal = {Numerical methods and programming},
     pages = {10--19},
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     volume = {8},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2007_8_1_a2/}
}
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G. G. Ryabov; V. A. Serov. The mapping of integer sets and Euclidean approximations. Numerical methods and programming, Tome 8 (2007) no. 1, pp. 10-19. http://geodesic.mathdoc.fr/item/VMP_2007_8_1_a2/