Optimization of 3D Objects Layout into a Multiply Connected Domain with Account for Shortest Distances

Stoyan, Yu. G.; Semkin, V. V.; Chugay, A. M.

doi:10.1007/s10559-014-9626-4

Cited by 16 publications

(2 citation statements)

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“…Indeed, to solve equation ( 34) with respect to x, we need to find the collection x 1 , ..., x n of its roots, that exactly coincides with the multiset G, thus making condition (33) true. Now we shall rewrite (34) in terms of its roots according to Viete formula:…”

Section: Example 5 (B ′mentioning

confidence: 99%

“…Similar to (35), the system of equations ( 40) can be considered from two points of view: first, as a system used to determine a set of solutions of equation (34); second, as a system that defines a set of varieties in R n whose intersection is exactly the set E nk (G). Thus, we found another f-representation ( 40) of E nk (G) (further referred to as (E nk (G).SR2)).…”

Section: Example 5 (B ′mentioning

confidence: 99%

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Continuous Extensions On Euclidean Combinatorial Configurations

Pichugina¹,

Yakovlev²

2022

BASM

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In this paper, we introduce a concept of the Euclidean combinatorial configuration as a mapping of a set of certain objects into a point of Euclidean space. We classify Euclidean combinatorial configurations sets based on their structure and constraints. The proposed typology forms the basis for studying continuous functional representations of combinatorial configurations. Special classes of functional extensions are introduced, their properties are described, and corresponding examples are given.

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Section: Example 5 (B ′mentioning

confidence: 99%

Section: Example 5 (B ′mentioning

confidence: 99%