Mathematical model for a cutting path avoiding intersections

Makarovskikh, Tatiana; Panyukov, Anatoly V.

doi:10.1016/j.ifacol.2020.12.2788

Cited by 2 publications

(3 citation statements)

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“…Algorithm 6 AOE-CHAIN is used for running the algorithm NOE-CHAIN (see Algorithm 8) to obtain the non-intersecting OE-chain for plane connected graph [26].…”

Section: Noe-routesmentioning

confidence: 99%

“…Checked(v 1 (e)) := true; Mark the vertex as considered In lines 18-23, we not only change the pointers to edges, but also create a new (fictive) face F, incident to all fictive vertices and edges, and also define the ranks of fictive edges [26]. until (e = e f irst );…”

Section: Algorithm 7 Algorithm Aoe-chainmentioning

confidence: 99%

“…A rigorous formalization of these problems in terms of OE-chains is given in our paper [24]; however, the OE-chain allows the possibility of self-intersection of the trajectory. Representation of a plane Euler graph in the form of a self-intersecting Jordan curve has been announced at conferences [25,26]. We proved the necessary and sufficient conditions of PPOE-routes existence and built the polynomial algorithm PPOE-routing constructing such routes for any plane graph.…”

Section: Introductionmentioning

confidence: 99%

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Special Type Routing Problems in Plane Graphs

Makarovskikh

Panyukov

2022

Mathematics

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We considered routing problems for plane graphs to solve control problems of cutting machines in the industry. According to the cutting plan, we form its homeomorphic image in the form of a plane graph G. We determine the appropriate type of route for the given graph: OE-route represents an ordered sequence of chains satisfying the requirement that the part of the route that is not passed does not intersect the interior of its passed part, AOE-chain represents OE-chain consecutive edges which are incident to vertex v and they are neighbours in the cyclic order O±(v), NOE-route represents the non-intersecting OE-route, PPOE-route represents the Pierce Point NOE-route with allowable pierce points that are start points of OE-chains forming this route. We analyse the solvability of the listed routing problems in graph G. We developed the polynomial algorithms for obtaining listed routes with the minimum number of covering paths and the minimum length of transitions between the ending of the current path and the beginning of the next path. The solutions proposed in the article can improve the quality of technological preparation of cutting processes in CAD/CAM systems.

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“…Algorithm 6 AOE-CHAIN is used for running the algorithm NOE-CHAIN (see Algorithm 8) to obtain the non-intersecting OE-chain for plane connected graph [26].…”

Section: Noe-routesmentioning

confidence: 99%

Section: Algorithm 7 Algorithm Aoe-chainmentioning

confidence: 99%