Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions
A new approach to investigate the two-dimensional, regular packing of arbitrary geometric objects (GOs), using cognitive visualization, is presented. GOs correspond to congruent non-convex polygons with their associated coordinate system. The origins of these coordinate systems are accepted by objec...
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| Format: | Article |
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MDPI AG
2021-05-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/11/11/5128 |
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| author | Nikolay N. Klevanskiy Sergey I. Tkachev Ludmila A. Voloshchuk Rouslan B. Nourgaziev Vladimir S. Mavzovin |
| author_facet | Nikolay N. Klevanskiy Sergey I. Tkachev Ludmila A. Voloshchuk Rouslan B. Nourgaziev Vladimir S. Mavzovin |
| author_sort | Nikolay N. Klevanskiy |
| collection | DOAJ |
| description | A new approach to investigate the two-dimensional, regular packing of arbitrary geometric objects (GOs), using cognitive visualization, is presented. GOs correspond to congruent non-convex polygons with their associated coordinate system. The origins of these coordinate systems are accepted by object poles. The approach considered is based on cognitive processes that are forms of heuristic judgments. According to the first heuristic judgment, regular packing of congruent GOs on the plane have a honeycomb structure, that is, each GO contacts six neighboring GO, the poles of which are vertices of the pole hexagon in the honeycomb construction of packing. Based on the visualization of the honeycomb constructions a second heuristic judgment is obtained, according to which inside the hexagon of the poles, there are fragments of three GOs. The consequence is a third heuristic judgment on the plane covering density with regular packings of congruent GOs. With the help of cognitive visualization, it is established that inside the hexagon of poles there are fragments of exactly three objects. The fourth heuristic judgment is related to the proposal of a triple lattice packing for regular packing of congruent GOs. |
| first_indexed | 2024-03-10T10:49:33Z |
| format | Article |
| id | doaj.art-2cae4b8db1574b738cfeb52dc77ea036 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T10:49:33Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-2cae4b8db1574b738cfeb52dc77ea0362023-11-21T22:17:54ZengMDPI AGApplied Sciences2076-34172021-05-011111512810.3390/app11115128Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb ConstructionsNikolay N. Klevanskiy0Sergey I. Tkachev1Ludmila A. Voloshchuk2Rouslan B. Nourgaziev3Vladimir S. Mavzovin4Department of Economic Cybernetics, Saratov State Agrarian University, 410012 Saratov, RussiaDepartment of Economic Cybernetics, Saratov State Agrarian University, 410012 Saratov, RussiaDepartment of Economic Cybernetics, Saratov State Agrarian University, 410012 Saratov, RussiaDepartment of Economic Cybernetics, Saratov State Agrarian University, 410012 Saratov, RussiaDepartment of Mathematics, National Research Moscow State Construction University, 129337 Moscow, RussiaA new approach to investigate the two-dimensional, regular packing of arbitrary geometric objects (GOs), using cognitive visualization, is presented. GOs correspond to congruent non-convex polygons with their associated coordinate system. The origins of these coordinate systems are accepted by object poles. The approach considered is based on cognitive processes that are forms of heuristic judgments. According to the first heuristic judgment, regular packing of congruent GOs on the plane have a honeycomb structure, that is, each GO contacts six neighboring GO, the poles of which are vertices of the pole hexagon in the honeycomb construction of packing. Based on the visualization of the honeycomb constructions a second heuristic judgment is obtained, according to which inside the hexagon of the poles, there are fragments of three GOs. The consequence is a third heuristic judgment on the plane covering density with regular packings of congruent GOs. With the help of cognitive visualization, it is established that inside the hexagon of poles there are fragments of exactly three objects. The fourth heuristic judgment is related to the proposal of a triple lattice packing for regular packing of congruent GOs.https://www.mdpi.com/2076-3417/11/11/5128regular packing of GO on a planeoptimizationcognitive visualizationhoneycomb conjecturelattice packingdouble-lattice packing |
| spellingShingle | Nikolay N. Klevanskiy Sergey I. Tkachev Ludmila A. Voloshchuk Rouslan B. Nourgaziev Vladimir S. Mavzovin Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions Applied Sciences regular packing of GO on a plane optimization cognitive visualization honeycomb conjecture lattice packing double-lattice packing |
| title | Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions |
| title_full | Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions |
| title_fullStr | Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions |
| title_full_unstemmed | Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions |
| title_short | Regular Two-Dimensional Packing of Congruent Objects: Cognitive Analysis of Honeycomb Constructions |
| title_sort | regular two dimensional packing of congruent objects cognitive analysis of honeycomb constructions |
| topic | regular packing of GO on a plane optimization cognitive visualization honeycomb conjecture lattice packing double-lattice packing |
| url | https://www.mdpi.com/2076-3417/11/11/5128 |
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