A Review of Embedding Hexagonal Cells in the Circular and Hexagonal Region of Interest (CROSBI ID 279857)
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Podaci o odgovornosti
Prvan, Marina ; Ožegovic, Julije ; Burazin Mišura, Arijana
engleski
A Review of Embedding Hexagonal Cells in the Circular and Hexagonal Region of Interest
Hexagonal cells are applied in various fields of research. They exhibit many advantages, and one of the most important is their possibility to be closely packed and to form a hexagonal grid that fully covers the Region of Interest (ROI) without overlaps or gaps. ROI can be of various geometrical shapes, but this paper deals with the circular or hexagonal ROI approximations. The main purpose of our research is to provide a short review on the literature concerning the hexagonal grid, summarizing the existing state-of-the-art approaches on embedding hexagonal cells in the targeted ROI shapes and offering application-specific advantages. We report on formulas and algebraic expressions given in the existing researches that are used for calculating the number of embedded inner hexagonal cells or their vertices and/or edges. We contribute by integrating all researches in one place, finding a connection between previously unrelated applications concerning the use of embedded hexagonal grid and extracting commonality between previous researches on whether it provides the formulas on calculating the inner hexagon cells. In case only the number of edges or vertices is provided for the targeted application, we derive formulas for calculating the number of inner hexagons. Therefore, our survey results with the overview on solving the problem of embedding hexagonal cells in the desired circular or hexagonal ROI. The contribution of the review is the following: first it provides the existing and the derived formulas for calculating the embedded hexagons and second, it provides a theoretical background that is necessary to encourage further research. Namely, our main motivation, that is the geometrical design of the one of the world’s largest CERN particle detectors, Compact Muon Solenoid (CMS) is analyzed as a source for the future research directions.
Detector design ; hexagon tessellation ; region of Interest ; regular grid
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Podaci o izdanju
10 (7)
2019.
339-348
objavljeno
2158-107X
10.14569/ijacsa.2019.0100747
Povezanost rada
Elektrotehnika, Interdisciplinarne tehničke znanosti, Računarstvo