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Sphere construction on the FCC grid interpreted as layered hexagonal grids in 3D.(English)Zbl 1519.68299

Barneva, Reneta P. (ed.) et al., Combinatorial image analysis. 19th international workshop, IWCIA 2018, Porto, Portugal, November 22–24, 2018. Proceedings. Cham: Springer. Lect. Notes Comput. Sci. 11255, 82-96 (2018).
Summary: In this paper, we propose an algorithm to build discrete spherical shell having integer center and real-valued inner and outer radii on the face-centered cubic (FCC) grid. We address the problem by mapping it to a 2D scenario and building the shell layer by layer on hexagonal grids with additive manufacturing in mind. The layered hexagonal grids get shifted according to need as we move from one layer to another and forms the FCC grid in 3D. However, we restrict our computation strictly to 2D in order to utilize symmetry and simplicity.
For the entire collection see [Zbl 1400.68016].

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)

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