Discrete circles: analytical definition and generation in the hexagonal grid

Rita Zrour (), Lidija Čomić (), Eric Andres () and Gaëlle Largeteau Skapin ()
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Rita Zrour: University of Poitiers
Lidija Čomić: University of Novi Sad
Eric Andres: University of Poitiers
Gaëlle Largeteau Skapin: University of Poitiers

Journal of Combinatorial Optimization, 2025, vol. 49, issue 1, No 14, 23 pages

Abstract: Abstract We propose an analytical definition of discrete circles in the hexagonal grid. Our approach is based on a non-constant thickness function. We determine the thickness using the (edge and vertex) flake model. Both types of circles are connected. We prove that edge flake circles are without simple points for integer radii. Incremental generation algorithms are deduced from the analytical characterization of both edge and vertex flake circles. We compare our approach with existing algorithms for the circle generation on the hexagonal grid. Our approach offers simpler algorithm and an analytical characterization that the other algorithms do not offer. The benefit of an analytical characterization is that it makes the question of the membership of a point to a primitive trivial.

Keywords: Hexagonal grid; Arithmetic discrete circles; Simple points; Flake model; Incremental algorithm (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10878-024-01246-3

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