Now showing 1 - 3 of 3
• Publication
Algorithms for Pixelwise Shape Deformations Preserving Digital Convexity
(2022)
Kenmochi, Y
;
Djerroumi, H
;
Coeurjolly, D.
;
Romon, P.
;
Borel, JP
In this article, we propose algorithms for pixelwise deformations of digital convex sets preserving their convexity using the combinatorics on words to identify digital convex sets via their boundary words, namely Lyndon and Christoffel words. The notion of removable and insertable points are used with a geometric strategy for choosing one of those pixels for each deformation step. The worst-case time complexity of each deflation and inflation step, which is the atomic deformation, is also analysed.
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• Publication
Further steps on the reconstruction of convex polyominoes from orthogonal projections
(2022)
Dulio, Pablo
;
Frosini, Andrea
;
Rinaldi, Simone
;
Vuillon, Laurent
A remarkable family of discrete sets which has recently attracted the attention of the discrete geometry community is the family of convex polyominoes, that are the discrete counterpart of Euclidean convex sets, and combine the constraints of convexity and connectedness. In this paper we study the problem of their reconstruction from orthogonal projections, relying on the approach defined by Barcucci et al. (Theor Comput Sci 155(2):321â€“347, 1996). In particular, during the reconstruction process it may be necessary to expand a convex subset of the interior part of the polyomino, say the polyomino kernel, by adding points at specific positions of its contour, without losing its convexity. To reach this goal we consider convexity in terms of certain combinatorial properties of the boundary word encoding the polyomino. So, we first show some conditions that allow us to extend the kernel maintaining the convexity. Then, we provide examples where the addition of one or two points causes a loss of convexity, which can be restored by adding other points, whose number and positions cannot be determined a priori.