Abstract
While connected arithmetic discrete lines are entirely characterized by their arithmetic thickness, only partial results exist for arithmetic discrete hyperplanes in any dimension. In the present paper, we focus on 0-connected rational arithmetic discrete planes in ℤ3. Thanks to an arithmetic reduction on a given integer vector n, we provide an algorithm which computes the thickness of the thinnest 0-connected arithmetic plane with normal vector n.
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Reveillès, J.P.: Géométrie discrète, Calcul en Nombres Entiers et Algorithmique. Thèse d’Etat, Université Louis Pasteur, Strasbourg (1991)
Andres, E., Acharya, R., Sibata, C.: Discrete analytical hyperplanes. CVGIP: Graphical Models and Image Processing 59(5), 302–309 (1997)
Gérard, Y.: Periodic graphs and connectivity of the rational digital hyperplanes. Theoritical Computer Science 283(1), 171–182 (2002)
Brimkov, V., Barneva, R.: Connectivity of discrete planes. Theoritical Computer Science 319(1-3), 203–227 (2004)
Debled-Rennesson, I.: Etude et reconnaissance des droites et plans discrets. Thèse de Doctorat, Université Louis Pasteur, Strasbourg (1995)
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© 2006 Springer-Verlag Berlin Heidelberg
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Jamet, D., Toutant, JL. (2006). On the Connectedness of Rational Arithmetic Discrete Hyperplanes. In: Kuba, A., Nyúl, L.G., Palágyi, K. (eds) Discrete Geometry for Computer Imagery. DGCI 2006. Lecture Notes in Computer Science, vol 4245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11907350_19
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DOI: https://doi.org/10.1007/11907350_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47651-1
Online ISBN: 978-3-540-47652-8
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