Abstract
A digital discrete hyperplane in ℤd is defined by a normal vector v, a shift μ, and a thickness θ. The set of thicknesses θ for which the hyperplane is connected is a right unbounded interval of ℝ + . Its lower bound, called the connecting thickness of v with shift μ, may be computed by means of the fully subtractive algorithm. A careful study of the behaviour of this algorithm allows us to give exhaustive results about the connectedness of the hyperplane at the connecting thickness in the case μ = 0. We show that it is connected if and only if the sequence of vectors computed by the algorithm reaches in finite time a specific set of vectors which has been shown to be Lebesgue negligible by Kraaikamp & Meester.
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Domenjoud, E., Provençal, X., Vuillon, L. (2014). Facet Connectedness of Discrete Hyperplanes with Zero Intercept: The General Case. In: Barcucci, E., Frosini, A., Rinaldi, S. (eds) Discrete Geometry for Computer Imagery. DGCI 2014. Lecture Notes in Computer Science, vol 8668. Springer, Cham. https://doi.org/10.1007/978-3-319-09955-2_1
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DOI: https://doi.org/10.1007/978-3-319-09955-2_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-09954-5
Online ISBN: 978-3-319-09955-2
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