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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Facet Connectedness of Discrete Hyperplanes with Zero Intercept: The General Case
verfasst von : Eric Domenjoud, Xavier Provençal, Laurent Vuillon
Erschienen in: Discrete Geometry for Computer Imagery
Verlag: Springer International Publishing
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A digital discrete hyperplane in ℤ
d
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.