Facet Connectedness of Discrete Hyperplanes with Zero Intercept: The General Case
Résumé
A digital discrete hyperplane in Zd is defined by a normalvector v, a shift µ, and a thickness θ. The set of thicknesses θ for whichthe hyperplane is connected is a right unbounded interval of R+ . Itslower bound, called the connecting thickness of v with shift µ, may becomputed by means of the fully subtractive algorithm. A careful study ofthe behaviour of this algorithm allows us to give exhaustive results aboutthe connectedness of the hyperplane at the connecting thickness in thecase µ = 0. We show that it is connected if and only if the sequence ofvectors computed by the algorithm reaches in finite time a specific set ofvectors which has been shown to be Lebesgue negligible by Kraaikamp& Meester.