Facet Connectedness Of Arithmetic Discrete Hyperplanes With Non-Zero Shift
DISCRETE GEOMETRY FOR COMPUTER IMAGERY, DGCI 2019(2019)
Abstract
We present a criterion for the arithmetic discrete hyper-plane P(v, mu, theta) to be facet connected when theta is the connecting thickness Omega(v, mu). We encode the shift mu in a numeration system associated with the normal vector v and we describe an incremental construction of the plane based on this encoding. We deduce a connectedness criterion and we show that when the Fully Subtractive algorithm applied to v has a periodic behaviour, the encodings of shifts mu for which the plane is connected may be recognised by a finite state automaton.
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Key words
Discrete hyperplane, Connectedness, Connecting thickness, Fully subtractive algorithm, Numeration system, Finite state automaton
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