A digital plane is the set of integer points located between the parallel planes. We solve the
following problem: how to compute the exact normal vector of a digital plane given only a …

The critical thickness of an arithmetical discrete plane refers to the infimum thickness that
preserves its 2-connectedness. This infimum thickness can be computed thanks to a …

We present a criterion for the arithmetic discrete hyperplane to be facet connected when θ is
the connecting thickness. We encode the shift μ in a numeration system associated with the …

We show that the plane-probing algorithms introduced in Lachaud et al.(J. Math. Imaging
Vis., 59, 1, 23–39, 2017), which compute the normal vector of a digital plane from a starting …

We introduce a multi-dimensional generalization of the Euclidean algorithm and show how it
is related to digital geometry and particularly to the generation and recognition of digital …

We investigate a construction scheme for digital planes that is guided by generalized
continued fractions algorithms. This process generalizes the recursive construction of digital …

Discrete geometry is a geometry specific to computers that studies Z d structures. It appears
naturally in image analysis or 3D printing. Our goal is to find efficient algorithms to …

Le monde numérique est parsemé de structures mathématiques discrètes, destinées à être
facilement manipulables par un ordinateur tout en donnant à notre cerveau l'impression …

We work on the Réveillès hyperplane P (v, 0, ω) with normal vector v∈ R d, shift μ= 0 and
thickness ω∈ R. Such a hyperplane is connected as soon as ω is greater than some value …