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 …

We define a generic algorithmic framework to prove a pure discrete spectrum for the
substitutive symbolic dynamical systems associated with some infinite families of Pisot …

A substitution is a rule that replaces letters by words. A famous example is the Fibonacci
substitution defined by a↦→ ab and b↦→ a. It can be iterated to produce an infinite word: a …

A digital plane is a digitization of a Euclidean plane. A plane is specified by its normal, which
is a 3D vector with integer coordinates, as considered in this case. It is established here that …

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 …

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 …

Given a finite set S of unimodular Pisot substitutions, we provide a method for characterizing
the infinite sequences over S that allow to generate a full discrete plane when, starting from …

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

This paper is meant as a short survey on analytically defined digital geometric objects. We
will start by giving some elements on digitizations and their relations to continuous …