Digital planarity is defined by digitizing Euclidean planes in the three-dimensional digital space of voxels; voxels are given either in the grid-point or the grid-cube model. The paper summarizesâ€¦ (More)

Studying connectivity of discrete objects is a major issue in discrete geometry and topology. In the present work we deal with connectivity of discrete planes in the framework of ReveillÃ¨s analyticalâ€¦ (More)

In this paper we investigate the advantages of using hexagonal grids in raster and volume graphics. In 2D, we present a hexagonal graphical model based on a hexagonal grid. In 3D, we introduce twoâ€¦ (More)

Weconsider the following problem: Given a finite set of straight line segments in the plane, find a set of points of minimum size, so that every segment contains at least one point in the set. Thisâ€¦ (More)

In the framework of the theory of arithmetic geometry (Reveill. es, G/ eom/ etrie Discr. ete, Calcul en Nombres Entiers et Algorithmique, Th. ese dâ€™/ etat, Universit/ e Louis Pasteur, Strasbourg,â€¦ (More)

In this paper, we study the algebraic complexity of the knapsack problem in the form aTz = 1, z E Zn (KPR), and its Boolean version aTx = 1, x E (0, l}n (O/l-KPR), in the framework of a real numberâ€¦ (More)

We propose and discuss a novel method for enhancing books and other printed materials with layers of digital data blended with their page content. In document digitizing a patented Cluster Patternâ€¦ (More)

The theta function of a graph, also known as the Lovv asz number, has the remarkable property of being computable in polynomial time, despite being \sandwiched" between two hard to compute integers,â€¦ (More)