Medians of discrete sets according to a linear distance

Alain Daurat (1) , Alberto del Lungo (2) , Maurice Nivat (3)

1 LLAIC1 - Laboratoire de Logique, Algorithmique et Informatique
2 Dipartimento di Matematica
3 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

In this paper, we present some results concerning the median points of a discrete set according to a distance defined by means of two directions p and q. We describe a local characterization of the median points and show how these points can be determined from the projections of the discrete set along directions p and q. We prove that the discrete sets having some connectivity properties have at most four median points according to a linear distance, and if there are four median points they form a parallelogram. Finally, we show that the 4-connected sets which are convex along the diagonal directions contain their median points along these directions.

Mots clés: discrete set; linear distance; median point; projection; connected set; convexity

Domaines: Mathématique discrète [cs.DM]

Alain Daurat, Alberto del Lungo, Maurice Nivat. Medians of discrete sets according to a linear distance. Discrete and Computational Geometry, 2000, 23, pp.465-483. ⟨hal-00023083⟩