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Discrete & Computational Geometry 23 (2000) 465-483

Medians of discrete sets according to a linear distance

Alain Daurat 1, Alberto Del Lungo 2, Maurice Nivat 3

(2000)

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.

1 :	Laboratoire de Logique, Algorithmique et Informatique (LLAIC1)
	Université d'Auvergne - Clermont-Ferrand I
2 :	Dipartimento di Matematica
	Università degli studi di Siena
3 :	Laboratoire d'informatique Algorithmique : Fondements et Applications (LIAFA)
	CNRS : UMR7089 – Université Paris VII - Paris Diderot

Domaine

:

Informatique/Mathématique discrète

Mots Clés : discrete set – linear distance – median point – projection – connected set – convexity

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Contributeur : Alain Daurat <>

Soumis le : Mercredi 19 Avril 2006, 18:45:09

Dernière modification le : Mercredi 19 Avril 2006, 19:25:39