Weighted Model Sets and their Higher Point-Correlations

Weighted Model Sets and Their Higher Point-correlations

Examples of distinct weighted model sets with equal 2, 3, 4, 5-point correlations are given. AMS Classification Codes: 52C23, 51P05, 74E15, 60G55

How Model Sets Can Be Determined by Their Two-point and Three-point Correlations

We show that real model sets with real internal spaces are determined, up to translation and changes of density 0, by their 2and 3-point correlations. We also show that there exist pairs of real (even 1D) aperiodic model sets with internal spaces that are products of real spaces and finite cyclic groups whose 2and 3-point correlations are identical but which are not related by either translatio...

Polyhedral Model Retrieval Using Weighted Point Sets

Due to the recent improvements in laser scanning technology, 3D visualization and modelling, there is an increasing need for tools supporting the automatic search for 3D objects in archives. In this paper we describe a new geometric approach to 3D shape comparison and retrieval for arbitrary objects described by 3D polyhedral models that may contain gaps. In contrast with existing approaches, o...

Spanners of Additively Weighted Point Sets

We study the problem of computing geometric spanners for (additively) weighted point sets. A weighted point set is a set of pairs (p, r) where p is a point in the plane and r is a real number. The distance between two points (pi, ri) and (pj , rj) is defined as |pipj | − ri − rj . We show that in the case where all ri are positive numbers and |pipj | ≥ ri + rj for all i, j (in which case the po...

A pseudo - metri for weighted point sets ?