Spanners of additively weighted point sets

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...

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...

A pseudo - metri for weighted point sets ?

A Pseudo-Metric for Weighted Point Sets

We present a pseudo-metric for weighted point sets. There are numerous situations, for example in the shape description domain, where the individual points in a feature point set have an associated attribute, a weight. A distance function that incorporates this extra information apart from the points' position can be very useful for matching and retrieval purposes. There are two main approaches...

On Sparse Spanners of Weighted Graphs

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