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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
38/2003

On reconstructing $n$-point configurations from the distribution of distances or areas.

Gregor Kemper and Mireille Boutin

Abstract

One way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between the points. This paper deals with the question if point configurations are uniquely determined by this distribution. After giving some counterexamples, we prove that this is the case for the vast majority of configurations. In the second part of the paper, the distribution of aread of subtriangles is used for characterizing point configurations. Again it turns out that most configurations are reconstructible from the distribution of areas, though there are counterexamples.

Received:
Apr 21, 2003
Published:
Apr 21, 2003
MSC Codes:
13A50, 13-04, 68T45
Keywords:
separating invariants, object recognition

Related publications

inJournal
2004 Repository Open Access
Mireille Boutin and G Kemper

On reconstructing n-point configurations from the distribution of distances or areas

In: Advances in applied mathematics, 32 (2004) 4, pp. 709-735