Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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