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MiS Preprint

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

Gregor Kemper and Mireille Boutin


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.

MSC Codes:
13A50, 13-04, 68T45
separating invariants, object recognition

Related publications

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