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

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dc.creatorBoutin, Mireille
dc.creatorKemper, Gregor
dc.date2003-04-15
dc.date.accessioned2026-07-07T04:56:52Z
dc.date.available2026-07-07T04:56:52Z
dc.descriptionOne way to characterize configurations of points up to congruence is by considering the distribution of all mutual distances between 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 areas of sub-triangles is used for characterizing point configurations. Again it turns out that most configurations are reconstructible from the distribution of areas, though there are counterexamples.
dc.description21 pages, latex
dc.identifierhttps://arxiv.org/abs/math/0304192
dc.identifierhttp://arxiv.org/abs/math/0304192
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/67080
dc.subjectCommutative Algebra
dc.subjectComputer Vision and Pattern Recognition
dc.subjectSymbolic Computation
dc.subject13A50;13-04;68T45
dc.titleOn reconstructing n-point configurations from the distribution of distances or areas
dc.typetext

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