Which Point Configurations are Determined by the Distribution of their Pairwise Distances?

Mireille Boutin; Gregor Kemper

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arXiv · math/0311004

Which Point Configurations are Determined by the Distribution of their Pairwise Distances?

Mireille Boutin·Gregor Kemper

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Abstract

In a previous paper we showed that, for any $n \ge m+2$, most sets of $n$ points in $\RR^m$ are determined (up to rotations, reflections, translations and relabeling of the points) by the distribution of their pairwise distances. But there are some exceptional point configurations which are not reconstructible from the distribution of distances in the above sense. In this paper, we present a reconstructibility test with running time $O(n^{11})$. The cases of orientation preserving rigid motions (rotations and translations) and scalings are also discussed.

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BibTeX RIS

Mireille Boutin, Gregor Kemper. 2003-11-02. Which Point Configurations are Determined by the Distribution of their Pairwise Distances?. https://arxiv.org/abs/math/0311004

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