Mathematics – Metric Geometry
Scientific paper
2003-11-02
Mathematics
Metric Geometry
10 pages
Scientific paper
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.
Boutin Mireille
Kemper Gregor
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