WHICH POINT CONFIGURATIONS ARE DETERMINED BY THE DISTRIBUTION OF THEIR PAIRWISE DISTANCES?-Reference-Cited by-同舟云学术

WHICH POINT CONFIGURATIONS ARE DETERMINED BY THE DISTRIBUTION OF THEIR PAIRWISE DISTANCES?

Published:2007-02 Issue:01 Volume:17 Page:31-43
ISSN:0218-1959
Container-title:International Journal of Computational Geometry & Applications
language:en
Short-container-title:Int. J. Comput. Geom. Appl.

Author:

BOUTIN MIREILLE¹,KEMPER GREGOR²

Affiliation:

1. School of Electrical and Computer Engineering, Purdue University, 465 Northwestern Avenue, West Lafayette, IN 47907, USA

2. Technische Universitët München, Zentrum Mathematik M11, Boltzmannstr. 3, D-85748 Garching, Germany

Abstract

In a previous paper we showed that, for any n ≥ m + 2, most sets of n points in ℝm 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 concentrate on the planar case m = 2 and present a reconstructibility test with running time O(n11). The cases of orientation preserving rigid motions (rotations and translations) and scalings are also discussed.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218195907002239

Reference18 articles.

1. Generalized procrustes analysis

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

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