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On Recognizing Shapes of Polytopes from Their Shadows

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Abstract

Let P and Q be two convex polytopes both contained in the interior of a Euclidean ball \(r\mathbf B ^{d}\). We prove that \(P=Q\) provided that their sight cones from any point on the sphere \(rS^{d-1}\) are congruent. We also prove an analogous result for spherical projections.

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Acknowledgements

The author is very grateful the anonymous referees for their suggestions that greatly improved the manuscript; and also to Vlad Yaskin and Dmitry Ryabogin for many fruitful and interesting discussions.

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  1. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada

    Sergii Myroshnychenko

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  1. Sergii Myroshnychenko
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Correspondence to Sergii Myroshnychenko.

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Myroshnychenko, S. On Recognizing Shapes of Polytopes from Their Shadows. Discrete Comput Geom 62, 856–864 (2019). https://doi.org/10.1007/s00454-019-00079-w

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  • DOI: https://doi.org/10.1007/s00454-019-00079-w

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