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Riemannian space tessellation with polyhedral room images

Abstract : We show that Riemannian geometry is the natural setting for developing polyhedral rooms of arbitrary shapes into their image rooms, and therefore counting the image sources. This new setting makes it also possible to account for scattering on particular edges, called hinges, characterized by negative deficit dihedral angles created by reflections on the adjacent faces. Using energy conservation, we show that sound rays are then deviated by the hinges, depending on their frequencies and the distances they pass by.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03598258
Contributor : Jean-Dominique Polack Connect in order to contact the contributor
Submitted on : Friday, March 4, 2022 - 5:24:16 PM
Last modification on : Thursday, March 10, 2022 - 3:31:41 AM
Long-term archiving on: : Sunday, June 5, 2022 - 7:31:22 PM

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  • HAL Id : hal-03598258, version 1

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Jean-Dominique Polack, Aidan Meacham, Roland Badeau, Jean-Christophe Valière. Riemannian space tessellation with polyhedral room images. 2022. ⟨hal-03598258⟩

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