Riemannian space tessellation with polyhedral room images
Résumé
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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