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Communication Dans Un Congrès Année : 2022

Riemannian space tessellation with polyhedral room images

Résumé

Counting the images sources of rectangular rooms is a well known technique, based on mirroring the original rooms on all its walls in order to tesselate the Euclidian space, leading to a quadratic increase with layer order. We show that a similar mirroring technique can be applied to polygonal and polyhedral rooms of arbitrary shapes, leading to the tessellation of a Riemannian space with negative curvature. From this tessellation we derive a close formulation for counting the numbers of image sources, which increases exponentially with layer order. Thus, a bridge between rooms with flat walls and generic mixing rooms with partially curved walls is obtained.
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Dates et versions

hal-03848222 , version 1 (10-11-2022)

Identifiants

  • HAL Id : hal-03848222 , version 1

Citer

Jean-Dominique Polack, Aidan Meacham, Roland Badeau, Jean-Christophe Valière. Riemannian space tessellation with polyhedral room images. 16ème Congrès Français d'Acoustique, CFA2022, Société Française d'Acoustique; Laboratoire de Mécanique et d'Acoustique, Apr 2022, Marseille, France. ⟨hal-03848222⟩
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