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.
Domaines
Acoustique [physics.class-ph]| Origine | Fichiers produits par l'(les) auteur(s) |
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