Generalization of a 3-D resonator model for the simulation of spherical   enclosures
  A rectangular enclosure has such an even distribution of resonances that it can be accurately and efficiently modelled using a feedback delay network. Conversely, a non rectangular shape such as a sphere has a distribution of resonances that challenges the construction of an efficient model. This work proposes an extension of the already known feedback delay network structure to model the resonant properties of a sphere. A specific frequency distribution of resonances can be approximated, up to a certain frequency, by inserting an allpass filter of moderate order after each delay line of a feedback delay network. The structure used for rectangular boxes is therefore augmented with a set of allpass filters allowing parametric control over the enclosure size and the boundary properties. This work was motivated by informal listening tests which have shown that it is possible to identify a basic shape just from the distribution of its audible resonances. 
Davide Rocchesso and Pierre Dutilleux