Since the digital waveguide mesh is *lossless* by construction
(when modeling lossless membranes and volumes), and since it is also
linear and time-invariant by construction, being made of ordinary
digital filtering computations, there is only one type of error
exhibited by the mesh: *dispersion*. Dispersion can be
quantified as an error in propagation speed as a function of frequency
and direction along the mesh. The mesh geometry (rectilinear,
triangular, hexagonal, tetrahedral, etc.) strongly influences the
dispersion properties. Many cases are analyzed in [55]
using von Neumann analysis (see also Appendix D).

The *triangular waveguide mesh* [147] turns out to be the
simplest mesh geometry in 2D having the least dispersion
*variation* as a function of direction of propagation on the
mesh. In other terms, the triangular mesh is closer to
*isotropic* than all other known elementary geometries. The
*interpolated waveguide mesh* [401] can also be
configured to optimize isotropy, but at a somewhat higher compuational
cost.

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University