Abstract

sical instruments, such as strings and flutes [Smith 1992]. Two-dimensional (2D) and threedimensional (3D) extensions of waveguides have been proposed for simulation of plates and drums [Van Duyne and Smith 1993]. A 3D mesh is needed for modeling the vibrations of air in a room [Savioja et al. 1994]. A higher-dimensional waveguide mesh is a regular array of 1-D waveguides arranged along each perpendicular dimension, interconnected at their crossings. Two conditions must be satisfied at a lossless junction connecting lines of equal impedance: (1) the sum of inputs equals the sum of outputs (flows add to zero) and (2) the signals in each crossing waveguide are equal at the junction (continuity of impedances). Based on these a difference equation can be derived for the nodes of an N-dimensional rectangular mesh: where represents in this application the signal pressure (in this application) at a junction at time step n, k is the position of the junction to be

Citations