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The Rectilinear 2D Mesh

Figure C.32: The 2D rectilinear digital waveguide mesh.
\includegraphics[width=4in]{eps/SchematicWaveguideMesh}

Figure C.32 shows the basic layout of the rectilinear 2D waveguide mesh. It can be thought of as simulating a plane using 1D digital waveguides in the same way that a tennis racket acts as a membrane composed of 1D strings.

At each node (string intersection), we have the following simple formula for the node velocity $ v$ in terms of the four incoming traveling-wave components:

$\displaystyle v = \frac{\mbox{in}_{1} + \mbox{in}_{2} + \mbox{in}_{3} + \mbox{in}_{4}}{2}
$

By continuity of velocity in a series connection (all string endpoints must move together at the node), the outgoing velocity-wave components must be given by

$\displaystyle \hbox{out}_k = v -$   in$\displaystyle _{k}, \qquad k=1,2,3,4.
$

This computation is performed by the following Faust [155] program:
import("math.lib");
process=bus(4)<:par(i,4,*(-1)),(bus(4):>*(.5)<:bus(4)):>bus(4);


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA