- There are a variety of ways to ``physically model'' a vibrating system.
- One approach involves the representation of a system in terms of ideal ``lumped'' masses, springs, and dashpots. Differential equations can be derived to describe the system motion and then discretized for computer implementation (as demonstrated for a simple example in the previous section).
- The Cordis-Anima
system by Claude Cadoz et al. at ACROE is based around these types of particle interactions.
- Another approach involves the creation of a spatially sampled grid or mesh that approximates the shape of a system. By correctly accounting for the interaction of mesh junctions and boundary conditions, the vibrations of the system can be visualized and sound can be generated by ``listening'' to a particular grid point or points.
- The Matlab script mesh2d.m
implements a 2D rectilinear digital waveguide mesh structure, allowing visualization of wave propagation over time in the structure. This same algorithm is also implemented for realtime synthesis in the
`Mesh2D`class of the Synthesis ToolKit in C++ (STK). - Some modeling techniques, such as modal synthesis and Perry Cook's PhISEM models, are based on a physical understanding of how objects vibrate and/or interact, without actually attempting to accurately model those vibrations or interactions.
- The ``so-called'' digital waveguide techniques provide an efficient and accurate method for simulating one-dimensional traveling wave motion in such media as strings and air columns.

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