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In discrete-time digital models of contact of vibrating objects stability and therefore control over system energy is an important issue. While numerical approximation is problematic in this context digital algorithms may meat this challenge when based on exact mathematical solution of the underlying equation. The latter may generally be possible under certain conditions of linearity. While a system of contacting solid objects is non-linear by definition, piece-wise linear models may be used. Here however the aspect of “switching” between different linear phases is crucial. An approach is presented for exact preservation of system energy when passing between different phases of contact. One basic principle used may be pictured as inserting appropriate ideal, massless and perfectly stiff, “connection rods” at discrete moments of phase switching. Theoretic foundations are introduced and the general technique is explained and tested at two simple examples.

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Ideal three-dimensional resonators are “labeled” (identified) by infinite sequences of resonance modes, whose distribution depends on the resonator shape. We are investigating the ability of human beings to recognize these shapes by auditory spectral cues. Rather than focusing on a precise simulation of the resonator, we want to understand if the recognition takes place using simplified “cartoon” models, just providing the first resonances that identify a shape. In fact, such models can be easily translated into efficient algorithms for real-time sound synthesis in contexts of human-machine interaction, where the resonator shape and other rendering parameters can be interactively manipulated. This paper describes the method we have followed to come up with an application that, executed in real-time, can be used in listening tests of shape recognition and together with human-computer interfaces.

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