Little work has been done in the study of loudspeaker directivity dynamics, particularly with arrays of drivers suitable for sound reinforcement applications. We have developed a mathematical model which allows the three-dimensional directivity characteristics of an arbitrarily configured arrangement of "real" drivers (that is, loudspeakers with defined amplitude, phase, and horizontal/vertical polar directivity characteristics as a function of frequency) to be simulated using a set of interactive computer programs. The mathematical basis of the author`s model is derived and the set of computer programs in the simulation package is described. Results of several case studies illustrate its utility.
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