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Constant Power Panning with focus and size parameters

These are empirical controls for spatial audio rendered in multiple speakers with simple amplitude panning.

Focus

The idea of focus is to give a way to reduce the image of the source when there are a large number of speakers in the source's vicinity. We use a cosine raised to a power to give the amplitude in each speaker, then normalize the amplitude to lie between 0.0 and 1.0.

At most, only speakers in the hemisphere centered on the source direction will have non-zero contributions.

Size

To allow the apparent size of the source to exceed a hemisphere, a size parameter is used. With the size set to 0.0, we get the usual behavior, with the sound potentially affecting all speakers in the hemisphere centered toward the source. Increasing the size from 0.0 to 1.0 will increase the size to cover the entire sphere, while still being strongest in the source direction.