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Stereo Example 1:
The Mid envelope is constrained to a maximum radius of 1. The area of the blue cardioid is aπ. It may be desirable to clamp the Mid channel by area. Note that though the area varies in a, this is consistent with M/S recording: b= 0 (a circle) and b=1 (cardioid) are both classic recording formats.
The dashed lines inside the Mid and Side envelopes show the unsquared functions
Mid: r = a + b cos(kθ)
Side: r = W sin(kθ)
ToDo: Hold the power constant when adjusting the stereo width. (I.e. determine if the ears agree that the power is unaffected by the Side channel).
Then Onward to mappings among the various perspectives (microphone, source, listener) and test solutions (making recordings and trying it).
This is just one step. There are a very very many such steps to move away from interpolating mono files betwixt speakers, and toward spatialize audio files as images. But there is no fundamental difficulty modeling the problem. Each step follows in an elementary fashion from the previous.
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