For mono sources, third-order ambisonics is utilized to generate panning gains.
The general idea is that a panned mono sound can be encoded into b-format
ambisonics as:
w[i] = sample[i] * 0.7071;
x[i] = sample[i] * dir[0];
y[i] = sample[i] * dir[1];
...
and subsequently rendered using:
output[chan][i] = w[i] * w_coeffs[chan] +
x[i] * x_coeffs[chan] +
y[i] * y_coeffs[chan] +
...;
By reordering the math, channel gains can be generated by doing:
gain[chan] = 0.7071 * w_coeffs[chan] +
dir[0] * x_coeffs[chan] +
dir[1] * y_coeffs[chan] +
...;
which then get applied as normal:
output[chan][i] = sample[i] * gain[chan];
One of the reasons to use ambisonics for panning is that it provides arguably
better reproduction for sounds emanating from between two speakers. As well,
this makes it easier to pan in all 3 dimensions, with for instance a "3D7.1" or
8-channel cube speaker configuration by simply providing the necessary
coefficients (this will need some work since some methods still use angle-based
panpot, particularly multi-channel sources).
Unfortunately, the math to reliably generate the coefficients for a given
speaker configuration is too costly to do at run-time. They have to be pre-
generated based on a pre-specified speaker arangement, which means the config
options for tweaking speaker angles are no longer supportable. Eventually I
hope to provide config options for custom coefficients, which can either be
generated and written in manually, or via alsoft-config from user-specified
speaker positions.
The current default set of coefficients were generated using the MATLAB scripts
(compatible with GNU Octave) from the excellent Ambisonic Decoder Toolbox, at
https://bitbucket.org/ambidecodertoolbox/adt/
The old code would improperly handle speakers just inside or outside the
coverage area if it had to be inverted. It also didn't properly handle when
only one speaker was outside of the covered area.
The half-width ranges from 0 to pi, and essentially specifies the coverage area
around the listener. At 0, it's an infinitely small point sound and behaves
like a usual panning sound. At pi/2 it covers half the area, and at pi it
covers the whole area.
A separate "headphones" configuration may be nice to add for -90,+90, however
not many audio APIs can detect this. Ideally HRTF would be used with
headphones too, which largely ignores the speaker positions, however there
could be situations where this is unfeasible or unwanted.
