[PD] multi-speaker panning.. problamtic maths

[Charles Henry]

I have been thinking about this problem and think that I've got a
suggestion now, but I'm struggling with the implementation.  I'll
enclose the suggested patch anyway....and hopefully someone will have
an idea how to fix it.

The equations I suggest for four signal amplitudes whose squares add
up to 1 comes from a geometric idea.
If we have a circle of radius 1/2, and center coordinates x1,y1 within
a circle (radius 1/2) centered at the origin, then the squares of the
locations of intercepts always add up to 1.

So, I tried to implement this, in a few steps:
1.  convert to polar coordinates; and if the radius is greater than 1,
limit it to 1
2. divide the radius by 2, and convert back to cartesian coordinates
3. use the following equations for signal amplitudes
s1=y1+sqrt( 0.25 - x1^2)
s2=sqrt( 0.25 - x1^2) - y1
s3=x1+sqrt( 0.25 - y1^2)
s4=sqrt( 0.25 - y1^2) - x1

s1 and s2 correspond to the speakers opposite from one another, same with s3, s4

what a mess....

Chuck
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