Pioneered by Michael Gerzon in the 70's, it was derived from the creation of a microphone that would capture a full 3D sound field at a point in space.
The sound directional components are encoded in spherical harmonics - look at the shape of the harmonics in this link (in the simplest case of first order Ambisonics 4 signals called "B format", W, X, Y and Z surf to this page to see a current proposal for naming of the Ambisonics channels, including the encoding formulas for them)
These components can be "decoded" to almost any regular arragement of loudspeakers (see this Wikipedia article for some pointers...
CAVEAT: Ambisonics does not include any distance cues, those have to be simulated separately...
Pros and cons
You can find a good summary of pros and cons in Wikipedia's Ambisonics article...
A very good FAQ on the topics...
Two very practical papers with a Linux flavor:
- Ambi @ Home - The search for extrafrontal intelligence by Joern Nettingsmeier
- Ardour and Ambisonics, A FLOSS approach to the next generation of sound spatialisation by Joern Nettingsmeier
Also available is Jerome Daniels thesis work on High Order Ambisonics (but you have to read french... page 150 for the math), see here for a short AES paper that has some information about HOA (page 5 for the mathematical foundation, 6 for sweet spot for various orders).
- PanB, PanB2: first order panner
- BFEncode1, BFEncode2: first order (JoshUGens)
- FMHEncode*: second order (JoshUGens)
- ... more ...
In the AmbIEM collection:
- PanAmbi2O.ar: 2nd order panner
- PanAmbi3O.ar: 3rd order panner (#w, x, y, z, u, v, s, t, r, p, q, k, l, m, n, o)