On Wed, Oct 10, 2012 at 08:03:04AM +0200, Fabio Kaiser wrote: > So my concern is with finding a uniform distribution of points > on a hemisphere. Assuming L available points my approach of > checking uniformity is that: > > - Making an educated guess of a L-point distribution on hemisphere > - Mirror down to southern hemisphere to get a full sphere point distribution > LS > - Compute Spherical Harmonic matrix Y with order N <= sqrt(LS)-1 > - Compute condition Number, k = cond(Y'*Y) > - If k is close to one, the distribution is quite uniform
A valid approach, the only problem is when you truncate the actual implementation to the 'above the horizon' speakers things won't work as expected. Even if you want to reproduce only sources with positive elevation you need speakers with negative elevation, not the full down hemisphere, but some. At least if the result has to be 'Ambisonic'. You can compare creating a source image between some speakers to interpolation in the time domain. The simplest way is linear interpolation, just use the two nearest samples. In the spatial domain this corresponds to pairwise panning (2D) or VBAP (3D). Ambisonics OTOH is similar to 'constant bandwidth' interpolation. This requires more samples than just the nearest ones, i.e. below the horizon speakers even for a hemisphere. Apart from that, a simple way to get good and very practical (but slightly suboptimal in the number of speakers required) 3D layouts is to use rings at specific elevations. The number of speakers required in each ring is proportional to the cosine of the elevation. For example, a system using (bottom to top) 1 + 6 + 8 + 6 + 1 speakers (the rings of 6 at +/- 45 degrees) will do 3rd order 3D perfectly. You can leave out the nadir and zenith speakers if you don't have significant sources there, this requires only minor changes to the decoder. Ciao, -- FA A world of exhaustive, reliable metadata would be an utopia. It's also a pipe-dream, founded on self-delusion, nerd hubris and hysterically inflated market opportunities. (Cory Doctorow) _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
