Am 10.10.2012 um 22:57 schrieb Fons Adriaensen: > 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'.
So that means, for sound source directions in the near of the horizon, speakers below the horizon also contribute and if I leave them out I am missing something and get a false localization!? > > 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. So, Ambisonics in the end is also just creating phantom sources, just using a little fancier approach!? What do you mean by 'constant bandwidth'? Do you mean spatial bandwidth dependent on the order? > 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. That's what I did so far and it yields good results. When shifting single rings in azimuth I can even optimize the condition number. Still, practically I cannot place source below the horizon, I even have to shift the horizontal ring in elevation by somewhat 15°. So, is my approach still valid for the layout and I just have to take care of that in the decoder design? What decoding approach would you recommend? best Fabio _______________________________________________ Sursound mailing list Sursound@music.vt.edu https://mail.music.vt.edu/mailman/listinfo/sursound
