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

Reply via email to