I'm analyzing and working on some clarinet facing curves.  While I 
have found that the best facing curves for sax mouthpieces are a 
radial curves, this does not appear to be the case for clarinet.

I still have to plot a few more curves, but it looks like the 
clarinet curve likes to have a generous flat spot in the middle of 
it.  It curves where it breaks away from the table (it kinda has to) 
and good ones often flip up approaching the tip.  But in the midlle 
of the curve they are often nearly flat.

On a sax, flat spots can create some edge as the reed slaps against 
them.  I would think the same thing can happen on a clarinet.  But 
mostly I hear a greater projection, even tone throughout and good 
response.