Directional subwoofer? I was thinking.  The subwoofers that I've seen are a circular parabolic surface section (or perhaps a circular circlic(?) surface section?) and are considered omni directional. 

I would guess that this is because the longitudinal waves would have to move through the focus of the parabola/circular section, dispersing the wave in all directions in front of the speaker (and behind, depending on the acoustic shielding).
However, if a subwoofer was made from a circular triangular surface section, whose height is the same as the radius of the circular section:

Would this make the subwoofer directional?  I.e. could I point at someone very far away and it would be heard but wouldn't be heard by those not in it's path?
 A: A typical subwoofer range might go all the way up to 200Hz.  That would produce a wavelength of over 1.5m.  Lower sounds will have even longer wavelengths.  A lot of the energy from the sound is just going to step around objects that are much smaller in size.  
If that cone is small, the shape doesn't matter much.  The sound isn't being reflected inside it.
A: Audio speakers are, in general, not particularly directional. That is to say, the sound emitted from the speaker spreads out in all directions. With the exception of ultrasound frequencies, it is impossible to 'beam' sound energy along a narrow path with a speaker of practical dimensions.
This is due to the relative size of sound-waves and speakers. A normal stereo speaker will have a diaphragm 5-30 cm in diameter; a middle-C note has a wavelength just over a meter. So sound typically disperses from a speaker in all directions - similar to the way that light disperses in all directions when it passes through a pinhole.
If you wanted to have a directional sub-woofer, with sound wavelengths in the range 1-10m (~30-300 Hz), it would require an enormous active surface - bigger than the side of a barn - in order to focus or project sound in a significantly directional manner. So speaker shape will have only a very insignificant effect on sound-volume as a function of angle.
