Room Prep for Ambisonics, or the Many Ways To Bake a Pi

In further preparation for an ambisonic performance in the Davis studio, I undertook a fairly exacting survey of the speaker positions in the room in order to use the information to fine tune the ambisonic 'sweet spot'.  This is a short description of my methods and results. 

One thing I have learned implementing this project is how to translate between various 'azimuth' orientations depending on which coordinate system and compass orientation each system uses.  For example, my sensor gives out Euler angles in relation to gravity and magnetic north; on the other hand the ambisonic library's map function uses compass agnostic Cartesian coordinates or Polar coordinates.  The Cartesian coordinates of a sound position have to be extrapolated from the angles sent by the sensor using various trig manipulations.  Or if I choose to go polar coordinates, 0 degrees is to the right side of the graph on the 'x' axis.  This presents confusion when orienting the project because on a magnetic compass 0 degrees is north, which happens to be the 'back' wall of the Davis studio.  Furthermore, the polar system doesn't operate in degrees, but in Radians, so a translation has to be made there as well.  Lastly, with the 'front' of house being due south, the speaker numbering system starts with the center speaker over the top of the projector screen.

For Ambisonics, the Davis studio presents an 'irregular' (though mildly so) loudspeaker arrangement.  Ideally for Ambisonics, a evenly spaced circular array of speakers is ideal, but there are compensations written because this is rarely the case in real world situations.  The authors of the library I am using described their method in this paper from the 2014 ICMC.  Their description of the solution is "...we implement an algorithm that combines Ambisonic decoding and standard panning to offset the missing loudspeakers.  With this technique we can go up to any high order and adapt the decoding to many loudspeaker configurations.  We made tests for stereophonics, quadraphonic, 5.1 and 7.1 loudspeaker systems and other more eclectic configurations at several decomposition orders with good perceptual results."

The practical implementation in the library for irregular speaker arrangements takes the number of speakers and the progressive angle of the speakers and recalcualtes the decoding as described above.  Here is a screen shot of the help file:

 

You can see to the right of the main objects some umenus for channels and angles.  Also, inside the hoa.2d.decoder~ you can see flags for mode irregular, channels and angles.  I haven't implemented this yet, but it looks from the help file that the array starts at the top of the circle and progresses around clockwise in a compass style, as opposed to a polar radian or cartesian -pi,pi arrangement.  (the optim~ object above the decoder object is also important for irregular arrangements, it's utility is also addressed in the paper.)

So all that is left to do is to find out the angles of the speakers in relation to the room.  I did this first by establishing the very center of the room.  I marked this with masking tape and in the future it may be valuable to actually add a permanent paint spike at the spot.  After that I went around the room with the laser ruler and took the distance from the cone of the speakers to the north and the west walls.  I then subtracted those numbers from the wall to center of room distances to position them in an x-y relationship with the center of the room  I then did the operation arctan(opposite/adjacent) to get the angle measurements of all the speakers in relation to the 0 degree line represented as the line between the center of the room and the center speaker over the screen.  As the room is fairly symmetrical over that line, I assumed the east side of the room to have roughly the same measurements as the west side of the room.  Although it isn't needed for Ambisonics, I also ran the numbers through Pythagoras to get the distance from center of room to the speaker cone for future reference; I believe VBAP likes to have that number.  

Here's the results:

1. 0 degrees, 15' 2'
2. 68.7 deg, 15.65'  ( and 7)
3. 113 deg, 15.6'  (and 6)
4. 161 deg, 15.1'  (and 5)

   the  Genelecs came out to 24.4 degrees at 14.45 feet, but I don't know if they're going to be included in the array.  I am giving some thought to just using 1, 2, 4, 5 and 7.  If you look at the numbers, they are very evenly oriented in R from center of the room, and their angle is wandering around the 72 degree area, which is the even division of 360 by 5.  That would give me a regular speaker array and eliminate the need for processing for an irregular array. 

I have two goals going forward for this.  With the relationship of the speakers to the center of room now established, I'm going to go around and see, and maybe adjust, the angle of address of the speakers to tune them to the center of the room.  I also intend to double check these measurements and then prepare them into a detailed picture that can be kept on hand for further work and learning in the Davis Studio.

BREAAAK!