Commits on Jun 9, 2024

1. Correct DOA Rotation …

   Reasoning
   ---------
   
   Let
   r: DOA in room coordinates
   h: DOA in head coordinates
   Z: Rotation Matrix around z-axis with azimuth angle of head
   Y: Rotation Matrix around y-axis with elevation angle of head
   
   We start with the fact that the DOA in head coordinates can be forward
   transformed to the room coordinates by
   r = ZYh
   because the z-direction must only depend on elevation (Y) and not on
   azimuth (Z). Since the matrix Z does not touch the z-component, this
   order ensures that.
   
   Invert the formula by multiplying from the left by Y^(-1)Z^(-1):
   h = Y^(-1)Z^(-1)r,
   yielding the now implemented formula.
   
   Note that the inverse rotation matrix is either the transpose or the
   rotation matrix with the negative angle. The negative angle variant is
   now implemented.
   
   Example
   -------
   
   Imagine a auralizing a source straight above the listener, i.e. at 90°
   elevation. The listener is looking upwards 45° and and 90° to the left.
   
   By intuition, the source should be heard from the front at 45° upwards
   elevation.
   
   Imagine first rotating around the y-axis by -45° (downwards), then
   around the z-axis by -90° (right). This is wrong, as you would hear the
   source from the right instead of the front.
   
   Instead, imagine first rotating around the y-axis by -90° (right), then
   the y-axis by -45° (downwards). In the first step, the location of the
   source is not changed at all, then it is moved to the front. This is
   as expected.

   

   Firionus committed Jun 9, 2024
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