Coordinate system

Ambisonics are usually described in a spherical coordinate system. In Ambitools, the following coordinate system is used and shown in Fig. 1:

$x = r \cos(\theta) \cos(\delta), \quad y = r \sin(\theta) \cos(\delta), \quad z = r \sin(\delta).$

 

Spherical_Coordinates.png
Figure1. Spherical coordinate system in use. A point $P (x,y,z)$ is described by radius $r$, azimuth $\theta$ and elevation $\delta$.

The azimuth angle $\theta \in [0~~360^\circ]$.
The elevation angle $\delta \in [-90^\circ~~90^\circ]$.
The convention for rotation is counterclockwise direction (i.e. trigonometric direction).

Thus, the main directions from the listener point of view are:

  • Front: $(\theta = 0^\circ, \delta=0^\circ)$
  • Left: $(\theta = 90^\circ, \delta=0^\circ)$
  • Rear: $(\theta = 180^\circ, \delta=0^\circ)$
  • Right: $(\theta = 270^\circ, \delta=0^\circ)$
  • Top: $(\theta = 0^\circ, \delta = 90^\circ)$
  • Bottom: $(\theta = 0^\circ, \delta = -90^\circ)$

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