Computes the inclination matrix I as well as the rotation matrix R transforming a vector from the device coordinate system to the world's coordinate system which is defined as a direct orthonormal basis, where:

• X is defined as the vector product Y.Z (It is tangential to the ground at the device's current location and roughly points East).
• Y is tangential to the ground at the device's current location and points towards the magnetic North Pole.
• Z points towards the sky and is perpendicular to the ground.

By definition:

[0 0 g] = R * gravity (g = magnitude of gravity)

[0 m 0] = I * R * geomagnetic (m = magnitude of geomagnetic field)

R is the identity matrix when the device is aligned with the world's coordinate system, that is, when the device's X axis points toward East, the Y axis points to the North Pole and the device is facing the sky.

I is a rotation matrix transforming the geomagnetic vector into the same coordinate space as gravity (the world's coordinate space). I is a simple rotation around the X axis. The inclination angle in radians can be computed with SensorManager.GetInclination(Single[]).

Each matrix is returned either as a 3x3 or 4x4 row-major matrix depending on the length of the passed array:

If the array length is 16:

   /  M[ 0]   M[ 1]   M[ 2]   M[ 3]  \
   |  M[ 4]   M[ 5]   M[ 6]   M[ 7]  |
   |  M[ 8]   M[ 9]   M[10]   M[11]  |
   \  M[12]   M[13]   M[14]   M[15]  /

Note that because OpenGL matrices are column-major matrices you must transpose the matrix before using it. However, since the matrix is a rotation matrix, its transpose is also its inverse, conveniently, it is often the inverse of the rotation that is needed for rendering; it can therefore be used with OpenGL ES directly.

Also note that the returned matrices always have this form:

   /  M[ 0]   M[ 1]   M[ 2]   0  \
   |  M[ 4]   M[ 5]   M[ 6]   0  |
   |  M[ 8]   M[ 9]   M[10]   0  |
   \      0       0       0   1  /

If the array length is 9:

   /  M[ 0]   M[ 1]   M[ 2]  \
   |  M[ 3]   M[ 4]   M[ 5]  |
   \  M[ 6]   M[ 7]   M[ 8]  /

The inverse of each matrix can be computed easily by taking its transpose.

The matrices returned by this function are meaningful only when the device is not free-falling and it is not close to the magnetic north. If the device is accelerating, or placed into a strong magnetic field, the returned matrices may be inaccurate.

[Android Documentation]