order of android rotation matrix conversion

Question

android uses the following code to calculate rotation matrix:

    float Ax = gravity[0];
    float Ay = gravity[1];
    float Az = gravity[2];
    final float Ex = geomagnetic[0];
    final float Ey = geomagnetic[1];
    final float Ez = geomagnetic[2];
    float Hx = Ey*Az - Ez*Ay;
    float Hy = Ez*Ax - Ex*Az;
    float Hz = Ex*Ay - Ey*Ax;
    final float normH = (float)Math.sqrt(Hx*Hx + Hy*Hy + Hz*Hz);
    if (normH < 0.1f) {
        // device is close to free fall (or in space?), or close to
        // magnetic north pole. Typical values are  > 100.
        return false;
    }
    final float invH = 1.0f / normH;
    Hx *= invH;
    Hy *= invH;
    Hz *= invH;
    final float invA = 1.0f / (float)Math.sqrt(Ax*Ax + Ay*Ay + Az*Az);
    Ax *= invA;
    Ay *= invA;
    Az *= invA;
    final float Mx = Ay*Hz - Az*Hy;
    final float My = Az*Hx - Ax*Hz;
    final float Mz = Ax*Hy - Ay*Hx;
    if (R != null) {
        if (R.length == 9) {
            R[0] = Hx;     R[1] = Hy;     R[2] = Hz;
            R[3] = Mx;     R[4] = My;     R[5] = Mz;
            R[6] = Ax;     R[7] = Ay;     R[8] = Az;
        } else if (R.length == 16) {
            R[0]  = Hx;    R[1]  = Hy;    R[2]  = Hz;   R[3]  = 0;
            R[4]  = Mx;    R[5]  = My;    R[6]  = Mz;   R[7]  = 0;
            R[8]  = Ax;    R[9]  = Ay;    R[10] = Az;   R[11] = 0;
            R[12] = 0;     R[13] = 0;     R[14] = 0;    R[15] = 1;
        }
    }

i would like to know what is the logic behind this also, what is the order of rotation used? i want to correct the rotation using the rotation matrix. so the order of calculation by android is important.

Answer 1

Android assumes the gravity parameter is a vector lying on the world sky axis. That is if (w_1, w_2, w_3) is the world basis where w_1 is a unit vector pointing East, w_2 is a unit vector pointing North and w_3 is a vector pointing toward the sky, then the gravity parameter is a vector that is a multiple of w_3. Therefore the normalize of the gravity parameter is w_3.
Also, the code assume the geomagnetic field parameter is a vector lying on the plane spanned by w_2 and w_3 Thus the cross product of the normalize geomagnetic field parameter and the normalize gravity parameter is a unit vector orthogonal to the plane spanned by w_2 and w_3. Therefore this product is just w_1.
Now the cross product of w_3 and w_1 is w_2. Thus you get the change of basis from the device coordinate to the world coordinate.
I do not understand what do you mean by "the order of rotation used" and thus cannot answer that question.