Problem with Euler angles from YZX Rotation Matrix

Question

I've gotten stuck getting my euler angles out my rotation matrix.

My conventions are:

• Left-handed (x right, z back, y up)
• YZX
• Left handed angle rotation

My rotation matrix is built up from Euler angles like (from my code):

    var xRotationMatrix = $M([
        [1,  0,   0, 0], 
        [0, cx, -sx, 0], 
        [0, sx,  cx, 0], 
        [0,  0,   0, 1]
    ]);

    var yRotationMatrix = $M([
        [ cy, 0, sy, 0], 
        [  0, 1,  0, 0], 
        [-sy, 0, cy, 0], 
        [  0, 0,  0, 1]
    ]);
    var zRotationMatrix = $M([
        [cz, -sz, 0, 0], 
        [sz,  cz, 0, 0], 
        [ 0,   0, 1, 0], 
        [ 0,   0, 0, 1]
    ]);

Which results in a final rotation matrix as:

R(YZX) = | cy.cz, -cy.sz.cx + sy.sx,  cy.sz.sx + sy.cx, 0|
         |    sz,             cz.cx,            -cz.sx, 0|
         |-sy.cz,  sy.sz.cx + cy.sx, -sy.sz.sx + cy.cx, 0|
         |     0,                 0,                 0, 1|

I'm calculating my euler angles back from this matrix using this code:

this.anglesFromMatrix = function(m) {
    var y = 0, x = 0, z = 0;

    if (m.e(2, 1) > 0.999) {
        y = Math.atan2(m.e(1, 3), m.e(3, 3));
        z = Math.PI / 2;
        x = 0;
    } else if (m.e(2, 1) < -0.999) {
        y = Math.atan2(m.e(1, 3), m.e(3, 3));
        z = -Math.PI / 2;
        x = 0;
    } else {
        y = Math.atan2(-m.e(3, 1), -m.e(1, 1));
        x = Math.atan2(-m.e(2, 3), m.e(2, 2));
        z = Math.asin(m.e(2, 1));
    }
    return {theta: this.deg(x), phi: this.deg(y), psi: this.deg(z)};
};

I've done the maths backwards and forwards a few times, but I can't see what's wrong. Any help would hugely appreciated.

Answer 1

Your matrix and euler angles aren't consistent. It looks like you should be using

y = Math.atan2(-m.e(3, 1), m.e(1, 1));

instead of

y = Math.atan2(-m.e(3, 1), -m.e(1, 1));

for the general case (the else branch).

I said "looks like" because -- what language is this? I'm assuming you have the indexing correct for this language. Are you sure about atan2? There is no single convention for atan2. In some programming languages the sine term is the first argument, in others, the cosine term is the first argument.