How to know that object has been rotated only in 15 degree chunks in 3D?

I have an 3D object in 3D space oriented in some orientation. How can I know it has been rotated from its initial rotation q (in euler angles: 0, 0, 0) only in arbitrary number of 15 degree rotations in any axis. E.g, rotated in X-axis 4*15 degrees, and in Y-axis 7*15 degrees and in Z-axis 13*15 degrees. How can I detect this?

I have tried to take euler angles from the object's rotation matrix but it seems to detect the situation corre开发者_C百科ctly only if I rotate only in one axis. If I start to mix X,Y and Z axis 15 degree rotations, the euler angles gets messed up.

I am 100% sure that the object has been rotated only in 15 degree chunks.

Rotation matrices can only be decomposed into quaternions, I believe, and cannot be decomposed into per-axis rotations.

I am not sure what math library you are using, but, if provided, you could use quaternions, which will quite straightforward the functionality you want. They can be translated to rotation matrices afterwards.

Rotations are not commutative, therefore describing them with Euler angles is problematic if you don't know the right order. If you know the order, you can set up an equation system with a multiplication of three rotation matrices (parameterized by the rotation angle) on one side and the final rotation matrix on the other side. Gives you three equations and three unknowns. But watch out for singularities in Euler angle representation!

If you can, the dead simplest way is to store both the components (float3 m_Translation, m_Rotation, m_Scale) and a matrix that is updated whenever they change (float4x4 m_Matrix). To get the data out, simply grab the vector for that part and return it. The memory use is small (12-16 floats) and computational overhead is minimal (recalculate the matrix when a part is updated).

However, if that can't be done, Google suggests you can decompose rotation matrices with a bit of work like so. It does take a chunk of math.

As noted in that page, the D3DX libraries also have a function to decompose matrices: D3DXMatrixDecompose.