I was programming 3DCG and got a 4x4 matrix like this:
Matrix =
([[0.99601513, 0.029798018, -0.0840575, 0.0],
[-0.020157712, 0.9933577, 0.11328788, 0.0],
[0.08687492, -0.11114215, 0.9900001, 0.0],
[0.023758167, 0.17372838, -0.37385422, 1.0]])
But I don't know what this matrix means.
Probably it contains position information of x, y, z, rotation information, scale information, but I don't know how to extract it.
What do you think this matrix means?
And how can I extract the following information from this matrix?
・ Rotation information around x-axis
・ Rotation information around y-axis
・ Rotation information around z-axis
Extract the $3\times 3$ rotation matrix at the upper left $$R = \pmatrix{ \,\,0.99601513&\,\,\,\,\,\,0.029798018& -0.0840575 \\ -0.020157712& \,\,0.9933577&\,\,\,\,\,\,0.11328788 \\ \,\,0.08687492& -0.11114215&\; \,\,0.9900001 }$$ The Rodrigues formula is $$\eqalign{ R &= I + N\sin\theta + N^2(1-\cos\theta) \\ }$$ where $N=n\times I$ is the skew symmetric cross-product matrix for the (normalized) axis of rotation vector $n=\left[n_1\quad n_2\quad n_3\right]^T$
Since the matrices $(I,N^2)$ are symmetric and $(N-N^T)=2N$ $$\eqalign{ R-R^T &= 2N \sin\theta \\ \frac{R-R^T}{2\sin\theta}&=N=\pmatrix{0&-n_3&n_2\\n_3&0&-n_1\\-n_2&n_1&0}\\ }$$ But the angle of rotation can also be calculated from the trace $$\eqalign{ {\rm tr}(N) &= 0 \\ {\rm tr}(N^2) &= {\rm tr}(nn^T-I) = (n^Tn-3) = -2 \\ {\rm tr}(R) &= 3+0-2(1-\cos\theta) \\ &= 1+2\cos(\theta) \quad\implies \theta = \pm0.143745 \\ }$$ Pick a sign, substitute into the above, and solve for $N$ and $n$.
To convert to Euler angles or other representations, the Wikipedia article is fairly comprehensive.