How to parse the transformation matrix into components?

Question

C++ / C#

Greetings!
There is a 3x3 matrix, it only has rotation and movement ,
how to disassemble it into its components?
those. get back the angle of rotation and how much moved?

Answer 1

As I understand it, your 3x3 matrix is ​​\u200b\u200bhomogeneous coordinates in 2D? I would do so.
1. Make sure that the elements 3-1 and 3-2 are zero (otherwise, this is not an affine transformation).
2. Turn element 3-3 into a unit, respectively increasing the rest (by what - read what homogeneous coordinates are).
3. Elements 1-3 and 2-3 - transfer. We cut them off, we get a 2 × 2 matrix.
4. What is left should be of the form (c, s), (-s, c). If this is not the case with some error and the 2-norm of the rows is not one (also with some error), then this is not a rotation (i.e., there may be scaling or skew). It remains to take atan2(c, s) - we get an angle.

Answer 2

0_o
Of course, I have little idea about 3D graphics, but in affine transformations, the matrix seems to be 4x4 / (although, in theory, for 2D, you can throw out the third row and third column from the matrix)
Here is a good article, everything is chewed:
compgraph.tpu.ru/3d .htm