matrix question

[grimoire]

I am reading Biped's FAQ and he shows this matrix
0.707, -0.707, 0, 10
0.707, 0.707, 0, 10
0 , 0 , 1, 0
0 , 0 , 0, 1and I understand everything about what he is saying except he says it has a 45 degree rotation around the z axis. Where does it say that?

[endash]

It also translates by (10, 10, 0).

The right column is translation, the uppler-left 3x3 matrix accounts for rotation (and then some).

If you multiply this by a vector, you should see how those sqrt(0.5) fiddle with the x and y coordinates.

[Lelik]

Basically, the upper left 2x2 submatrix is
[cos(45) -sin(45);
sin(45) cos(45)],
which corresponds to 45 degrees rotation.