I'm trying to implement a 2D isometric game, well diametric with a 2:1 pixel ratio. Trouble is the rotation matrix I made doesn't seem to work. It's off by a little bit and doesn't line up: enter image description here

I'm not sure if I did my rotation matrix correctly:

$$ \begin{bmatrix} 1/\sqrt{2} & 0 & -1/\sqrt(2) \\ 1\sqrt{10} & 2/\sqrt{5} & -1/\sqrt{10} \\ -1\sqrt{2/5} & 1/\sqrt{5} & \sqrt{2/5} \\ \end{bmatrix} $$

For the angles I used 45 degrees and arctan(1/2) which is roughly 26.5 degrees. I need all 3 axis, as I'm using lights and need the tiles to have depth.


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