Confusion about Rotation matrices from Euler Angles

Posted by xEnOn on Game Development See other posts from Game Development or by xEnOn
Published on 2012-10-18T18:45:51Z Indexed on 2012/10/18 23:18 UTC
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math

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rotation

I am trying to learn more about Euler Angles so as to help myself in understanding how I can control my camera better in the game.

I came across the following formula that converts Euler Angles to rotation matrices: enter image description here

In the equation, I could see that the first matrix from the left is the rotation matrix about x-axis, the second is about y-axis and the third is about z-axis.

From my understanding about ordinary matrix transformations, the later transformation is always applied to the right hand side. And if I'm right about this, then the above equation should have a rotation order starting from rotating about z-axis, y-axis, then finally x-axis.

But, from the symbols enter image description here it seems that the rotation order start rotating about x-axis, then y-axis, then finally z-axis. What should the actual order of the rotation be?

Also, I am confuse about if the input vector, in this case, would be a row vector on the left, or a column vector on the right?

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