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Forgive me if this isn't well phrased, it's been a while since I've done any maths!

I have a 2d image whose central point is located at the world origin, and it is in the plane $z = 0$.

If I rotate the image $\alpha$ degrees about the $z$-axis and $\beta$ degrees about the $x$-axis, how can I calculate the normal vector to the plane the image is now on?

Thanks in advance.

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...just apply the transformations you did to the plane to the normal vector as well? Alternatively, if all you have is the equation of the plane, you can always convert it to Hessian normal form... –  J. M. Aug 13 '12 at 16:05
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The first rotation is not influent on the result. –  enzotib Aug 13 '12 at 16:07
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If I understand you correctly, the original normal is $(0,0,1)^T$. Rotating this around the z-axis has no effect, and rotating by β degrees around the x-axis will rotate the normal similarly, so the normal will be $(0,-\sinθ,\cosθ)^T$, where $θ=\frac{π}{180}β$. –  copper.hat Aug 13 '12 at 16:17
    
@enzotib: Thanks, I missed that, I corrected my comment. –  copper.hat Aug 13 '12 at 16:18
    
@enzotib, damn, I was hoping OP'd figure that out on his own by actually trying to apply those transformations to his normal vector... –  J. M. Aug 13 '12 at 16:32

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