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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...2012-08-13
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    The first rotation is not influent on the result.2012-08-13
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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 $θ=\frac{π}{180}β$.2012-08-13
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    @enzotib: Thanks, I missed that, I corrected my comment.2012-08-13
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    @enzotib, damn, I was hoping OP'd figure that out on his own by actually trying to apply those transformations to his normal vector...2012-08-13
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    I don't think I described it well enough - I'm sure there needs to be three changing components here. I need to be able to move the image in the direction it is facing. If you imagine multiple flat images all originating from the same source point, all tilted slightly upwards at the same angle, but all facing in different directions relative to the z-axis, and I need them to move in the direction they are facing. So you can imaging them all moving in different directions, but pointing at the same angle upwards. If I keep α = 0, then (0, -1, 1.73) gives me the correct result...2012-08-14

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