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A camera at a point $(x,y,z)$ inside a dome of radius $r$ is focused on the dome wall with a radial angle $\phi$ and polar angle $\theta$. I know the values for $x,y,z,\theta, \phi$ and $r$.

How can I calculate new values for $\theta$ and $\phi$ at coordinates $(0,0,0)$ so that the camera is pinting at the same point in the dome's wall?

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    I don't know the answer, but you might look into vector algebra for the framework to develop a solution. I would try either putting the position into spherical coordinates, or stating a vector rather than two angles for the camera direction, just so you would be dealing with similar data. – 2017-01-05
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    That seems like the most straightforward approach: taking the dome’s center as the origin, convert the camera angles into a direction vector and use that to find the cartesian coordinates of the point on the dome that it’s aimed at, then convert that into spherical coordinates. – 2017-01-05

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