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I know the pose (in camera frame) of an object related to a camera in real world (results are coming from a 6d-pose estimator). In the simulation I want to replicate the same view and same position (in camera frame) of a simulated object related to a simulated camera (for the sake of simplicity I want to keep the object static and rotate the camera - so the object is placed at the origin of the world frame). In other world where should be the camera coordinates in the simulator's world frame to match the same setting in real world.

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Well, say in the real world, your object has coordinate $x(t)$, and your camera has coordinate $y(t)$ (where $x$ and $y$ are functions $\mathbb{R} \to \mathbb{R}^n$ which are parametrized by time, and $n$ is the dimension of the space you work in).

If you want your new frame of reference to be the one where $x(t)$ is always equal to $0$ (ie, your object is at the center), then your camera must have coordinate $y(t) - x(t)$. (Keep in mind that for all $t$, $x(t)$ and $y(t)$ are vectors, so this is a difference of vectors).

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    $\begingroup$ For the sake of simplicity lets ignore time. Assumes I have only on image, and wnat to replicate it in sim. I know the Tobj_wrt_camera in real. I assume that in sim: Tobj_wrt_world is known (cause i placed the obj at origin - so its identity(4))- now I am looking for Tcam_wrt_world. $\endgroup$
    – hosh0425
    Oct 22, 2022 at 21:38
  • $\begingroup$ Well, what you need to know is the relative position between the object and the camera in the real world. For example, say the object in the real world has coordinates (x,y,z), and that the camera in the real world has coordinates (a,b,c). The camera can be rewritten as (x,y,z) + [(a,b,c) - (x,y,z)]. The second part (in square brackets) is the vector going from the object to the camera. This gives you the new coordinates of the camera in your simulation - since it denotes the position relatively to the object. $\endgroup$
    – Azur
    Oct 22, 2022 at 22:02

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