Can someone from the dev team or other can share the fish-eye formula between single 3d position in world space or camera space into final image coordinates. (image space). as used in cycles.
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I found the answer to your question in the functions
fisheye_to_direction in the Blender source code: https://github.com/blender/blender/blob/main/intern/cycles/kernel/camera/projection.h. Even though the code talks about directions, I was able to use a version of these formulas to map 3D points from camera space to final image coordinates.