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I'm using the node setup from this answer:

Particle color distance to empty in Eeevee?

Is there a way of having this to work without needing the origins of the affected object to be at the center of the world?

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Yes. This made me realize the setup from my answer is not optimal. You want to simply get the length of the vector from your empty to the pixel on your mesh :

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    $\begingroup$ Thanks again! The relation between these two answers will hopefully enable to understand the relation between nodes and the 3D view better. $\endgroup$
    – eobet
    Commented May 26, 2020 at 7:26

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