That is very difficult and requires careful coordination of the prop holding the "particular Poser material".

Could you explain more what you need to accomplish, instead of asking how you would do this particular subproblem? It may be entirely avoidable.

For example, my procedural water displacements are nodes connected to world coordinates and can be reproduced in multiple shaders, requiring no knowledge of the water's position, size, orientation, etc.

If you use an image map, then the UV mapping gets involved and it's desperately difficult to sort that out.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)