Wow, thanks, Art. Those are quite fun and lovely! And thanks for the article that helps answer some of my immediate questions. Such a 3-D is basically fabricated based on some assumptions. At a distance of 6000 Ly, we cannot get any meaningful parallax information, right? Apparently the limit of what we can measure accurately thereby is a mere 300 Ly. So, such renderings have to be made with a lot of guessing. Fascinating work, though.
The article you linked mentions use of the colors and knowledge of the ionization energies to place some distances. I remember a discussion here once where a fortuitous light flash (I don't think it was a supernova, just a variable) was able to be used to map the shape of a cavity, as the delay of the flash bouncing off of material allowed distance measurements. Perhaps there are some other methods as well.
I don't know of any scientific value in this case, it is just a natural curiosity to me to wonder about the 3-D shape. In this case, J-P Metsavainio has gone
from the science
to the 3-D, as opposed to having a 3-D that might help establish any scientific conclusions. His images render the bright turquoise band pretty far forward in the image, whereas I would have thought it was back in the middle of the "cave".
Finally, I also have a bit of a sense of despair about the 3-D shape anyway. Our everyday experience as humans on earth gives a notion of a cave where you would often have a single light source bouncing off the walls and illuminating a real shape to a clearly-defined cavity. And if you were looking at the cave mouth from outside, you might also see the outer boundary of the rock surrounding the cave. Here, we are looking at thin gas and dust that is probably everywhere around this region, and we only see what is illuminated by some means. I always have to check myself and realize that an astronomical image such as this is not the same as the little structures I live with on Earth that may shape my thinking about what the image is. If I understand nebula images at all, yet, they show regions of higher emission or reflection. From this we can make some deductions about the shape of "regions of higher density", but that may sometimes be misleading. And they are so thin that If you were right in the middle of them, you would not even know it, without highly sensitive instruments. Pretty different than a cave wall, in some ways.
NGC 6357: The Lobster Nebula