A pdf file is a program, written in the postscript language, directing a 2D printer to create some 2D object. I can't print copies of someone's book and sell them without permission based on the argument that the book is the output of the PDF program.
I don't see how adding an extra D changes that.
It doesn't. But not all pdf's are copyrightable.
You can't print someone's book because the book is a work of literary authorship. If you get a non-copyrightable pdf, such as a simple list of facts or ingredients, then you can print that and sell it. We will likely see something similar happen in the 3D printing world.
At issue here is not whether or not the printer has two dimensions or three, but rather if the underlying object would be considered an original work of authorship. Probably not.
If you compare this to the fashion industry, for example, where a designs for clothing are *not* eligible for copyright. The fashion industry has responded to this by elevating trademarkable labels to be elements of fashion themselves. I can take a Tommy Hilfiger t-shirt and produce another shirt with its dimensions exactly, but I can't put that logo on it.