What do you call the act of mapping a 2d space into a 3d space and vice versa? Is there a word for this? I am trying to think of a word, but I don't know any word that refers to this.
The word you're looking for is "projection". This is generally used when talking about the process of mapping points in 3D space to points in 2D space.
There's no single word for the reverse process, i.e. mapping points from a 2D space to a 3D space, but that process is generally referred to as "reverse-projection".