How is parametric 3D graphing done on a 2D graph/area?

Question

I currently use desmos.com for graphs, and came across a graph which is Parametric '3D'. Desmos itself uses a 2D graph, with no Z axis to work with. There seems to be some complicated equations everywhere, and I just want a pointer on how it works and what functions they used and why. You can access the graph and see all of it's equations at https://www.desmos.com/calculator/zcf2lhklhm, and you can move certain points on the graph to affect the perspective. Thanks for any pointers! (Also, any basic equations with explanation would be GREAT!)

Answer 1

From what I can tell, it seems like it does have an ostensible z-axis. It gives three axes when you move it (black, red, blue).

The way that is would generally work would involve ideas of othrnographic projections. These are concepts covered in a linear algebra course, and they're pretty interesting. You can read more about that specifically at https://en.wikipedia.org/wiki/Orthographic_projection

I'm not sure how much of a math background you have, but that's the gist of it!