3D graphing

you should also have a point that changes the view of the 3d graph kindof like this one https://www.desmos.com/calculator/shw1wthey5  

Is this a project or just a subjunctive situation?

How can I graph my own things on this? The formulas are so complex, I don't know where to put my functions!

You should also consider to have a perspective, zooming and create the possibility of rotating the graph with a point and with sliders so that you can also animate a axis. Made the whole chart also a bit more clear and added some more explanatory comments. 

Here: https://www.desmos.com/calculator/zcf2lhklhm 

wtf jkjk

Has anyone here played Eye Wire before? If not, then go check it out. It solves the problem of 3D movement by allowing you to scroll through a cross-section of the block. The same could be applied to graphs with 3 variables.

BTW, Eye Wire is a cool game ;-)

A bit confusing.

With something like this: https://www.desmos.com/calculator/omcaw59kxc 

You can even plot the solution to an equation f(x, y, z) = 0

Sorry its extremely laggy - turns out doing this requires a lot of calculating.

Desmos is great for 2D graphs, but 3D plotting is computation-intense and require GPU processing.
For real-time rendering of 3D equations you can try this:
http://www.runiter.com/graphing-calculator/

3D Coordinate system made with Desmos

3C Coordinate system (elaborated) made with Desmos

This is an enhanced version from the one made by Ansgar F26. It can accept any function now, instead of being stuck to only using f, g and h.

https://www.desmos.com/calculator/lqe0zjjgzc

Would someone be kind enough to help me by showing (if possible) how to place the point of intersection (s1, s2, s3) between the plane and the line through the points (i) and (r), so that it lies on the line and not next to it. The coordinates seem to be calculated correctly, but the placement in the coordinate system turns out wrong:

Line-plane-intersection

Well, after redrawing the line the point of intersection seems to be right on spot:

Line-plane-intersection

Intersection of two lines in 3d:

Line-line-intersection

After some bug-fixing:

Line 3D

Line-line-intersection

Plane 3D

Line-plane-intersection

Plane-plane-intersection-calculator

Plane-plane 3D

@DarbyRathbone That is an amazing tool, thanks so much! The thing that rules about it is that I can replace your function with what I want and all the stuff you designed still works on it.

Also @SaeidNourian thanks for that link! As cool as the workaround is, it's nice to not need a workaround.

Here's an example of a 3D graph with perspective: https://www.desmos.com/calculator/rwcweuncgp

Here's an example of what can be done with such a thing: https://www.desmos.com/calculator/kd0cyidgtx

Here's how one may go about creating one: https://www.desmos.com/calculator/m6kzuslsr6

Here's one that interprets 3D functions like the ones in Informationaether's graph, but with perspective: https://www.desmos.com/calculator/wwwwtli3ss

Here's an example of what can be done with the function method: https://www.desmos.com/calculator/s77y1vtzsb

https://www.desmos.com/calculator/razfq8pjev
I took the 3D graph and added moveable points w/ labels to make rotating the graph more intuitive. =)

The parametric 3D graph is good, but it doesn't allow graphing of explicit relations though. Only equations of the form z=f(x,y) can be graphed.