# TikZ Planes Intersecting Hyperboloid

I would like to draw something like the image below (or as close as possible!).

I cannot copy and paste it directly into the presentation I am writing as I need to do quite a few edits.

Unfortunately this is way beyond my TikZ skills but if anyone is able to help me produce this it would be greatly appreciated and then hopefully I can take it from there and perform the edits I need (adding extra planes etc...)

If it helps, out of the planes shown, I only need the leftmost one.

Thanks very much for any help!

• This looks more like a job for Asymptote. – Henri Menke Jan 3 '16 at 22:49
• @HenriMenke Sorry I don't understand. What do you mean? – user11128 Jan 3 '16 at 22:50
• Here is a really nice tutorial for Asymptote. – Henri Menke Jan 3 '16 at 22:56
• I don't necessarily need the plane to be "hidden" in places inside/behind the hyperboloid. If it's possible to just draw a hyperboloid with a plane through the origin of the ambient space (doesn't have to be as beautiful as the picture above haha!) in TikZ then I'd probably prefer that option.... – user11128 Jan 3 '16 at 23:00

## 1 Answer

Here is a try with Asymptote (I'm a total Asymptote newbie myself). I copy-pasted parts from this answer and from this tutorial. Unfortunately, Ghostscript in Debian GNU/Linux is buggy. Therefore, I could not place labels.

settings.outformat="pdf";
settings.render = 16;
settings.prc = false;
import three;
import graph;

size(8cm,0);

currentprojection = orthographic(2,0,10, up=Y);

draw(-2X--2X,arrow=Arrow3(),L=Label("$X$", position=EndPoint));
draw(-2Y--2Y,arrow=Arrow3(),L=Label("$U$", position=EndPoint));
draw(-2Z--2Z);
label("$w \to \infty$",(2,1,0));

draw((0.5,-1,1)--(0.7,-0.2,1),arrow=Arrow3(size=5bp),L=Label("$\Pi_w$", position=BeginPoint));
draw((1.5,-1.3,0)--(1.3,-0.8,0),arrow=Arrow3(size=5bp),L=Label("$X+U = L \mathrm{e}^{w/L}$", position=BeginPoint));

pen color = red;
material surfacepen = material(diffusepen=color+opacity(1.0), emissivepen=0.5*color);
pen color = blue;
material planepen = material(diffusepen=opacity(0.4), emissivepen=0.8*color);

real f(real x) { return .5*x*x+.5; }
path3 p3 = path3(graph(f, -1, 1, operator..));

surface solidsurface = surface(p3, c=O, axis=X);
draw(solidsurface, surfacepen=surfacepen);

path3 p = (-1,1,1) -- (1,-1,1)  -- (1,-1,-1)  -- (-1,1,-1) -- cycle;
for (real s=0.0; s<=1.0; s+=0.5)
{
draw(shift(s*X)*p);
draw(surface(shift(s*X)*p), surfacepen=planepen);
}

shipout(scale(4.0)*currentpicture.fit());


• This is nice. I've never used Asymptote. However, what is the large black dot poking out for? Is that intentional? – cfr Jan 4 '16 at 0:05
• @cfr That is the projection of the arrow head. I can remove it if you wish. – Henri Menke Jan 4 '16 at 0:11
• It is not my question so you should certainly not remove it on my account. And I cannot upvote your answer again even if you do ;). – cfr Jan 4 '16 at 0:13
• Nice job +1 :D I just have a non-crucial suggestion, would it be possible to make the planes more transparent (less dark blue), and reduce the light/shadow contrast on the hyperboloid? Like I said, it's not crucial, but I think it could make the figure more pleasing to the eye. :P – Alenanno Jan 4 '16 at 1:22
• @Alenanno I processed your requests and found a computer with a non-broken Ghostscript, so now with labels. You are right, it looks much nicer this way. – Henri Menke Jan 4 '16 at 9:05