# How to create interactive 3D graph using latex

About two years ago, I saw an interactive 3D graph online in this forum made by latex maybe using pgfplots. Basically, a user could use mouse to drag (or slide through) the pdf graph to change the angle viewing the graph. Based on the original code, I created two static graphs as shown below (please ignore the black lines added). Somehow, I lost the original code for the interactive 3d graph which I need for a current project. I have searched online for the whole afternoon and evening but still couldn't find it (maybe it is deleted by the original author), so could anyone point me to the right direction or provide a similar example so that I have something to start with. By the way, I'd like to create an interactive pdf so that I can drag to see the different views of the shape in the third picture from different angles. Thank you.

These are the code I used to create the two graphs.

\documentclass[tikz]{standalone}

\usepackage{tikz}
\usepackage{pgfplots}

\pgfplotsset{compat=1.15}

\begin{document}

% 3D
\pgfplotsset{%
colormap={myblack}{rgb255(0cm)=(0,0,0); rgb255(1cm)=(0,0,0)},
}

% First, swap axis such that we can apply polarrad->cart.
\pgfkeysgetvalue{/data point/x}\X
\pgfkeysgetvalue{/data point/y}\Y
\pgfkeyslet{/data point/y}\X
\pgfkeyslet{/data point/x}\Y
\pgfplotsaxistransformcs
{cart}%
%
% Ok, now we have cartesian. Swap axes such that we have them
% along X:
\pgfkeysgetvalue{/data point/x}\X
\pgfkeysgetvalue{/data point/y}\Y
\pgfkeysgetvalue{/data point/z}\Z
\pgfkeyslet{/data point/y}\X
\pgfkeyslet{/data point/z}\Y
\pgfkeyslet{/data point/x}\Z
}%

\begin{tikzpicture}
% This creates a color gradient for the filled area of the two functions
rgb(0bp)=(0.1,0.55,0);
rgb(100bp)=(0.8,0.9,0)
}
%
rgb(0bp)=(0.5,0.75,0);
rgb(100bp)=(0,0.5,0)
}
%
\begin{axis}[axis lines=middle,
title={},
view={30}{30},
colormap name=myblack]

\def\generatrix{(x^0.5)}

surf,
samples=30,
domain=0:3,
domain y=0:-2*pi,
z buffer=sort,
({\generatrix},y,x);

surf,
samples=30,
domain=1.5:1.6,
domain y=0:-2*pi,
z buffer=sort,
({\generatrix},y,x);

\end{axis}
\end{tikzpicture}

\begin{tikzpicture}
% This creates a color gradient for the filled area of the two functions
rgb(0bp)=(0.1,0.55,0);
rgb(100bp)=(0.8,0.9,0)
}
%
rgb(0bp)=(0.5,0.75,0);
rgb(100bp)=(0,0.5,0)
}
%
\begin{axis}[axis lines=middle,
title={},
view={90}{0},
colormap name=myblack]

\def\generatrix{(x^0.5)}

surf,
samples=30,
domain=0:3,
domain y=0:-2*pi,
z buffer=sort,
({\generatrix},y,x);

surf,
samples=30,
domain=1.5:1.6,
domain y=0:-2*pi,
z buffer=sort,
({\generatrix},y,x);

\end{axis}
\end{tikzpicture}

\end{document}


• I remember I dragged the pdf to see the graph from different angles, and I definitely think the two pictures I posted are created based on that original code (otherwise, I wouldn't had been able to do it myself), but I couldn't find it any more. But it is definitely copied from the Internet. That's why I ask whether anyone saw it and remembered it to provide some help. – shj37 Sep 20 '18 at 16:34
• The asymptote program can do this, but you have to use a pdf viewer that can support the output. As far as I know, that's only viewers made by Adobe. – Teepeemm Sep 20 '18 at 17:21
• In support of @Teepeemm's statement I'd like to encourage you to look at page 51 of this great asymptote tutorial, where you can also learn about possible pitfalls. – user121799 Sep 20 '18 at 18:43

The open source asymptote and the media9 package combine nicely to pull this off. Starting with an asymptote file from Charles Staats:

// code from https://tex.stackexchange.com/a/228963/121799

import graph3;

size(400,400,IgnoreAspect);
currentprojection=orthographic(4,4.1,2);
defaultrender.merge=true;

defaultpen(0.5mm);

//Draw the surface z^2 - x^2 - y^2=1
triple f(pair t) {
return (cos(t.y)*tan(t.x), sin(t.y)*tan(t.x),1/cos(t.x));
}

surface s=surface(f,(-1,0),(1,2*pi),32,16,
usplinetype=new splinetype[] {notaknot,notaknot,monotonic},
vsplinetype=Spline);

pen p=rgb(0,0,.7);
draw(s,rgb(.6,.6,1)+opacity(.7),meshpen=p);


We can compile this to a prc file with the command:
asy -prc -outformat prc asyfile.asy
Then we can use the tex source

\documentclass{article}
\usepackage{media9}
\begin{document}

\includemedia[
width=0.8\linewidth,height=0.8\linewidth,
3Dc2c=.37 -.72 -.58, % magic numbers
3Dcoo=109 -199 188, % magic numbers
3Droo=499, % magic number
]{alternate output}{asyfile.prc}

\end{document}


Then using pdf viewers that support the prc format (only those by Adobe, to the best of my knowledge), you can interact with the resulting pdf by clicking "alternate output" (and trusting the document and clicking again). One of the first things you'll want to do is to find the magic numbers. Fiddle with the interactive image until it looks right, and then right click on the image and select "Get Current View". This will bring up the javascript console with the numbers for you to copy and paste.

A separate thing you will probably want to do is have something better than "alternate output". Most likely, you will want to \includegraphics the same image as a static pdf, which can be created with
asy -noprc -outformat pdf asyfile.asy
Another possibility would be the same image as a static png, which comes from
asy -noprc -outformat png -render 4 asyfile.asy

Through all of this, you'll need to keep an asymptote documentation or tutorial handy. The documentation is available at the asymptote site; Marmot found a great tutorial by Charles Staats as well.

• Thank you @Teepeemm. The asymptote code ran successfully after I ran "asy test.asy" (I can rotate the graph interactively), but when I ran the latex code after I ran "asy -prc -outformat prc asyfile.asy" to successfully generate "test.prc"(does exist in the folder), an error showed: "! Undefined control sequence. <argument> \file_get_full_name:nN {test.prc}\l_mix_file_tl l.13 ]{alternate output}{test.prc}", I tried to search everywhere online but couldn't find similar questions, so please help. – shj37 Sep 25 '18 at 11:12
• To add more details, it seems the problem happens when compiling rotatable graph (similar error message) as it works fine when I compile static graph. I use win7 system. – shj37 Sep 25 '18 at 11:34
• @shj37 This looks like a problem with LaTeX3 code (which I'm not familiar with). If this happens when you've copy and pasted my code, then it may be a problem with the media9 package. Either way, it may warrant a new question. (Unless - your asy command should have produced asyfile.prc, but you're trying to include test.prc.) – Teepeemm Sep 25 '18 at 11:41
• @shj37 A probably not too helpful comment: did you try to add the full path of the prc file? (BTW, even though on my Mac everything works as described in this very nice answer, unfortunately I cannot rotate the embedded 3d file even though I use acroread and trust the file. Yet this might well be my fault.) – user121799 Sep 28 '18 at 1:17