Plotting intersection of a sphere with a plane

Question

I've made the following code:

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{tikz}
\usepackage[english]{babel}
\usetikzlibrary{arrows}

\begin{document}

\begin{tikzpicture}

\shade[ball color=red] (0,0,0) circle (2cm);
\fill[opacity=0.5,blue] (-3,0,1) -- (-1,2,1) -- (5,2,1) -- (3,0,1) -- cycle;

\end{tikzpicture}


\end{document}

Which I've adapted from this post (thank you very much!). And which produces:

But I want to do is this:

Question: How could I do the intersection of the sphere with the plane?

Does it need to be "true" 3D? Or is it sufficient to look like it? The former is more difficult (especially with TikZ), the latter is way less flexible. — Tom Bombadil, Dec 05 '15 at 02:32
It doesn't need to be true 3D. I just want it to look like if it was. ;) — francolino, Dec 05 '15 at 02:34
Relevant: http://tex.stackexchange.com/questions/169681/draw-parallels-of-a-sphere-with-tikz/169685#169685 — hpekristiansen, Dec 05 '15 at 03:26
it helps if the ellipse has the same aspect ration (width to height) at the parallelogram. — John Kormylo, Dec 05 '15 at 04:13

score 13 · Answer 1 · answered Dec 05 '15 at 04:23

Here's a solution with Asymptote:

The code to produce it:

\documentclass{standalone}
\usepackage{asypictureB}

\begin{document}

\begin{asypicture}{name=SphereAndPlane}
settings.outformat = "png";
settings.render = 8;
size(10cm, 0);  // Final image will be 10cm wide, unlimited height.
import three;   // Enable three-dimensional functionality.
currentprojection = orthographic(2,5,1);

draw(unitsphere, red);
draw(surface((-2,-2,0) -- (-2,2,0) -- (2,2,0) -- (2,-2,0) -- cycle), blue + opacity(0.5));

\end{asypicture}

\end{document}

% file: foo.tex
% to compile: pdflatex --shell-escape foo
%
% For MikTeX users: Asymptote requires a separate program that cannot be installed
% by the package manager. You can get the installation file from
% https://sourceforge.net/projects/asymptote/files/2.35/
% (specifically, the file ending in setup.exe).

If you are using a relatively recent version of MacTeX (or, I assume, TeX Live), with a full installation, this should just work. If you are using MikTeX, you will need to install the Asymptote program as described in the comments after \end{document}.

Nice! Sorry I forgot to mention Asymptote. Probably one day I'll have a look at it. — Tom Bombadil, Dec 05 '15 at 09:21

score 11 · Answer 2 · answered Dec 05 '15 at 03:05

Here you have an idea for both: the "fake" 3D draws two planes, one "behind" the ball, and one "in front of". The 3D effect is achieved by cutting out a half ellipse. The "less fake" 3D approach uses pgfplots to first draw the lower hemisphere, then the surface, and then the upper hemisphere. Probably someone will upload a pstricks solution, as it is vastly superior at 3D stuff.

Code

\documentclass[tikz, border=2mm]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}

\begin{document}

\begin{tikzpicture}
    \fill[blue!50!gray, opacity=0.7] (0,0) -- (5,0) -- (4,2) -- (1,2) -- cycle;
    \shade[ball color=red] (2.5,0) circle (1);
    \fill[blue!50!gray, opacity=0.7] (0,0) -- (1.5,0) arc (180:360:1 and 0.5) -- (5,0) -- (6,-2) -- (-1,-2) -- cycle;
\end{tikzpicture}

\begin{tikzpicture}
    \begin{axis}
    [   axis equal,
        hide axis,
        view={30}{30},
        z buffer=sort,
    ]
        \addplot3
        [   domain=0:360,
            y domain=0:180,
            surf,
            shader=flat,
            red,
            opacity=0.5
        ] ({sin(y)*cos(x)},{sin(y)*sin(x)},{cos(y)});
        \addplot3
        [   domain=-2:2,
            y domain=-2:2,
            surf,
            shader=flat,
            blue,
            opacity=0.5,
        ] (x,y,0);
        \addplot3
        [   domain=0:360,
            y domain=0:90,
            surf,
            shader=flat,
            red,
            opacity=0.5,
        ] ({sin(y)*cos(x)},{sin(y)*sin(x)},{cos(y)});
    \end{axis}
\end{tikzpicture}

\end{document}

Output

score 8 · Answer 3 · answered Dec 05 '15 at 06:59

Run with xelatex

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}

\begin{document}
\psset{viewpoint=50 0 10 rtp2xyz,Decran=70,lightsrc=80 20 70,
       linewidth=0.001pt,action=none}
\begin{pspicture}[solidmemory](-4,-2)(4,2)
%\axesIIID(3,3,6)
\psSolid[object=plan,definition=equation,args={[0 0 1 0]},
base=-3 3 -2 2,ngrid=20 20,fillcolor=red!30,name=B1]
\psSolid[object=sphere,r=1,fillcolor=cyan,ngrid=18 36,
name=C1,action=none]
\psSolid[object=fusion,base=B1_s C1,action=draw**]
\end{pspicture}

\end{document}

I knew I could count on you to provide a pstricks solution :-) — Tom Bombadil, Dec 05 '15 at 09:20

Plotting intersection of a sphere with a plane

3 Answers3

Code

Output