How to draw a circular cone

Question

I want to draw the circular cone given by the equation z²=x²+y². (I do not mind using any given package.) I tried to use the pst-solides3d package with the help of its manual to generate the following code. However, my code produced only the axes. I received the following error messages (I am using TeXShop with XeLaTeX and "TeX and DVI" options selected to typeset):

** WARNING ** Image format conversion for PSTricks failed.
** WARNING ** Interpreting special command pst: (ps:) failed.

\documentclass{article}
\usepackage{pst-solides3d}
\begin{document}

\psset{Decran=20}
\begin{pspicture}(-5,-5)(5,5)
\axesIIID(4,4,4)
\psSurface(0,0)(3,3){sqrt(x^2+y^2)}
\psSurface(-3,-3)(0,0){-sqrt(x^2+y^2)}
\end{pspicture}

\end{document}

Jake · Answer 1 · 2011-09-18T04:50:00.287

You could also use pgfplots for this. To add a three dimensional surface, use \addplot3 [surf] {<expression for z>}. You could produce the cone using

\documentclass{article}
\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}[
    domain=-5:5,
    y domain=-5:5,
    xmin=-10,
    xmax=10,
    ymin=-10,
    ymax=10,
    restrict z to domain=-5:5]
\addplot3 [surf,shade=interp] {sqrt(x^2 + y^2};
\addplot3 [surf] {-sqrt(x^2 + y^2};
\end{axis}
\end{tikzpicture}

\end{document}

If you want the grid points to lie on isolines, you can use the syntax \addplot3 ({<x expression>}, {<y expression>}, {<z expression}); for parametric plots:

\begin{tikzpicture}
\begin{axis}[
    domain=0:5,
    y domain=0:2*pi,
    xmin=-10,
    xmax=10,
    ymin=-10,
    ymax=10,
    samples=20]
\addplot3 [surf,z buffer=sort] 
    ({x*cos(deg(y))},
     {x*sin(deg(y))},
     {x});
\addplot3 [surf,z buffer=sort] 
    ({x*cos(deg(y))},
     {x*sin(deg(y))},
     {-x});
\end{axis}
\end{tikzpicture}

score 6 · Accepted Answer · edited Apr 13 '17 at 12:35

PSTricks needs to know that you want to define your surface algebraically, and not using Reverse Polish Notation (RPN).

If you want to work algebraically, then you have to define the function first using \defFunction[algebraic]... as shown below.

\documentclass{article}
\usepackage{pst-solides3d}

\begin{document}

\psset{Decran=20}
\begin{pspicture}(-5,-5)(5,5)
\axesIIID(4,4,4)
\defFunction[algebraic]{cone}(x,y)
   {x}
   {y}
   {sqrt(x^2+y^2)}
\defFunction[algebraic]{negcone}(x,y)
   {x}
   {y}
   {-1*sqrt(x^2+y^2)}
\psSolid[object=surfaceparametree,base=0 3 0 3,
  ngrid=20 20,
  function=cone]
\psSolid[object=surfaceparametree,base=0 3 0 3,
  ngrid=20 20,
  function=negcone]
\end{pspicture}

\end{document}

For more information:

see the documentation: texdoc pst-solides3d
see the PSTricks gallery: http://www.tug.org/PSTricks/main.cgi?file=Examples/Gallery3D/Gallery3D
and the answer to Ghostscript error with a surface in pst-solides-3d

EDIT

Alternatively, you could follow the examples in Chapter 8 of the pst-solides3d documentation:

\documentclass{article}
\usepackage{pst-solides3d}

\begin{document}

\centering
\psset{unit=0.5,viewpoint=50 40 30 rtp2xyz}
\begin{pspicture}(-7,-8)(7,8)
 \psSurface[ngrid=.25 .25,incolor=yellow,fillcolor=red,
algebraic](-4,-4)(4,4){sqrt(x^2+y^2)}
 \psSurface[ngrid=.25 .25,incolor=yellow,fillcolor=blue,
axesboxed,algebraic,Zmin=-6,Zmax=6](-4,-4)(4,4){-1*sqrt(x^2+y^2)}
\end{pspicture}

\end{document}

enter image description here

score 6 · Answer 3 · edited Sep 18 '11 at 15:11

@jake and @ cmhughes: Thank you very much. Very nice. I appreciate it.

@cmhughes: I used your idea to parametrize the cone using polar parameters.

\documentclass{article}
\usepackage{pst-solides3d}
\usepackage{pst-3dplot}

\begin{document}

\psset{Decran=20, linecolor=gray}
\begin{pspicture}(-5,-5)(5,5)
\defFunction[algebraic]{cone}(r,t)
{r*cos(t)}
{r*sin(t)}
{r}
\psSolid[object=surfaceparametree,base=-3 3 0 360,
ngrid=36 60,
function=cone,incolor=white]
\axesIIID(4,4,5)
\end{pspicture}
\end{document}

enter image description here

@jake: I realized that you are using polar parameters already. A slightly simplified version is given below.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
domain=-5:5,
y domain=0:2*pi,
xmin=-10,
xmax=10,
ymin=-10,
ymax=10,
samples=20]
\addplot3 [surf,z buffer=sort] 
({x*cos(deg(y))},
{x*sin(deg(y))},
{x} );
\end{axis}
\end{tikzpicture}
\end{document}

enter image description here

@Sony: You're welcome. I cropped your images. Don't forget to up-vote and accept whichever answer you deem most appropriate to your question. — cmhughes, Sep 18 '11 at 15:09

How to draw a circular cone

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