Help to plot a surface

Question

I would like to plot the surface

$S=\{(x,y,z)\in\mathbb{R}^3\ z=xy\}$

for an exercise of affine geometry but I am a novice in graphics! Can I use GeoGebra? or TikZ or Asymptote?

Answer 1

You can use the pgfplots package at will. Please check the manual for lots of other possibilities such as view angle, shader types etc.

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}
\begin{axis}[grid=both]
\addplot3[surf,shader=faceted] {x*y};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 2

run with latex->dvips->ps2pdf or with xelatex (that takes some time)

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

\psset{viewpoint=60 20 15 rtp2xyz,Decran=70,lightsrc=viewpoint}
\begin{pspicture}(-4,-6)(5,8.7)
\psframe[fillstyle=solid,fillcolor=blue!10](-4,-6)(5,8.7)
 \psSurface[ngrid=.2 .2,incolor=yellow,linewidth=0.3pt,
 axesboxed,algebraic,hue=0 1](-2,-2)(2,2){ x*y }
\end{pspicture}

\end{document}

Answer 3

You can also use asymptote, the following will produce the plot you want:

import graph3;
import grid3;
import palette;

currentprojection=perspective(12,23,1.5);

size(400,300,IgnoreAspect);

defaultrender.merge=true;

real f(pair z) {return z.x*z.y;}

surface s=surface(f,(-1/2,-1/2),(1/2,1/2),50,Spline);

draw(s,mean(palette(s.map(zpart),Rainbow())),mean(palette(s.map(zpart),Rainbow())));

grid3(XYZgrid);

Another advantage of using asymptote is that if you produce a pdf by running asy -f pdf yourfile.asy, and view it in Adobe reader, it will render the actual 3d model, and you will be able to rotate it, zoom in and out, change the way it is displayed, etc. You can then include the 3d model in your LaTeX document usingthe movie15 package.

Another option is Metapost with the mp-solid module. There is a documentation (in French) and number of examples here.