\section{Presentation}

The command has the following form:
\begin{verbatim}
\psSurface[options](xmin,ymin)(xmax,ymax){equation of the surface z=f(x,y)}
\psSurface*[options,r=...,xytranslate](xmin,ymin)(xmax,ymax){equation of the surface z=f(x,y)}
\end{verbatim}
 with the same options which apply to solids, and these additional
ones:
\begin{itemize}
  \item The surface grid is defined by the parameter
    \texttt{\Lkeyword{ngrid}=n1 n2}, which has these specifics:

\begin{minipage}{1\linewidth}
  \begin{itemize}
    \item If \texttt{n1} and/or  \texttt{n2} are integers, the
      number(s) represent(s) the number of grids following $Ox$ and/or
      $Oy$.
    \item If \texttt{n1} and/or  \texttt{n2 } are decimals, the
      number(s) represent(s) the incrementing steps following $Ox$
      and/or $Oy$.
    \item If \texttt{\Lkeyword{ngrid}=n}, with only one parameter value,
      the number of grids, or the incrementing steps,
      are identical on both axes.
    \item \Lkeyword{r} defines the length of an origin vector (radius) which controls
	the calculated points which must be inside the sphere, defined by the vector $\vec{r}$.
    \item \Lkeyword{xytranslate}\verb|= x y| defines the translation of the vector in the
	$x-y$-plane. 
	
  \end{itemize}
\end{minipage}

  \item \Lkeyword{algebraic}: this option allows you to write the function in
algebraic notation; \texttt{pstricks.pro} meanwhile contains
the code \texttt{AlgToPs}
   from Dominique \textsc{Rodriguez}, which allows this notation and which is
included in the \texttt{pstricks-add.pro} file. This version
of \texttt{pstricks} %%%% should this be pstricks-add(.pro) ??
   is provided with \texttt{pst-solides3d}. If necessary, you must load the
\texttt{pstricks-add} package in the document preamble.
  \item \Lkeyword{grid}: by default the grid is activated. If the
  option \Lkeyword{grid} is used, the grid will be deactivated! %%%% this seems perverse; would [nogrid] be better?
  \item \Lkeyword{axesboxed}: this option allows you to draw the 3D
  coordinate axes
in a semi-automatic way, but because of the need to specify
the limits of $z$ by hand this option is deactivated by
default:
   \begin{itemize}
     \item \Lkeyword{Zmin}: minimum value;
     \item \Lkeyword{Zmax}: maximum value;
     \item \Lkeyword{QZ}: allows a vertical shift of the coordinate axes
with the value \texttt{\Lkeyword{QZ}=value};
     \item \Lkeyword{spotX}: alters the placing of the $x$-axis tick values
     at the end of ticks, if the default behaviour is unsatisfactory.
     The positioning can be altered with the command
\verb+\uput[angle](x,y){ticklabel}+;
     \item \Lkeyword{spotY}: is similar;
     \item \Lkeyword{spotZ}: likewise.
   \end{itemize}
\end{itemize}
If the option \Lkeyword{axesboxed} doesn't meet your needs, it is
possible to adapt the following command, which is appropriate for
the first example:



\small
\begin{verbatim}
\psSolid[object=parallelepiped,a=8,b=8,c=8,action=draw](0,0,0)
\multido{\ix=-4+1}{9}{%
    \psPoint(\ix\space,4,-4){X1}
    \psPoint(\ix\space,4.2,-4){X2}
    \psline(X1)(X2)\uput[dr](X1){\ix}}
\multido{\iy=-4+1}{9}{%
    \psPoint(4,\iy\space,-4){Y1}
    \psPoint(4.2,\iy\space,-4){Y2}
    \psline(Y1)(Y2)\uput[dl](Y1){\iy}}
\multido{\iz=-4+1}{9}{%
    \psPoint(4,-4,\iz\space){Z1}
    \psPoint(4,-4.2,\iz\space){Z2}
    \psline(Z1)(Z2)\uput[l](Z1){\iz}}
\end{verbatim}

%L'option \Cadre{[hue=0 1]} permet de remplir les facettes avec des d\'{e}grad\'{e}s
%de couleur.
\section{Example 1: a \Index{saddle}}
\begin{LTXexample}[width=7.5cm]
\psset{unit=0.45}
\psset{viewpoint=50 40 30 rtp2xyz,Decran=50}
\psset{lightsrc=viewpoint}
\begin{pspicture}(-7,-8)(7,8)
\psSurface[ngrid=.25 .25,incolor=yellow,
   linewidth=0.5\pslinewidth,axesboxed,
   algebraic,hue=0 1](-4,-4)(4,4){%
   ((y^2)-(x^2))/4 }
\end{pspicture}
\end{LTXexample}

\newpage
\section{Example 2: a saddle without a grid}

The grid lines are suppressed, when using in the option:
\Lkeyword{grid}.
\begin{LTXexample}[width=7.5cm]
\psset{unit=0.5}
\psset{lightsrc=30 30 25}
\psset{viewpoint=50 40 30 rtp2xyz,Decran=50}
\begin{pspicture}(-7,-8)(7,8)
\psSurface[fillcolor=red!50,ngrid=.25 .25,
   incolor=yellow,linewidth=0.5\pslinewidth,
   grid,axesboxed](-4,-4)(4,4){%
   y dup mul x dup mul sub 4 div }
\end{pspicture}
\end{LTXexample}

%\newpage

\section{Example 3: a \Index{paraboloid}}

\begin{LTXexample}[width=7.5cm]
\psset{unit=0.5}
\psset{lightsrc=30 -10 10,linewidth=0.5\pslinewidth}
\psset{viewpoint=50 40 30 rtp2xyz,Decran=50}
\begin{pspicture}(-7,-4)(7,12)
\psSolid[object=grille,base=-4 4 -4 4,action=draw]%
\psSurface[
   fillcolor=cyan!50,
   intersectionplan={[0 0 1 -5]},
   intersectioncolor=(bleu),
   intersectionlinewidth=3,
    intersectiontype=0,
     ngrid=.25 .25,incolor=yellow,
   axesboxed,Zmin=0,Zmax=8,QZ=4](-4,-4)(4,4){%
   y dup mul x dup mul add 4 div }
\end{pspicture}
\end{LTXexample}

\newpage

\section{Star version of \texttt{\textbackslash pstSurface}}

\begin{lstlisting}
\psset{viewpoint=50 20 20 rtp2xyz,Decran=100,lightsrc=viewpoint}
\begin{pspicture}(-5,-4)(6,6)
\psSolid[object=grille,base=-2 2 -2 2,action=draw]%
\axesIIID(0,0,0)(2,2,1)
\psSurface*[
fillcolor=cyan,r=1,
ngrid=.25 .25,incolor=yellow,grid,
algebraic](-1,-1)(1,1){ e^(x*y) }
\psSolid[object=cylindre,r=1,h=2,action=draw,ngrid=1 18]
\psPoint(0,0,1){O}
\psPoint(0,0,3){Z}
\psline{->}(O)(Z)
\uput[r](Z){$z$}
\psPoint(0.5,0.5,0){C}
\psdot[linecolor=red,dotstyle=x,dotscale=2](C)
\end{pspicture}
%
\begin{pspicture}(-5,-4)(6,10)
\psSolid[object=grille,base=-2 2 -2 2,action=draw]%
\axesIIID(0,0,0)(2,2,1)
\psSurface*[
fillcolor=cyan,r=1,xytranslate=0.5 0.5,
ngrid=.25 .25,incolor=yellow,grid,
algebraic](-1,-1)(1,1){ e^(x*y) }
\psSolid[object=cylindre,r=1,h=4,action=draw,ngrid=1 18](0.5,0.5,0)
\psPoint(0,0,1){O}
\psPoint(0,0,5){Z}
\psline{->}(O)(Z)
\uput[r](Z){$z$}
\psPoint(0.5,0.5,0){C}
\psdot[linecolor=red,dotstyle=x,dotscale=2](C)
\end{pspicture}
\end{lstlisting}

\begin{landscape}
\psset{viewpoint=50 20 20 rtp2xyz,Decran=100,lightsrc=viewpoint}
\begin{pspicture}(-5,-4)(6,6)
\psSolid[object=grille,base=-2 2 -2 2,action=draw]%
\axesIIID(0,0,0)(2,2,1)
\psSurface*[
fillcolor=cyan,r=1,
ngrid=.25 .25,incolor=yellow,grid,
algebraic](-1,-1)(1,1){ e^(x*y) }
\psSolid[object=cylindre,r=1,h=2,action=draw,ngrid=1 18]
\psPoint(0,0,1){O}
\psPoint(0,0,3){Z}
\psline{->}(O)(Z)
\uput[r](Z){$z$}
\psPoint(0.5,0.5,0){C}
\psdot[linecolor=red,dotstyle=x,dotscale=2](C)
\end{pspicture}
%
\begin{pspicture}(-5,-4)(6,10)
\psSolid[object=grille,base=-2 2 -2 2,action=draw]%
\axesIIID(0,0,0)(2,2,1)
\psSurface*[
fillcolor=cyan,r=1,xytranslate=0.5 0.5,
ngrid=.25 .25,incolor=yellow,grid,
algebraic](-1,-1)(1,1){ e^(x*y) }
\psSolid[object=cylindre,r=1,h=4,action=draw,ngrid=1 18](0.5,0.5,0)
\psPoint(0,0,1){O}
\psPoint(0,0,5){Z}
\psline{->}(O)(Z)
\uput[r](Z){$z$}
\psPoint(0.5,0.5,0){C}
\psdot[linecolor=red,dotstyle=x,dotscale=2](C)
\end{pspicture}
\end{landscape}



\section{Example 4: a \Index{sinusoidal wave}}
\begin{LTXexample}[width=7.5cm]
\psset{unit=0.35}
\psset{lightsrc=30 -10 10}
\psset{viewpoint=50 20 30 rtp2xyz,Decran=70}
\begin{pspicture}(-11,-8)(7,8)
\psSurface[ngrid=.2 .2,algebraic,Zmin=-1,Zmax=1,
           linewidth=0.5\pslinewidth,spotX=r,spotY=d,spotZ=l,
           hue=0 1](-5,-5)(5,5){%
   sin((x^2+y^2)/3) }
\end{pspicture}
\end{LTXexample}

%\newpage

\section{Example 5: another \Index{sinusoidal wave}}

In this example we show how to colour the faces, each with a
different coloration, directly using PostScript code.

\begin{LTXexample}[width=7.5cm]
\psset{unit=0.25}
\psset{lightsrc=30 -10 10}
\psset{viewpoint=100 20 20 rtp2xyz,Decran=80}
\begin{pspicture}(-15,-10)(7,12)
\psSurface[ngrid=0.4 0.4,algebraic,Zmin=-2,Zmax=10,QZ=4,
           linewidth=0.25\pslinewidth,
           fcol=0 1 4225
           {/iF ED iF [iF 4225 div 0.75 1] (sethsbcolor) astr2str} for
          ](-13,-13)(13,13){%
   10*sin(sqrt((x^2+y^2)))/(sqrt(x^2+y^2)) }
\end{pspicture}
\end{LTXexample}

%\newpage

\section{Example 6: a \Index{hyperbolic paraboloid} with the equation $z = xy$}

In this example we combine the graph of the surface and the curves
of intersection of the paraboloid with the planes $z=4$ and
$z=-4$. In this case we use \verb+\psSolid[object=courbe]+.
\begin{verbatim}
\defFunction{F}(t){t}{4 t div 4 min}{4}
\psSolid[object=courbe,range=1 4,
   linecolor=red,linewidth=2\pslinewidth,
   function=F]
\end{verbatim}
You will note the use of the functions \texttt{min} and
\texttt{max}, which return the minimum and the maximum,
respectively, of two values.


\begin{LTXexample}[width=7.5cm]
\psset{unit=0.5}
\psset{viewpoint=50 20 30 rtp2xyz,Decran=50}
\psset{lightsrc=viewpoint,linewidth=0.5\pslinewidth}
\begin{pspicture}(-7,-8)(7,8)
\psSolid[object=datfile,file=data/paraboloid,hue=0 1 0.5 1,incolor=yellow]
\gridIIID[Zmin=-4,Zmax=4,spotX=r](-4,4)(-4,4)
\defFunction{F}(t){t}{4 t div 4 min}{4}
\psSolid[object=courbe,range=1 4,r=0,
   linecolor=red,linewidth=2\pslinewidth,
   function=F]
\defFunction{G}(t){t}{4 t div -4 max}{4}
\psSolid[object=courbe,range=-1 -4,r=0,
   linecolor=red,linewidth=2\pslinewidth,
   function=G]
\defFunction{H}(t){t neg}{4 t div -4 max}{-4}
\psSolid[object=courbe,range=-1 -4,r=0,
   linecolor=red,linewidth=2\pslinewidth,
   function=H]
\end{pspicture}
\end{LTXexample}
%\newpage

\section{Example 7: a surface with the equation $z = xy(x^2+y^2)$}

\begin{LTXexample}[width=7.5cm]
\psset{unit=0.35}
\psset{lightsrc=10 12 20,linewidth=0.5\pslinewidth}
\psset{viewpoint=30 50 60 rtp2xyz,Decran=50}
\begin{pspicture}(-10,-10)(12,10)
\psSurface[
   fillcolor=cyan!50,algebraic,
   ngrid=.25 .25,incolor=yellow,hue=0 1,
   Zmin=-3,Zmax=3](-3,-3)(3,3){%
   x*y*(x^2-y^2)*0.1}
\end{pspicture}
\end{LTXexample}


\newpage


\section{Example 8: a surface with the equation $z = \left(1-\frac{x^2+y^2}{2}\right)^2$}% $

\begin{LTXexample}[width=7.5cm]
\psset{unit=0.5cm,viewpoint=50 60 30 rtp2xyz,Decran=50}
\psset{lightsrc=viewpoint}
\begin{pspicture}(-4,-5)(6,8)
  \psSurface[ngrid=.25 .25,incolor=yellow,linewidth=0.5\pslinewidth,
    base= -2 2 -2 2, axesboxed, Zmin=-5,Zmax=2,hue=0 1](-5,-5)(5,5){%
    1 0.5 x dup mul y dup mul add mul sub dup -5 lt { pop -5 }if }
\end{pspicture}
\end{LTXexample}

\begin{LTXexample}[width=7.5cm]
\psset{unit=0.5cm,viewpoint=50 60 30 rtp2xyz,Decran=50,
  lightsrc=viewpoint}
\begin{pspicture}(-4,-5)(6,8)
  \psSurface*[ngrid=.25 .25,incolor=yellow,
    linewidth=0.5\pslinewidth,
    r = 3 sqrt 2 mul, axesboxed, Zmin=-5,Zmax=2,hue=0 1](-5,-5)(5,5){%
    1 0.5 x dup mul y dup mul add mul sub dup -5 lt { pop -5 }if }
\end{pspicture}
\end{LTXexample}



\endinput