[pstricks] implicit plots

[Herbert Voss]

Oscar Ecenarro wrote:
> Herbert,
> I'm trying to draw the equipotential lines of a system of two equal 
> charges at short distances (not a dipolar field), using the implicit 
> plotting scheme that you sugests.
> Briefly, the function to be plotted is:
> V=k(1/r+1/r')
> Placing the origin at the first charge, I use the next definition at the 
> pstVerb environment in Cartesian coordinates:

A problem with the Steffensen algorithm for zeros ...
a division by zero. I suppose it is not the right
tool here.

Herbert

\documentclass[12pt]{article}%
\usepackage{pstricks}%
\usepackage{pstricks-add}%
\begin{document}

\begin{pspicture*}(-5,-2.5)(5,2.5)
\psaxes(0,0)(-5,-2.5)(5,2.5)%
\pstVerb{
    /eps1 0.0001 def % x
    /eps2 0.001 def % x
    /MaxIter 10 def
%------------------------ the implicit function -----------------------
    /func { % parameter is the y value
      /yVal ED
      1 x 2 exp yVal 2 exp add sqrt % 1/sqrt(x^2+y^2)
      1 x 10 sub 2 exp yVal 2 exp add sqrt  % 1/sqrt((x-10)^2+y^2)
     add % add both
    1 sub
    } def
%------------------------ the implicit function -----------------------
    /Steffensen {
      /y0 ED % the start value
      /Iter 0 def
      {
        y0 func /F ED
        F abs eps2 lt { exit } if
        y0 F sub /Phi ED
        Phi func /F2 ED
        F2 abs eps2 le { exit }{%
          Phi y0 sub dup mul Phi F2 sub 2 Phi mul sub y0
	 add dup abs eps1 gt { div } { pop } ifelse /Diff
	 ED
          y0 Diff sub /y0 ED
          Diff abs eps1 le { exit } if
        } ifelse
        /Iter Iter 1 add def
        Iter MaxIter gt { exit } if
      } loop
      y0
    } def
}
  \psplot[plotpoints=200,linecolor=red,polarplot]{-180}{180}{ 2 Steffensen }
\end{pspicture*}

\end{document}