%% 
%%  A DANTE-Edition example
%% 
%%  Example 14-04-1 on page 161.
%% 
%%  Copyright (C) 2011 Herbert Voss
%% 
%%  It may be distributed and/or modified under the conditions
%%  of the LaTeX Project Public License, either version 1.3
%%  of this license or (at your option) any later version.
%% 
%%  See http://www.latex-project.org/lppl.txt for details.
%% 
%% 
%% ==== 
% Show page(s) 1
%% 
\documentclass[]{article}
\pagestyle{empty}
\setlength\textwidth{201.70511pt}
\setlength\parindent{0pt}

\usepackage{pstricks,pst-node}  \SpecialCoor
\makeatletter
\define@boolkey[psset]{}[Pst@]{showFP}[true]{}% mark focal point?
\psset{showFP}                           % true as default
\def\focalPoint{\@ifnextchar[{\focalPoint@i}{\focalPoint@i[]}}
\def\focalPoint@i[#1](#2)(#3)(#4)#5{{    % everything stays local
  \psset{#1}                             % set parameters
  \pst@getcoor{#2}\pst@tempA% point A    % get coordinates as x y
  \pst@getcoor{#3}\pst@tempB% point B    %
  \pst@getcoor{#4}\pst@tempC% point C    %
  \pnode(!                               % set node
     \pst@tempA /YA exch \pst@number\psyunit div def
     /XA exch \pst@number\psxunit div def % x y in user coordinates
     \pst@tempB /YB exch \pst@number\psyunit div def
     /XB exch \pst@number\psxunit div def
     \pst@tempC /YC exch \pst@number\psyunit div def
     /XC exch \pst@number\psxunit div def
     XA XB XC add add 3.0 div            % xSP
     YA YB YC add add 3.0 div            % ySP
  ){#5}                                  % #5 = node name
  \ifPst@showFP\qdisk(#5){2pt}\fi}\ignorespaces}
\makeatother

\begin{document}
\begin{pspicture}[showgrid](4,4)  \psset{linewidth=2pt}
  \pspolygon[linecolor=red](0,0)(2,4)(4,0)%
  \focalPoint[showFP=true,linecolor=red](0,0)(2,4)(4,0){SP1}%
  \pnode(0,0){A}\pnode(0,4){B}\pnode(4,2){C}%
  \pspolygon[linecolor=blue](A)(B)(C)\focalPoint(A)(B)(C){SP2}%
  {\psset{linecolor=blue}\qdisk(SP2){2pt}}
  \ncline[linewidth=0.2pt]{<->}{SP1}{SP2}%
\end{pspicture}
\end{document}