Tukukkk

Given the following TikZ picture with an irregularly shaped polygon:

documentclass{article}

usepackage{tikz}



begin{document}

begin{tikzpicture}

path[draw=blue] (0,3) -- (5,4) -- (3,2) -- (4,0) -- (1,1) -- cycle;

node [circle,draw=none,fill=green,inner sep=0pt,minimum size=0.3cm] at (3.5,0.4) {};

node [circle,draw=none,fill=green,inner sep=0pt,minimum size=0.3cm] at (1.03,1.3) {};

node [circle,draw=none,fill=red,inner sep=0pt,minimum size=0.3cm] at (3.3,2) {};

node [circle,draw=none,fill=red,inner sep=0pt,minimum size=0.3cm] at (0.7,1.8) {};

end{tikzpicture}

end{document}

The two green circles in the picture lie completely inside the polygon, while the red ones lie partially or fully outside. Is there a way to automate that "ownership" test in TikZ? I know algorithms exist for such kind of tests, but does TikZ already provide this or similar features (e.g. tests for single points)?

Here is a solution. The c point is an arbitrary point outside of the polygon. The quality of the result depends on the accuracy of the intersection calculation.

Note: to remove help lines, you can comment the draw[help lines,... line and uncomment the path[nale path... line.

documentclass[tikz]{standalone}



usetikzlibrary{intersections}

defmycircles{

  {c1/red/3.5,0.4},{c2/blue/1.03,1.3},

  {c3/violet/3.3,2},{c4/lime/0.7,1.8},

  {c5/orange/2,0.55}% 

}

begin{document}

begin{tikzpicture}

  path[draw=blue,name path=polygon] (0,3) -- (5,4) -- (3,2) -- (4,0) -- (1,1) -- cycle;

  foreach cname/ccolor/ccoord in mycircles {

    node [circle,name path global=cname,draw=none,fill=ccolor,minimum size=3mm] (cname) at (ccoord) {};

  }

  begin{scope}[overlay]

    coordinate (c) at (-100,300);

    foreach cname/ccolor/ccoord in mycircles {

      draw[help lines,dashed,name path global=line-cname] (cname.center) -- (c);

      %path[name path global=line-mypath] (mypath.center) -- (c);

    }

  end{scope}



  coordinate (text) at (0,0);

  foreach cname/ccolor/ccoord in mycircles {

    path[%

    name intersections={of=polygon and cname,total=npc},

    name intersections={of=polygon and line-cname,total=nplc},

    ]

    pgfextra{

      node[align=flush left,at=(text),anchor=north west,node font=scriptsize,inner sep=.1em] (desc) {

        pgfmathsetmacromypartial{int((npc != 0)}

        pgfmathsetmacromyin{int(mod(nplc,2)!=0)}

        pgfmathsetmacromytexti{mypartial==1?"intersects":(myin==1?"is in":"is out")}

        pgfmathsetmacromytextii{myin==1?"center is in":"center is out")}

        ccolor{} circle mytexti{} (mytextii)

      };

      coordinate (text) at (desc.south west);

    };

  }

end{tikzpicture}

end{document}