Defines a TikZ node shape for a "rectangle with inverted corners".

myshape.tex

% Keys for rectangle with inverted corners
%
% /pgf/rectangle with inverted corners selected : specify the corners to invert.
% /pgf/rectangle with inverted corners radius   : set the radius of the corners.

\makeatletter
\pgfkeys{/pgf/rectangle with inverted corners selected/.store in=\pgf@lib@sh@misc@convrect@corners}
\pgfkeys{/tikz/rectangle with inverted corners selected/.store in=\pgf@lib@sh@misc@convrect@corners}

\def\pgf@lib@sh@misc@convrect@invertall{invert all}%
\def\pgf@lib@sh@misc@convrect@invert{invert}
\let\pgf@lib@sh@misc@convrect@corners\pgf@lib@sh@misc@convrect@invertall


\def\pgf@lib@sh@misc@convrect@getcorners{%
  \let\northeastcorner\pgfutil@empty%
  \let\southeastcorner\pgfutil@empty%
  \let\southwestcorner\pgfutil@empty%
  \let\northwestcorner\pgfutil@empty%
  \expandafter\pgfutil@in@\expandafter{\pgf@lib@sh@misc@convrect@corners}{invert all}%
  \ifpgfutil@in@%
    \let\northeastcorner\pgf@lib@sh@misc@convrect@invert%
    \let\southeastcorner\pgf@lib@sh@misc@convrect@invert%
    \let\southwestcorner\pgf@lib@sh@misc@convrect@invert%
    \let\northwestcorner\pgf@lib@sh@misc@convrect@invert%
    \let\pgf@next\relax%
  \else%
    \let\pgf@next\pgf@lib@sh@misc@convrect@parsecorners%
  \fi%
  \pgf@next}

\def\pgf@lib@sh@misc@convrect@parsecorners{%
  \expandafter\pgf@@concaverectangle@parsecorners\pgf@lib@sh@misc@convrect@corners,\pgf@stop,%
}

\def\pgf@@concaverectangle@parsecorners#1,{%
  \ifx#1\pgf@stop%
    \let\pgf@next\relax%
  \else%
    \pgfutil@in@{@#1@}{@north east@@top left@}%
    \ifpgfutil@in@%
      \let\northeastcorner\pgf@lib@sh@misc@convrect@invert%
    \else%
      \pgfutil@in@{@#1@}{@south east@@bottom right@}%
      \ifpgfutil@in@%
        \let\southeastcorner\pgf@lib@sh@misc@convrect@invert%
      \else%
        \pgfutil@in@{@#1@}{@south west@@bottom left@}%
        \ifpgfutil@in@%
          \let\southwestcorner\pgf@lib@sh@misc@convrect@invert%
        \else%
          \pgfutil@in@{@#1@}{@north west@@top right@}%
          \ifpgfutil@in@%
            \let\northwestcorner\pgf@lib@sh@misc@convrect@invert%
          \fi%
        \fi%
      \fi%
    \fi%
    \let\pgf@next\pgf@@@concaverectangle@parsecorners%
  \fi%
  \pgf@next%
}
\def\pgf@@@concaverectangle@parsecorners{%
  \pgfutil@ifnextchar x{\pgf@@concaverectangle@parsecorners}{\pgf@@concaverectangle@parsecorners}%
}%

\pgfkeys{/pgf/.cd,
  rectangle with inverted corners radius/.initial=.666ex%
}




% Shape rectangle with inverted corners.
%
%
\pgfdeclareshape{rectangle with inverted corners}{%
  \savedmacro\getconcaverectanglepoints{%
    \pgf@lib@sh@misc@convrect@getcorners%
    %
    % Get the node dimensions.
    %
    \pgfmathsetlength\pgf@xa{\pgfkeysvalueof{/pgf/inner xsep}}%
    \advance\pgf@xa.5\wd\pgfnodeparttextbox%
    \pgfmathsetlength\pgf@ya{\pgfkeysvalueof{/pgf/inner ysep}}%
    \advance\pgf@ya.5\ht\pgfnodeparttextbox%
    \advance\pgf@ya.5\dp\pgfnodeparttextbox%
    %
    % Get invert stuff.
    %
    \pgfmathsetlengthmacro\convsep{\pgfkeysvalueof{/pgf/rectangle with inverted corners radius}}%
    \pgfmathsetlength\pgf@xc{\convsep/sqrt(2)}%
    \pgfmathsetlength\pgf@yc{\convsep/sqrt(2)}%
    \addtosavedmacro\convsep%
    %
    % Check for minimum width and height%
    %
    \pgfutil@tempdima\pgf@xa%
    \advance\pgfutil@tempdima\convsep%
    \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum width}}%
    \ifdim\pgfutil@tempdima<.5\pgfutil@tempdimb%
      \pgf@xa.5\pgfutil@tempdimb%
    \fi%
    \pgfutil@tempdima\pgf@ya%
    \advance\pgfutil@tempdima\convsep%
    \pgfmathsetlength\pgfutil@tempdimb{\pgfkeysvalueof{/pgf/minimum height}}%
    \ifdim\pgfutil@tempdima<.5\pgfutil@tempdimb%
      \pgf@ya.5\pgfutil@tempdimb%
    \fi%
    %
    % Define the background path points.
    %
    \pgfextract@process\centerpoint{%
      \pgfmathsetlength\pgf@x{+.5\wd\pgfnodeparttextbox}%
      \pgfmathsetlength\pgf@y{+.5\ht\pgfnodeparttextbox}%
      \pgfmathaddtolength\pgf@y{+-.5\dp\pgfnodeparttextbox}%
    }%
    \pgfextract@process\beforenortheast{%
      \centerpoint%
      \advance\pgf@x\pgf@xa%
      \advance\pgf@y\pgf@ya%
      \advance\pgf@y-\convsep%
    }%
    \pgfextract@process\northeast{%
      \centerpoint%
      \advance\pgf@x\pgf@xa%
      \advance\pgf@y\pgf@ya%
      \ifx\northeastcorner\pgfutil@empty%
      \else
        \advance\pgf@x-\pgf@xc%
        \advance\pgf@y-\pgf@yc%
      \fi%
    }%
    \pgfextract@process\afternortheast{%
      \centerpoint%
      \advance\pgf@x\pgf@xa%
      \advance\pgf@x-\convsep%
      \advance\pgf@y\pgf@ya%
    }%
    \pgfextract@process\beforenorthwest{%
      \centerpoint%
      \advance\pgf@x-\pgf@xa%
      \advance\pgf@x\convsep%
      \advance\pgf@y\pgf@ya%
    }%
    \pgfextract@process\northwest{%
      \centerpoint%
      \advance\pgf@x-\pgf@xa%
      \advance\pgf@y\pgf@ya%
      \ifx\northwestcorner\pgfutil@empty%
      \else
        \advance\pgf@x\pgf@xc%
        \advance\pgf@y-\pgf@yc%
      \fi%
    }%
    \pgfextract@process\afternorthwest{%
      \centerpoint%
      \advance\pgf@x-\pgf@xa%
      \advance\pgf@y\pgf@ya%
      \advance\pgf@y-\convsep%
    }%
    \pgfextract@process\beforesouthwest{%
      \centerpoint%
      \advance\pgf@x-\pgf@xa%
      \advance\pgf@y-\pgf@ya%
      \advance\pgf@y\convsep%
    }%
    \pgfextract@process\southwest{%
      \centerpoint%
      \advance\pgf@x-\pgf@xa%
      \advance\pgf@y-\pgf@ya%
      \ifx\southwestcorner\pgfutil@empty%
      \else
        \advance\pgf@x\pgf@xc%
        \advance\pgf@y\pgf@yc%
      \fi%
    }%
    \pgfextract@process\aftersouthwest{%
      \centerpoint%
      \advance\pgf@x-\pgf@xa%
      \advance\pgf@x\convsep%
      \advance\pgf@y-\pgf@ya%
    }%
    \pgfextract@process\beforesoutheast{%
      \centerpoint%
      \advance\pgf@x\pgf@xa%
      \advance\pgf@x-\convsep%
      \advance\pgf@y-\pgf@ya%
    }%
    \pgfextract@process\southeast{%
      \centerpoint%
      \advance\pgf@x\pgf@xa%
      \advance\pgf@y-\pgf@ya%
      \ifx\southeastcorner\pgfutil@empty%
      \else
        \advance\pgf@x-\pgf@xc%
        \advance\pgf@y\pgf@yc%
      \fi%
    }%
    \pgfextract@process\aftersoutheast{%
      \centerpoint%
      \advance\pgf@x\pgf@xa%
      \advance\pgf@y-\pgf@ya%
      \advance\pgf@y\convsep%
    }%
    \addtosavedmacro\beforenortheast%
    \addtosavedmacro\afternortheast%
    \addtosavedmacro\beforesouthwest%
    \addtosavedmacro\aftersouthwest%
    %
    % Calculate the `miter' vectors.
    %
    \pgfmathsetlengthmacro\outerxsep{\pgfkeysvalueof{/pgf/outer xsep}}%
    \pgfmathsetlengthmacro\outerysep{\pgfkeysvalueof{/pgf/outer ysep}}%
    \addtosavedmacro\outerxsep%
    \addtosavedmacro\outerysep%
    \pgfextract@process\before@ne@anchor{%
      \beforenortheast%
      \advance\pgf@x\outerxsep%
      \advance\pgf@y\outerysep%
    }%
    \pgfextract@process\before@sw@anchor{%
      \beforesouthwest%
      \advance\pgf@x-\outerxsep%
      \advance\pgf@y-\outerysep%
    }%
    \pgfextract@process\after@ne@anchor{%
      \afternortheast%
      \advance\pgf@x\outerxsep%
      \advance\pgf@y\outerysep%
    }%
    \pgfextract@process\after@sw@anchor{%
      \aftersouthwest
      \advance\pgf@x-\outerxsep%
      \advance\pgf@y-\outerysep%
    }%
    \addtosavedmacro\before@ne@anchor%
    \addtosavedmacro\after@ne@anchor%
    \addtosavedmacro\before@sw@anchor%
    \addtosavedmacro\after@sw@anchor%
    \pgfextract@process\ne@anchor{%
      \northeast%
      \ifx\northeastcorner\pgfutil@empty%
        \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}%
        \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}%
      \else%
        \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}/sqrt(2)}%
        \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}/sqrt(2)}%
      \fi%
    }%
    \pgfextract@process\nw@anchor{%
      \northwest%
      \ifx\northwestcorner\pgfutil@empty%
        \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}}%
        \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}}%
      \else%
        \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}/sqrt(2)}%
        \pgfmathaddtolength\pgf@y{\pgfkeysvalueof{/pgf/outer ysep}/sqrt(2)}%
      \fi%
    }%
    \pgfextract@process\sw@anchor{%
      \southwest%
      \ifx\southwestcorner\pgfutil@empty%
        \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}}%
        \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}}%
      \else%
        \pgfmathaddtolength\pgf@x{-\pgfkeysvalueof{/pgf/outer xsep}/sqrt(2)}%
        \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}/sqrt(2)}%
      \fi%
    }%
    \pgfextract@process\se@anchor{%
      \southeast%
      \ifx\southeastcorner\pgfutil@empty%
        \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}}%
        \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}}%
      \else%
        \pgfmathaddtolength\pgf@x{\pgfkeysvalueof{/pgf/outer xsep}/sqrt(2)}%
        \pgfmathaddtolength\pgf@y{-\pgfkeysvalueof{/pgf/outer ysep}/sqrt(2)}%
      \fi%
    }%
    \addtosavedmacro\ne@anchor%
    \addtosavedmacro\nw@anchor%
    \addtosavedmacro\sw@anchor%
    \addtosavedmacro\se@anchor%
    \addtosavedmacro\northwestcorner
    \addtosavedmacro\northeastcorner
    \addtosavedmacro\southwestcorner
    \addtosavedmacro\southeastcorner
  }%
  \savedanchor\centerpoint{%
    \pgf@x.5\wd\pgfnodeparttextbox%
    \pgf@y.5\ht\pgfnodeparttextbox%
    \advance\pgf@y-.5\dp\pgfnodeparttextbox%
  }%
  \savedanchor\midpoint{%
    \pgf@x.5\wd\pgfnodeparttextbox%
    \pgfmathsetlength\pgf@y{+.5ex}%
  }%
  \savedanchor\basepoint{%
    \pgf@x.5\wd\pgfnodeparttextbox%
    \pgf@y0pt%
  }%
  \anchor{center}{\centerpoint}%
  \anchor{mid}{\midpoint}%
  \anchor{mid east}{%
    \getconcaverectanglepoints%
    \midpoint%
    \pgf@ya\pgf@y%
    \pgf@process{%
      \before@sw@anchor%
      \pgf@ya\pgf@y%
      \before@ne@anchor%
      \pgf@y\pgf@ya
    }%
    \ifdim\pgf@ya<\pgf@y%
      \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
        {\before@sw@anchor\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
        {\after@sw@anchor\pgf@ya\pgf@y\after@ne@anchor\pgf@y\pgf@ya}%
    \else%
      \pgf@process{\before@ne@anchor}%
      \ifdim\pgf@ya<\pgf@y%
        \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
          {\before@sw@anchor\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
          {\before@ne@anchor}%
      \else%
        \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
          {\before@ne@anchor}%
          {\after@ne@anchor}%
      \fi%
    \fi%
  }%
  \anchor{mid west}{%
    \getconcaverectanglepoints%
    \midpoint%
    \pgf@ya\pgf@y%
    \pgf@process{\before@sw@anchor}%
    \ifdim\pgf@ya<\pgf@y%
      \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
        {\before@sw@anchor}{\after@sw@anchor}%
    \else%
      \pgf@process{\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
      \ifdim\pgf@ya<\pgf@y%
        \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
          {\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
          {\before@sw@anchor}%
      \else%
        \pgfpointintersectionoflines{\midpoint}{\midpoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
          {\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
          {\after@ne@anchor\pgf@ya\pgf@y\after@sw@anchor\pgf@y\pgf@ya}%
      \fi%
    \fi%
  }%
  \anchor{base}{\basepoint}%
  \anchor{base east}{%
    \getconcaverectanglepoints%
    \basepoint%
    \pgf@ya\pgf@y%
    \pgf@process{%
      \before@sw@anchor%
      \pgf@ya\pgf@y%
      \before@ne@anchor%
      \pgf@y\pgf@ya
    }%
    \ifdim\pgf@ya<\pgf@y%
      \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
        {\before@sw@anchor\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
        {\after@sw@anchor\pgf@ya\pgf@y\after@ne@anchor\pgf@y\pgf@ya}%
    \else%
      \pgf@process{\before@ne@anchor}%
      \ifdim\pgf@ya<\pgf@y%
        \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
          {\before@sw@anchor\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
          {\before@ne@anchor}%
      \else%
        \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@ne@anchor\pgf@y\pgf@ya}%
          {\before@ne@anchor}%
          {\after@ne@anchor}%
      \fi%
    \fi%
  }%
  \anchor{base west}{%
    \getconcaverectanglepoints%
    \basepoint%
    \pgf@ya\pgf@y%
    \pgf@process{\before@sw@anchor}%
    \ifdim\pgf@ya<\pgf@y%
      \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
        {\before@sw@anchor}{\after@sw@anchor}%
    \else%
      \pgf@process{\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
      \ifdim\pgf@ya<\pgf@y%
        \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
          {\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
          {\before@sw@anchor}%
      \else%
        \pgfpointintersectionoflines{\basepoint}{\basepoint\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
          {\before@ne@anchor\pgf@ya\pgf@y\before@sw@anchor\pgf@y\pgf@ya}%
          {\after@ne@anchor\pgf@ya\pgf@y\after@sw@anchor\pgf@y\pgf@ya}%
      \fi%
    \fi%
  }%
  \anchor{before north east}{\getconcaverectanglepoints\before@ne@anchor}%
  \anchor{north east}{\getconcaverectanglepoints\ne@anchor}%
  \anchor{after north east}{\getconcaverectanglepoints\after@ne@anchor}%
  \anchor{north}{%
    \getconcaverectanglepoints%
    \centerpoint%
    \pgf@xa\pgf@x%
    \after@ne@anchor%
    \pgf@x\pgf@xa}%
  \anchor{before north west}{%
    \getconcaverectanglepoints%
    \after@sw@anchor%
    \pgf@xa\pgf@x%
    \after@ne@anchor%
    \pgf@x\pgf@xa}%
  \anchor{north west}{\getconcaverectanglepoints\nw@anchor}%
  \anchor{after north west}{%
    \getconcaverectanglepoints%
    \before@sw@anchor%
    \pgf@xa\pgf@x%
    \before@ne@anchor%
    \pgf@x\pgf@xa}%
  \anchor{west}{%
    \getconcaverectanglepoints%
    \centerpoint%
    \pgf@ya\pgf@y%
    \before@sw@anchor%
    \pgf@y\pgf@ya}%
  \anchor{before south west}{\getconcaverectanglepoints\before@sw@anchor}%
  \anchor{south west}{\getconcaverectanglepoints\sw@anchor}%
  \anchor{after south west}{\getconcaverectanglepoints\after@sw@anchor}%
    \anchor{south}{%
    \getconcaverectanglepoints%
    \centerpoint%
    \pgf@xa\pgf@x%
    \after@sw@anchor%
    \pgf@x\pgf@xa}%
  \anchor{before south east}{%
    \getconcaverectanglepoints%
    \after@sw@anchor%
    \pgf@ya\pgf@y%
    \after@ne@anchor%
    \pgf@y\pgf@ya}%
  \anchor{south east}{\getconcaverectanglepoints\se@anchor}%
  \anchor{after south east}{%
    \getconcaverectanglepoints%
    \before@sw@anchor%
    \pgf@ya\pgf@y%
    \before@ne@anchor%
    \pgf@y\pgf@ya}%
  \anchor{east}{%
    \getconcaverectanglepoints%
    \centerpoint%
    \pgf@ya\pgf@y%
    \before@ne@anchor%
    \pgf@y\pgf@ya}%
  \backgroundpath{%
    \pgfpathmoveto{\beforenortheast}%
    \ifx\northeastcorner\pgfutil@empty%
      \pgfpathlineto{\northeast}%
    \else%
      \pgfpatharc{-90}{-180}{\convsep}%
    \fi%
    \pgfpathlineto{\beforenorthwest}%
    \ifx\northwestcorner\pgfutil@empty%
      \pgfpathlineto{\northwest}%
    \else%
      \pgfpatharc{0}{-90}{\convsep}%
    \fi%
    \pgfpathlineto{\beforesouthwest}%
    \ifx\southwestcorner\pgfutil@empty%
      \pgfpathlineto{\southwest}%
    \else%
      \pgfpatharc{90}{0}{\convsep}%
    \fi%
    \pgfpathlineto{\beforesoutheast}%
    \ifx\southeastcorner\pgfutil@empty%
      \pgfpathlineto{\southeast}%
    \else%
      \pgfpatharc{180}{90}{\convsep}%
    \fi%
    \pgfpathclose%
    %
  }
  \anchorborder{%
    \pgfextract@process\externalpoint{%
      \pgf@xa\pgf@x%
      \pgf@ya\pgf@y%
      \centerpoint%
      \advance\pgf@x\pgf@xa%
      \advance\pgf@y\pgf@ya%
    }%
    \pgfmathanglebetweenpoints{\centerpoint}{\externalpoint}%
    \let\externalangle\pgfmathresult%
    \getconcaverectanglepoints%
    \pgfmathanglebetweenpoints{\centerpoint}{\before@ne@anchor\pgf@xa\pgf@x\before@sw@anchor\pgf@x\pgf@xa}%
    \ifdim\externalangle pt<\pgfmathresult pt\relax% < after south east.
      \pgfmathanglebetweenpoints{\centerpoint}{\after@ne@anchor\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}%
      \ifdim\externalangle pt<\pgfmathresult pt\relax% < before south east.
        \pgfmathanglebetweenpoints{\centerpoint}{\after@sw@anchor}%
        \ifdim\externalangle pt<\pgfmathresult pt\relax% < after south west.
          \pgfmathanglebetweenpoints{\centerpoint}{\before@sw@anchor}%
          \ifdim\externalangle pt<\pgfmathresult pt\relax% < before south west.
            \pgfmathanglebetweenpoints{\centerpoint}{\before@sw@anchor\pgf@xa\pgf@x\before@ne@anchor\pgf@x\pgf@xa}%
            \ifdim\externalangle pt<\pgfmathresult pt\relax% < after north west.
              \pgfmathanglebetweenpoints{\centerpoint}{\after@sw@anchor\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}%
              \ifdim\externalangle pt<\pgfmathresult pt\relax% < before north west.
                \pgfmathanglebetweenpoints{\centerpoint}{\after@ne@anchor}%
                \ifdim\externalangle pt<\pgfmathresult pt\relax% < after north east.
                  \pgfmathanglebetweenpoints{\centerpoint}{\before@ne@anchor}%
                  \ifdim\externalangle pt<\pgfmathresult pt\relax% < before north east.
                    % east side (> 0°)
                    \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                      {\before@ne@anchor\pgf@xa\pgf@x\before@sw@anchor\pgf@x\pgf@xa}{\before@ne@anchor}%
                  \else%
                    % top right corner
                    \ifx\northeastcorner\pgfutil@empty\relax%
                      % rectangle corner
                      \pgfmathanglebetweenpoints{\centerpoint}{\ne@anchor}%
                      \ifdim\externalangle pt<\pgfmathresult pt\relax% < north east.
                        % intersect with east side
                        \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                          {\before@ne@anchor\pgf@xa\pgf@x\before@sw@anchor\pgf@x\pgf@xa}{\before@ne@anchor}%
                      \else% > north west
                        % intersect with north side
                        \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                          {\after@ne@anchor}{\after@sw@anchor\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}%
                      \fi%
                    \else%
                      % inverted corner
                      \pgfextract@process\arccenter{%
                        \beforenortheast%
                        \pgf@xa\pgf@x%
                        \afternortheast%
                        \pgf@x\pgf@xa%
                      }%
                      \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}%
                        {\arccenter}{-80}{-190}{\convsep-\outerxsep and \convsep-\outerysep}%
                    \fi%
                  \fi%
                \else%
                  % north side
                  \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                    {\after@ne@anchor}{\after@sw@anchor\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}%
                \fi%
              \else%
                % top left corner
                \ifx\northwestcorner\pgfutil@empty\relax%
                  % rectangle corner
                  \pgfmathanglebetweenpoints{\centerpoint}{\nw@anchor}%
                  \ifdim\externalangle pt<\pgfmathresult pt\relax% < north west.
                    % intersect with north side
                    \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                      {\after@ne@anchor}{\after@sw@anchor\pgf@xa\pgf@x\after@ne@anchor\pgf@x\pgf@xa}%
                  \else% > north west
                    % intersect with west side
                    \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                      {\before@sw@anchor\pgf@xa\pgf@x\before@ne@anchor\pgf@x\pgf@xa}{\before@sw@anchor}%
                  \fi%
                \else%
                  % inverted corner
                  \pgfextract@process\arccenter{%
                    \beforesouthwest%
                    \pgf@xa\pgf@x%
                    \afternortheast%
                    \pgf@x\pgf@xa%
                  }%
                  \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}%
                    {\arccenter}{10}{-100}{\convsep-\outerxsep and \convsep-\outerysep}%
                \fi%
              \fi%
            \else%
              % west side
              \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                {\before@sw@anchor\pgf@xa\pgf@x\before@ne@anchor\pgf@x\pgf@xa}{\before@sw@anchor}%
            \fi%
          \else%
            % bottom left corner
            \ifx\southwestcorner\pgfutil@empty\relax%
              % rectangle corner
              \pgfmathanglebetweenpoints{\centerpoint}{\sw@anchor}%
              \ifdim\externalangle pt<\pgfmathresult pt\relax% < south west.
                % intersect with west side
                \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                  {\before@sw@anchor\pgf@xa\pgf@x\before@ne@anchor\pgf@x\pgf@xa}{\before@sw@anchor}%
              \else% > north west
                % intersect with south side
                \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
                  {\after@sw@anchor}{\after@ne@anchor\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}%
              \fi%
            \else%
              % inverted corner
              \pgfextract@process\arccenter{%
                \beforesouthwest%
                \pgf@xa\pgf@x%
                \aftersouthwest%
                \pgf@x\pgf@xa%
              }%
              \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}%
                {\arccenter}{100}{-10}{\convsep-\outerxsep and \convsep-\outerysep}%
            \fi%
          \fi%
        \else%
          % south side
          \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
            {\after@sw@anchor}{\after@ne@anchor\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}%
        \fi%
      \else%
        % bottom right corner
        \ifx\southeastcorner\pgfutil@empty\relax%
          % rectangle corner
          \pgfmathanglebetweenpoints{\centerpoint}{\se@anchor}%
          \ifdim\externalangle pt<\pgfmathresult pt\relax% < south east.
            % intersect with south side
            \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
              {\after@sw@anchor}{\after@ne@anchor\pgf@xa\pgf@x\after@sw@anchor\pgf@x\pgf@xa}%
          \else% > north west
            % intersect with east side
            \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
              {\before@ne@anchor\pgf@xa\pgf@x\before@sw@anchor\pgf@x\pgf@xa}{\before@ne@anchor}%
          \fi%
        \else%
          % inverted corner
          \pgfextract@process\arccenter{%
            \aftersouthwest%
            \pgf@ya\pgf@y%
            \beforenortheast%
            \pgf@y\pgf@ya%
          }%
          \pgfmathpointintersectionoflineandarc{\externalpoint}{\centerpoint}%
            {\arccenter}{190}{80}{\convsep-\outerxsep and \convsep-\outerysep}%
        \fi%
      \fi%
    \else%
      % east side (< 0°)
      \pgfpointintersectionoflines{\centerpoint}{\externalpoint}%
        {\before@ne@anchor\pgf@xa\pgf@x\before@sw@anchor\pgf@x\pgf@xa}{\before@ne@anchor}%
    \fi%
  }%
}
\makeatother