How to get the nodes on which a line intersects the hypothetical frame box of \ncput?

Question

I want to get the nodes on which the \*cline intersects the hypothetical edge of \ncput. The following animation shows my attempt to find the nodes by a trial & error approach.

I need the nodes because I want to have a transparent background in PNG format in which \ncput* fails to do so.

\documentclass[pstricks,border=12pt,multi]{standalone}
\usepackage{pst-eucl,multido}

\begin{document}
\multido{\n=0.1+0.1}{10}{%
\begin{pspicture}[showgrid=false](2,2)
    \pstGeonode
        [
            PosAngle={135,-45},
            PointName={default,default,none},
            PointSymbol={none}
        ]
        (0,1){A}
        (2,0){B}
        ([offset=15pt]{B}A){A'}
        ([offset=-15pt]{A}B){B'}
        ([nodesep=\n]{B'}A'){A''}
        ([nodesep=\n]{A'}B'){B''}
    %
    \psline(A)(B)
    %
    \bgroup
        \psset{linestyle=dashed,dash=1pt 1pt,linecolor=red,linewidth=0.5\pslinewidth}
        \psline(A)(A')
        \psline(B)(B')
    \egroup
    %
    \pcline{|<*-}(A')(A'')
    \pcline{->|*}(B'')(B')
    \ncline[linestyle=none]{A''}{B''}
    \ncput[nrot=:0]{$\sqrt{5}$}
\end{pspicture}}
\end{document}

Answer 1

Problem solved!

Now, I can get a transparent label in PNG as follows.

\documentclass[pstricks,border=12pt,multi]{standalone}
\usepackage{pst-eucl}
\newcommand\ncputtransparent[4][1pt]{%
    \ncline[linestyle=none]{#2}{#3}
    \ncput[nrot=:0]{\psDefBoxNodes{obj}{#4}}
    \pcline{|<*-}(#2)([nodesep=#1]{#2}obj:Cl)
    \pcline{->|*}([nodesep=#1]{#3}obj:Cr)(#3)
}

\begin{document}
\begin{pspicture}[showgrid=false](2,2)
    \pstGeonode
        [
            PosAngle={135,-45},
            PointName={default,default,none},
            PointSymbol={none}
        ]
        (0,1){A}
        (2,0){B}
        ([offset=15pt]{B}A){A'}
        ([offset=-15pt]{A}B){B'}
    %
    \psline(A)(B)
    %
    \bgroup
        \psset{linestyle=dashed,dash=1pt 1pt,linecolor=red,linewidth=0.5\pslinewidth}
        \psline(A)(A')
        \psline(B)(B')
    \egroup
    \ncputtransparent[3pt]{A'}{B'}{$\sqrt5$}
\end{pspicture}
\end{document}

Just for a comparison purpose, the following code uses the opaque \ncput*. Can you see the difference? Note: I deliberately enclose the image in a quote tag to emphasize the opaque label.

\documentclass[pstricks,border=12pt,multi]{standalone}
\usepackage{pst-eucl}

\begin{document}
\begin{pspicture}[showgrid=false](2,2)
    \pstGeonode
        [
            PosAngle={135,-45},
            PointName={default,default,none},
            PointSymbol={none}
        ]
        (0,1){A}
        (2,0){B}
        ([offset=15pt]{B}A){A'}
        ([offset=-15pt]{A}B){B'}
    %
    \psline(A)(B)
    %
    \bgroup
        \psset{linestyle=dashed,dash=1pt 1pt,linecolor=red,linewidth=0.5\pslinewidth}
        \psline(A)(A')
        \psline(B)(B')
    \egroup
    \pcline{|<*->|*}(A')(B')
    \ncput*[nrot=:0]{$\sqrt5$}
\end{pspicture}
\end{document}