How to mimic the behavior of \ncput* but without the unwanted opaque effect?

Question

My objective is to have a label with transparent background but any connecting curve passing through the hypothetical box of the label must be hidden.

Opaque Label

\ncput* produces an opaque label as follows. So it does not fit into my objective.

\documentclass[pstricks,multi]{standalone}
\usepackage{pst-eucl}

\begin{document}
\begin{pspicture}[showgrid=false](4,4)
    \pstGeonode[PosAngle={90}]
        (1,1){A}
        (3,3){B}
    \ncarc[arcangle=-30,linestyle=dashed,linecolor=gray]{A}{B}
  \ncput*[nrot=:0]{$2\sqrt2$}   
\end{pspicture}

\end{document}

Transparent Label

The following is my attempt to mimic the code above but with transparent background for the label. However, I failed to mimic the connecting curve.

\documentclass[pstricks,multi]{standalone}
\usepackage{pst-eucl}

\begin{document}

\begin{pspicture}[showgrid=false](4,4)
    \pstGeonode[PosAngle={90}]
        (1,1){A}
        (3,3){B}
    \ncarc[arcangle=-30,linestyle=none]{A}{B}
  \ncput[nrot=:0]{\psDefBoxNodes{obj}{$2\sqrt2$}}
    \pcarc[arcangle=-30,linestyle=dashed,linecolor=gray](A)([nodesep=3pt]{A}obj:Cl)
  \pcarc[arcangle=-30,linestyle=dashed,linecolor=gray]([nodesep=3pt]{B}obj:Cr)(B)
\end{pspicture}

\end{document}

How to solve this issue?

Answer 1

I've defined a macro for a simple quadratic bezier curve to connect two points. But, I've also added two parameters to allow you to specify the start and end of the portion of the bezier curve you want plotted.

The command is arguments are

 \mybeziercurve[options]{<t-start>}{<t-end>}{<n-start>}{<n-control>}{<n-end>}

where

t-start    is a value between 0 and 1
t-end      is a value between 0 and 1 (ideally larger than t-start)
n-start    is the first node to be connected
n-control  is a node to control the effect of the bezier curve
n-end      is the second node to be connected

There is also a command to place a point along the bezier curve

\myputnodeoncurve{<pos>}{<node-start>}{<control-node>}{<node-end>}{<new-node>}

where

pos  should be a number between 0 and 1

other parameters are as for \mybeziercurve

Please note that this implementation requires that you're using pst-eucl since I'm using pst-eucl's postscript dictionary.

Here's a MWE

\documentclass{article}
\usepackage{pstricks}
\usepackage{pst-plot}
\usepackage{pst-eucl}

\makeatletter
\newcommand{\@my@bezier@curve}[4]
    {%
            tx@EcldDict begin
            %% x coordinate
            1 #1 sub
            1 #1 sub
                    /N@#2 GetNode 0 mul add     mul
            #1
                    /N@#3 GetNode 0 mul add     mul add mul
            %--
              #1 
            1 #1 sub
                    /N@#3 GetNode 0 mul add     mul
              #1
                    /N@#4 GetNode 0 mul add     mul add mul add
            \pst@number\psxunit div
            %% y coordinate
            1 #1 sub
            1 #1 sub
                    /N@#2 GetNode exch 0 mul add     mul
            #1
                    /N@#3 GetNode exch 0 mul add     mul add mul
            %--
              #1 
            1 #1 sub
                    /N@#3 GetNode exch 0 mul add     mul
              #1
                    /N@#4 GetNode exch 0 mul add     mul add mul add
            \pst@number\psyunit div
            end
    }

\newcommand{\mybeziercurve}[6][]
    {%
        \def\@ParamStart{#2}%
        \def\@ParamEnd{#3}%
        \parametricplot[plotstyle=line,plotpoints=100,#1]
        {\@ParamStart}{\@ParamEnd}{ \@my@bezier@curve{t}{#4}{#5}{#6} }        
    }
%% a macro to place a node on the curve for labeling purposes
\newcommand{\myputnodeoncurve}[5]
    {%
        \pnode( !\@my@bezier@curve{#1}{#2}{#3}{#4} ){#5}%
    }
\makeatother
\pagestyle{empty}
\begin{document}

\begin{pspicture}[showgrid=false](0,0)(4,4)
    \pstGeonode[PosAngle={-135,45,-45},
                PointName={default,default,none},
                PointSymbol={default,default,none}]
        (2,1){A}
        (3,3){B}
        (3,1){C}

    \pstRotation[RotAngle=130,PointName=none,PointSymbol=none]{A}{C}[D]
    \pstTranslation[DistCoef=-1.5,PointName=none,PointSymbol=none]{C}{D}{C}[D]

    \mybeziercurve[linecolor=black,linewidth=0.4pt,linestyle=dashed]{0}{0.35}{A}{D}{B}
    \mybeziercurve[linecolor=black,linewidth=0.4pt,linestyle=dashed]{0.65}{1}{A}{D}{B}

    \myputnodeoncurve{0.5}{A}{D}{B}{E}
    \rput(E){$\sqrt{2}$}

\end{pspicture}
\end{document}

Something which looks more like what you want

\begin{pspicture}[showgrid=false](0,0)(4,4)
    \pstGeonode[PosAngle={-135,45,-45},
                PointName={default,default,none},
                PointSymbol={default,default,none}]
        (2,1){A}
        (5,5){B}
        (5,1){C}
\mybeziercurve[linecolor=black,linewidth=0.4pt,linestyle=dashed]{0}{0.40}{A}{C}{B}
\mybeziercurve[linecolor=black,linewidth=0.4pt,linestyle=dashed]{0.60}{1}{A}{C}{B}

\myputnodeoncurve{0.5}{A}{C}{B}{E}
\rput(E){$\sqrt{2}$}
\end{pspicture}

Your selection of where to place the control point will allow you to better shape the curve.

You can add the following to your preamble:

%% command to get angle 
\newcommand{\mygetangle}[2]
    {   !
        tx@EcldDict begin
        /N@#2 GetNode 0 mul add
        /N@#1 GetNode 0 mul add sub 
        /N@#2 GetNode exch 0 mul add
        /N@#1 GetNode exch 0 mul add sub 
        exch
        atan
        end
     } 

And then you can slope the label accordingly using

\begin{pspicture}[showgrid=false](0,0)(4,4)
   \pstGeonode[PosAngle={-135,45,-45},
               PointName={default,default,none},
               PointSymbol={default,default,none}]
       (2,1){A}
       (5,5){B}
       (5,1){C}


   \mybeziercurve[linecolor=black,linewidth=0.4pt,linestyle=dashed]{0}{0.40}{A}{C}{B}
   \mybeziercurve[linecolor=black,linewidth=0.4pt,linestyle=dashed]{0.60}{1}{A}{C}{B}

   %% Setting points to get slope of omitted section
   \myputnodeoncurve{0.40}{A}{C}{B}{E1}
   \myputnodeoncurve{0.50}{A}{C}{B}{E}
   \myputnodeoncurve{0.60}{A}{C}{B}{E2}
   \rput{\mygetangle{E1}{E2}}(E){$\sqrt{2}$}

\end{pspicture}