How to draw smooth curves with PSTricks?

Question

Consider the following example:

\documentclass{article}

\usepackage{pstricks-add}

\begin{document}

\begin{pspicture}(0,-0.25)(4,6.25)
 \pnode(2,0){A}
 \pnode(0,4){B}
 \pnode(2,6){C}
 \pnode(4,4){D}
 \rput(1.5,3.5){\small{$A$}}
 \rput(1.5,4.5){\small{$B$}}
 \rput(2.5,4.5){\small{$C$}}
 \rput(2.5,3.5){\small{$D$}}
 \multido{\iA=0+1}{7}{\psline[linestyle=dashed,linecolor=blue](0,\iA)(4,\iA)}
 \multido{\iB=0+1}{5}{\psline[linestyle=dashed,linecolor=blue](\iB,0)(\iB,6)}
 \psline[linewidth=1.25pt](A)(C)
 \psline[linewidth=1.25pt](B)(D)
 \pspolygon[linewidth=2pt,linecolor=red](A)(B)(C)(D)
 \pscurve[linewidth=1pt]{->}(2.75,4.75)(2.8,5.25)(2.65,5.75)(2,6.25)(1.25,6)(0.75,5.25)
 \pscurve[linewidth=1pt]{->}(2.5,2.5)(2.95,1)(2.65,0.2)(2,-0.25)(1,0)(0.5,1.5)
\end{pspicture}

\end{document}

How do I make the curved arrows smooth?

I guess the \psbezier function is the way to do it but I cannot make it look nice, so help will be much appreciated.

Update

In case someone finds the figure useful, here is a generalization of the code:

\documentclass[a4paper]{article}

\usepackage[hmargin=2.4cm,vmargin=3cm]{geometry}
\usepackage{subcaption}
\usepackage{auto-pst-pdf,pstricks-add}
\usepackage{expl3}

\ExplSyntaxOn
 \cs_new_eq:NN
  \calculate
 \fp_eval:n
\ExplSyntaxOff

\newcommand*{\betegn}[3]{%
  \rput(!#1 4 div \figur\space mul #2 4 div \figur\space mul){\small{$#3$}}
}

\begin{document}

\begin{figure}[htbp]
% Figure number.
\def\figur{2}
% Constants.
\def\hoejde{\calculate{3*\figur}}
\def\bredde{\calculate{2*\figur}}
\def\faktorA{\calculate{\hoejde+1}}
\def\faktorB{\calculate{\bredde+1}}
\def\faktorC{\calculate{\hoejde-1}}
\def\faktorD{\calculate{\figur-1}}
\def\skalering{\calculate{2.5/\figur}}
\centering
\psset{
 unit=\skalering
}
\begin{subfigure}{0.58\textwidth}
 \centering
  \begin{pspicture}(\bredde,\hoejde)
   \pnode(!\figur\space 0){A}
   \pnode(!0 \bredde\space){B}
   \pnode(!\figur\space \hoejde\space){C}
   \pnode(!\bredde\space \bredde\space){D}
   \betegn{3}{7}{A}
   \betegn{3}{9}{B}
   \betegn{5}{9}{C}
   \betegn{5}{7}{D}
  \psset{
   linestyle=dashed,
   linecolor=blue
  }
   \multido{\iA=0+1}{\faktorA}{\psline(0,\iA)(\bredde\space,\iA)}
   \multido{\iB=0+1}{\faktorB}{\psline(\iB,0)(\iB,\hoejde\space)}
  \psset{
   linewidth=1.25pt,
   linestyle=solid,
   linecolor=black
  }
   \psline(A)(C)
   \psline(B)(D)
   \pspolygon[linewidth=2pt,linecolor=red](A)(B)(C)(D)
  \end{pspicture}
 \subcaption{Before the rearrangement.}
\end{subfigure}
\begin{subfigure}{0.38\textwidth}
 \centering
  \begin{pspicture}(\figur,\hoejde)
   \pnode(0,0){A}
   \pnode(!0 \bredde\space){B}
   \pnode(!0 \hoejde\space){C}
   \pnode(!\figur\space \hoejde\space){D}
   \pnode(!\figur\space \bredde\space){E}
   \pnode(!\figur\space 0){F}
   \betegn{3}{7}{A}
   \betegn{3}{9}{B}
   \betegn{1}{11}{C}
   \betegn{1}{1}{D}
  \psset{
   linestyle=dashed,
   linecolor=blue
  }
   \multido{\iC=1+1}{\faktorC}{\psline(0,\iC)(\figur\space,\iC)}
   \multido{\iD=1+1}{\faktorD}{\psline(\iD,0)(\iD,\hoejde\space)}
  \psset{
   linewidth=1.25pt,
   linestyle=solid,
   linecolor=black
  }
   \pspolygon(A)(C)(D)(F)
   \psline(B)(E)
   \psline[linewidth=2pt,linecolor=red](F)(B)(D)
  \end{pspicture}
 \subcaption{After the rearrangement.}
\end{subfigure}
\caption{Figure~$\figur$.}
\end{figure}

\end{document}

All you have to do is change the value of \figur.

The document can be compiled with pdflatex -shell-escape filename.tex.

Answer 1

You can use the package \pst-bezier which gives you a nicer bezier function \psbcurve. This package also allows various modifiers that help you tweak the curve. The only problem with this approach is that arrows don't work.

\documentclass{article}

\usepackage{pstricks-add}
\usepackage{pst-bezier}

\begin{document}

\begin{pspicture}[showgrid=true](0,-0.25)(4,6.25)
 \pnode(2,0){A}
 \pnode(0,4){B}
 \pnode(2,6){C}
 \pnode(4,4){D}
 \pnode(2,4){E}
 \rput(1.5,3.5){\small{$A$}}
 \rput(1.5,4.5){\small{$B$}}
 \rput(2.5,4.5){\small{$C$}}
 \rput(2.5,3.5){\small{$D$}}
% \multido{\iA=0+1}{7}{\psline[linestyle=dashed,linecolor=blue](0,\iA)(4,\iA)}
% \multido{\iB=0+1}{5}{\psline[linestyle=dashed,linecolor=blue](\iB,0)(\iB,6)}
 \psline[linewidth=1.25pt](A)(C)
 \psline[linewidth=1.25pt](B)(D)
 \pspolygon[linewidth=2pt,linecolor=red](A)(B)(C)(D)
 \pscurve[linecolor=blue,linewidth=1pt]{->}(2.75,4.75)(2.8,5.25)(2.65,5.75)(2,6.25)(1.25,6)(0.75,5.25)
 \pscurve[linecolor=blue,linewidth=1pt]{->}(2.5,2.5)(2.95,1)(2.65,0.2)(2,-0.25)(1,0)(0.5,1.5)

  \psset{showpoints=false,linecolor=red,linewidth=2pt,arrows=->,arrowscale=1.5}
  \psbcurve(2.75,4.75)(2.5,6)(1.5,6.5)(0.75,5.25)
  \psbcurve(2.5,2.5)(3,0.5)(1,0)(0.5,1.5)

\end{pspicture}

\end{document}

I've superimposed my bezier curves (red) on your curves (blue).

Arrows

To get the arrows, you'll have to do a tad more work....

The lines passing through the end points and the first and last control interpolation will be tangent to the curve. If you can figure out the value of those interpolation points, you can create arrows by doing something like:

\ncnode[nodesepA=<value>,arrows=->]{interpolation_point}{end_point}

You'll have to create nodes to do this. If you set showpoints=true that can help with guessing where to define the node for the interpolation point. In fact, you don't really have to get the interpolation point, you just need to get a point that will match the curve formed by the last interpolation point and the end point of the curve.

After a bit of tweaking (using the show lines feature)

  \pnode(0.50,0){interpolationA}
  \pnode(0.5,1.5){endpointA}
  \ncline[nodesepA=4em,nodesepB=-0.1]{interpolationA}{endpointA}

Resulting in:

You can do something similar for the other side.

\documentclass{article}
\usepackage{pst-node}
\usepackage{pstricks-add}
\usepackage{pst-bezier}
\pagestyle{empty}
\begin{document}

\begin{pspicture}[showgrid=true](0,-0.25)(4,6.25)
 \pnode(2,0){A}
 \pnode(0,4){B}
 \pnode(2,6){C}
 \pnode(4,4){D}
 \pnode(2,4){E}
 \rput(1.5,3.5){\small{$A$}}
 \rput(1.5,4.5){\small{$B$}}
 \rput(2.5,4.5){\small{$C$}}
 \rput(2.5,3.5){\small{$D$}}
 % \multido{\iA=0+1}{7}{\psline[linestyle=dashed,linecolor=blue](0,\iA)(4,\iA)}
 % \multido{\iB=0+1}{5}{\psline[linestyle=dashed,linecolor=blue](\iB,0)(\iB,6)}
 \psline[linewidth=1.25pt](A)(C)
 \psline[linewidth=1.25pt](B)(D)
 \pspolygon[linewidth=2pt,linecolor=red](A)(B)(C)(D)
 % \pscurve[linecolor=blue,linewidth=1pt]{->}(2.75,4.75)(2.8,5.25)(2.65,5.75)(2,6.25)(1.25,6)(0.75,5.25)
 % \pscurve[linecolor=blue,linewidth=1pt]{->}(2.5,2.5)(2.95,1)(2.65,0.2)(2,-0.25)(1,0)(0.5,1.5)

  \psset{showpoints=false,linecolor=red,linewidth=2pt,arrows=->,arrowscale=1.5}
  \psbcurve(2.75,4.75)(2.5,6)(1.5,6.5)(0.75,5.25)
  \psbcurve(2.5,2.5)(3,0.5)(1,0)(0.5,1.5)

  \pnode(0.50,0){interpolationA}
  \pnode(0.5,1.5){endpointA}
  \ncline[nodesepA=4em,nodesepB=-0.1]{interpolationA}{endpointA}

  %\psset{linecolor=black}
  \pnode(1.15,6.5){interpolationB}
  \pnode(0.75,5.25){endpointB}
  \ncline[nodesepA=4em,nodesepB=-0.2]{interpolationB}{endpointB}

\end{pspicture}

\end{document}

Notice that I tweak both ends of the curve with nodesepA and nodesepB.

Answer 2

The only way to get a better shape is by adjusting the points. Turn on showpoints to make us easily adjust the points.

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

\addtopsstyle{gridstyle}
{
    gridcolor=blue!50,
    griddots=10,
    gridlabels=0pt,
}

\begin{document}
\begin{pspicture}(0,-0.25)(4,6.25)
    \pstGeonode[PointName=none,PointSymbol=none]
        (2,0){A}
        (0,4){B}
        (2,6){C}
        (4,4){D}
        %(2,4){E} <-- I don't know why the questioner defined this unused node.
    \rput(1.5,3.5){\small{$A$}}
    \rput(1.5,4.5){\small{$B$}}
    \rput(2.5,4.5){\small{$C$}}
    \rput(2.5,3.5){\small{$D$}}
    \psgrid[style=gridstyle](0,0)(0,0)(4,6)
    \psset{linewidth=1.25pt}
    \psline(A)(C)
    \psline(B)(D)
    \pspolygon[linewidth=2pt,linecolor=red](A)(B)(C)(D)
    \psset{linewidth=1pt,arrows=->,showpoints}
    \pscurve(2.75,4.75)(2.8,5.25)(2.65,5.75)(2,6.25)(1.25,6)(0.75,5.25)
    \pscurve(2.5,2.5)(2.95,1)(2.65,0.2)(2,-0.25)(1,0)(0.5,1.5)
\end{pspicture}
\end{document}

Answer 3

with package pst-bspline

 \psBspline[linewidth=1pt,arrows=->]{A}(2.75,4.75)(2.8,5.25)(2.65,5.75)(2,6.25)(1.25,6)(0.75,5.25)
\psBspline[linewidth=1pt,arrows=->]{B}(2.5,2.5)(2.95,1)(2.65,0.2)(2,-0.25)(1,0)(0.5,1.5)