Can we imitate the behavior of \pscurve in TikZ?

Question

Here it is with the pictures.

PSTricks has the very neat command \pscurve. The manual gives the example

\pscurve[showpoints=true]{<->}(0,1.3)(0.7,1.8) (3.3,0.5)(4,1.6)(0.4,0.4)

which yields

Does somebody knows how to get the same behavior in TikZ?

I have tried using all sorts of techniques including

\tikz \draw plot[smooth] coordinates {(0,1.3) (0.7,1.8) (3.3,0.5) (4,1.6) (0.4,0.4)};

which gives me

(I did try to play with the tension!). The resulting curve always looks like a succession of straight segments with rounded corners.

Thank you for the points!

Answer 1

As far as I'm aware, this can't be done "out of the box". However, with a little programming then there's no reason why it can't. Exactly what programming is needed depends a little on the exact specifications of the problem: is it to exactly replicate pstricks' behaviour, or to simply do something similar? If the former, then you will need to dig into the pstricks code and extract the formula of how it decides where to draw the lines. If the latter, then a little experimenting can produce a reasonable result.

I don't guarantee that the following will produce a nice smooth curve through any arbitrary family of points, but it is a reasonable method. The drawing command is done by bezier curves between the specified points. The difficulty is working out decent control points. For this, one needs to look ahead to the next point and work out a suitable pair of control points. What I chose to do was to imagine a line joining the prior and next points, take it's midpoint, then join that to the current point. Taking the orthogonal line to this through the current point gave me the direction of my control points. The length is then proportional to the distance between the current point and the prior/next point (as appropriate).

For the control points specified, this gives me:

\documentclass{minimal}

\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}

\begin{tikzpicture}
\let\pcoord\relax
\let\tcoord\relax
\foreach [count=\num] \coord in {
  (0,1.3),
  (0.7,1.8),
  (3.3,0.5),
  (4,1.6),
  (0.4,0.4)
  } {
  \ifx\pcoord\relax
   \global\let\pcoord\coord
   \path \pcoord coordinate (c1);
  \else
   \ifx\tcoord\relax
   \global\let\tcoord\coord
   \else
    \path \pcoord coordinate (p);
    \path \tcoord coordinate (t);
    \path \coord coordinate (n);
    \path ($(p)!.75!(n)$) coordinate (m);
    \path ($(t)!1cm!90:(m)$) coordinate (r);
    \path ($(t)-(p)$);
    \pgfgetlastxy{\xx}{\yy}
    \pgfmathsetmacro{\len}{.5*veclen(\xx,\yy)}
    \path ($(t)!(p)!(r)$) coordinate (rp);
    \path ($(t)!\len pt!(rp)$) coordinate (c2);
    \draw (p) .. controls (c1) and (c2) .. (t);
    \path ($(t)-(n)$);
    \pgfgetlastxy{\xx}{\yy}
    \pgfmathsetmacro{\len}{.5*veclen(\xx,\yy)}
    \path ($(t)!(n)!(r)$) coordinate (rn);
    \path ($(t)!\len pt!(rn)$) coordinate (c1);
    \global\let\pcoord\tcoord
    \global\let\tcoord\coord
   \fi
  \fi
}
\draw (t) .. controls (c1) and (n) .. (n);

\end{tikzpicture}

\end{document}

(If done "in anger", one should probably worry about bounding boxes. I didn't.)

1. It would probably be better to use the tangent of the circumcircle to compute the direction of the control points (that would make the first one look better).
2. It would also be better to make the whole thing one path rather than a concatenation of several paths.

Answer 2

I tried to recreate @Andrew's idea as a plot handler. However for some reason I get a different result. Maybe someone can tell me what is wrong (it is late...). Anyway, here is the plot handler:

\makeatletter

\def\pgfplothandlermycurveto{%
  \def\pgf@plotstreamstart{%
    \global\let\pgf@plotstreampoint=\pgf@plot@mycurveto@handler@initial%
    \global\let\pgf@plotstreamspecial=\pgfutil@gobble%
    \global\let\pgf@plotstreamend=\pgf@plot@mycurveto@handler@finish%
    \global\pgf@plot@startedfalse%
  }%
}

\def\pgf@plot@mycurveto@handler@initial#1{%
  \pgf@process{#1}%
  \pgf@xa=\pgf@x%
  \pgf@ya=\pgf@y%
  \pgf@plot@first@action{\pgfqpoint{\pgf@xa}{\pgf@ya}}%
  \xdef\pgf@plot@mycurveto@first{\noexpand\pgfqpoint{\the\pgf@xa}{\the\pgf@ya}}%
  \global\let\pgf@plot@mycurveto@first@support=\pgf@plot@mycurveto@first%
  \global\let\pgf@plotstreampoint=\pgf@plot@mycurveto@handler@second%
}

\def\pgf@plot@mycurveto@handler@second#1{%
  \pgf@process{#1}%
  \xdef\pgf@plot@mycurveto@second{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  \global\let\pgf@plotstreampoint=\pgf@plot@mycurveto@handler@third%
  \global\pgf@plot@startedtrue%
}

\def\pgf@plot@mycurveto@handler@third#1{%
  \pgf@process{#1}%
  \xdef\pgf@plot@mycurveto@current{\noexpand\pgfqpoint{\the\pgf@x}{\the\pgf@y}}%
  % compute midpoint:
  \pgf@xa=\pgf@x%
  \pgf@ya=\pgf@y%
  \pgf@process{\pgf@plot@mycurveto@first}
  \advance\pgf@xa by\pgf@x%
  \advance\pgf@ya by\pgf@y%
  \pgf@xa=0.5\pgf@xa%
  \pgf@ya=0.5\pgf@ya%
  \pgf@xb=\pgf@xa%
  \pgf@yb=\pgf@ya%
  % vector from second to midpoint:
  \pgf@process{\pgf@plot@mycurveto@second}
  \advance\pgf@xa by-\pgf@x%
  \advance\pgf@ya by-\pgf@y%
  % vector from first to midpoint:
  \pgf@process{\pgf@plot@mycurveto@first}
  \advance\pgf@xb by-\pgf@x%
  \advance\pgf@yb by-\pgf@y%
  % normalize
  \pgfmathparse{\pgf@plottension / veclen(\pgf@xa,\pgf@ya)}%
  \let\pgf@l@dir=\pgfmathresult
  \pgfmathsetlength{\pgf@xa}{\pgf@xa * \pgf@l@dir}%
  \pgfmathsetlength{\pgf@ya}{\pgf@ya * \pgf@l@dir}%
  % compute orientation
  \pgfmathparse{\pgf@xa * \pgf@yb - \pgf@ya * \pgf@xb}%
  \pgfmathparse{-greater(\pgfmathresult,0) + less(\pgfmathresult,0)}
  \pgf@xa=\pgfmathresult\pgf@xa%
  \pgf@ya=\pgfmathresult\pgf@ya%
  % load second point
  \pgf@process{\pgf@plot@mycurveto@second}%
  \pgf@xb=\pgf@x%
  \pgf@yb=\pgf@y%
  \pgf@xc=\pgf@x%
  \pgf@yc=\pgf@y%
  % compute lengths
  \pgf@process{\pgf@plot@mycurveto@first}%
  \pgfmathparse{veclen((\pgf@xb-\pgf@x),(\pgf@yb-\pgf@y))}%
  \let\pgf@l@first=\pgfmathresult%
  \pgf@process{\pgf@plot@mycurveto@current}%
  \pgfmathparse{veclen(\pgf@xb-\pgf@x,\pgf@yb-\pgf@y)}%
  \let\pgf@l@second=\pgfmathresult%
  % first marshal:
  \pgfmathaddtolength{\pgf@xb}{-\pgf@l@first * \pgf@ya}%
  \pgfmathaddtolength{\pgf@yb}{\pgf@l@first * \pgf@xa}%
  \pgfmathaddtolength{\pgf@xc}{\pgf@l@second * \pgf@ya}%
  \pgfmathaddtolength{\pgf@yc}{-\pgf@l@second * \pgf@xa}%
  \edef\pgf@marshal{\noexpand\pgfpathcurveto{\noexpand\pgf@plot@mycurveto@first@support}%
    {\noexpand\pgfqpoint{\the\pgf@xb}{\the\pgf@yb}}{\noexpand\pgf@plot@mycurveto@second}}%
  {\pgf@marshal}%
  % Prepare next:
  \global\let\pgf@plot@mycurveto@first=\pgf@plot@mycurveto@second%
  \global\let\pgf@plot@mycurveto@second=\pgf@plot@mycurveto@current%
  \xdef\pgf@plot@mycurveto@first@support{\noexpand\pgfqpoint{\the\pgf@xc}{\the\pgf@yc}}%
}

\def\pgf@plot@mycurveto@handler@finish{%
  \ifpgf@plot@started%
    \pgfpathcurveto{\pgf@plot@mycurveto@first@support}{\pgf@plot@mycurveto@second}{\pgf@plot@mycurveto@second}%
  \fi%
}

\tikzoption{mysmooth}[]{\let\tikz@plot@handler=\pgfplothandlermycurveto}
\makeatother

In order to get a single path for the plot, the calculations have to be done by hand without using any additional paths. If you include the above code somewhere after \usepackage{tikz}, you can use the mysmooth option to start the plot handler. It respects the tension and produces a single path.

For example:

\tikz {
\draw plot[mysmooth,mark=x] coordinates {(0,1.3)(0.7,1.8) (3.3,0.5)(4,1.6)(0.4,0.4)};
\draw[red,densely dotted] plot[mysmooth,tension=1.5] coordinates {(0,1.3)(0.7,1.8) (3.3,0.5)(4,1.6)(0.4,0.4)};
\draw[gray,dashed] plot[smooth,tension=0.5] coordinates {(0,1.3)(0.7,1.8) (3.3,0.5)(4,1.6)(0.4,0.4)};
\draw[dotted,gray] (0,0) grid (4,2);
}

produces

.

Answer 3

I just tried the following solutions which compiles and gives the "right" output: put a PSTricks picture inside a TikZ node (it is Christmas time and miracles abound).

\documentclass[10pt]{article} 

\usepackage{pstricks,tikz}
\begin{document}

\begin{tikzpicture}
\node {%
\begin{pspicture}(4,2)
\pscurve[showpoints=true]{<->}(0,1.3)(0.7,1.8) (3.3,0.5)(4,1.6)(0.4,0.4)
\end{pspicture}%
};
\draw [red] (0,0) -- (1,1);
\end{tikzpicture}
\end{document}

The red line is here just to make absolutely sure that we can mix PSTricks objects and Tikz objects.

I assume that if we try fancier things we might get into conflicts, but at least for simple things this seems to be a solution.

And thanks Herbert - it is your question which gave me the idea to try this hack.

Answer 4

\documentclass[10pt]{article} 

\usepackage{pstricks,tikz}
\begin{document}

\begin{tikzpicture}(4,2)
\node at (0,0){%
\pscurve[showpoints]{<->}(0,1.3)(0.7,1.8) (3.3,0.5)(4,1.6)(0.4,0.4)
};
\draw [red] (0,0) -- (1,1);
\end{tikzpicture}
\end{document}