Plot with increments

Question

I am trying to adapt the solution here to be inside a pgf axis and use axis coordinates. The solution is based on a draw command like the following

\draw (0,0) \foreach \x in {1,...,5} { -- ++ (1,0.1*\x)};

where the increments are specified instead of points.

I tried using the addplot command instead of draw (So I can specify axis coordinates). However I am running into problems. First the following simple example

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
  \begin{axis}
    \addplot [mark=*] (0,0) -- ++(0.1,0.1) -- ++(0.3, -0.4);
  \end{axis}
\end{tikzpicture}
\end{document}

compiles but the plot is not correct and I get the warning

Package pgfplots Warning: Axis range for axis x is approximately empty; enlarging it (it is [0.0:0.0]) on input line 40.

Specifying the axis limits removes the warning. Additionally, the example

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
  \begin{axis}
    \addplot [mark=*] (0,0) 
     \foreach \x in {1,...,5}
      {  -- ++(1,0.1*\x) };
  \end{axis}
\end{tikzpicture}
\end{document}

does not compile at all. Replacing \foreach by \pgfplotsforeachungrouped does not help.

Is there away to specify the increments in \addplot?

Answer 1

There are several things at play here.

1. You need at least an \addplot command if you want automatic scaling in an axis environment --- otherwise, you need to scale it manually;
2. As said by @hpekristiansen, foreach does not work as expected in an axis environment, and you have to resort to \pgfplotsinvokeforeach;
3. In an axis environment, the (default since 1.11) axis cs: coordinate system accepts only absolute coordinates; you need to use the axis direction cs: coordinate system to do incremental moves;
4. And finally, it seems that using the correct coordinates the \foreach does work, as notice by @hpekristiansen.

Example:

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
    % you need to manually scale the axis if you do not use "addplot"
    \begin{axis}[xmin=-5,xmax=5,ymin=-5,ymax=5]
      % let's unfold the "foerach" manually to see how it works
      % with the correct coordinate system
      \draw[red] (0,0) -- ++ (axis direction cs:1,0.1) 
          -- ++(axis direction cs:1,0.2)
          -- ++(axis direction cs:1,0.3)
          -- ++(axis direction cs:1,0.4)
          -- ++(axis direction cs:1,0.5);
      % to have the "foreach" function, we must use "pgfplotsinvokeforeach",
      % which accepts only full statement. Let's use a 
      % temporary coordinate to simulate the "last point"
      \coordinate (last) at (0,-0.5);
      \pgfplotsinvokeforeach{1,...,5}{%
        \draw[blue] (last) -- ++ (axis direction cs:1,0.1*#1) coordinate(last);}
       % in this case the plain foreach seems also to work
       % I do not know why...
       \draw[green] (0,-1) \foreach \x in {1,...,5} 
            { -- ++ (axis direction cs: 1,0.1*\x)};
  \end{axis}
\end{tikzpicture}
\end{document}

Answer 2

One option is to use the command \pgfplotsinvokeforeach (taken from this answer).

Here is the code. (I've also changed the -- from your addplot to coordinates. This was taken from the PGFPlots Gallery.)

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}
            \pgfplotsinvokeforeach{1, ..., 5} {
                \addplot coordinates {
                    (0, 0)
                    (1, 0.1*#1)
                };
            }
        \end{axis}
    \end{tikzpicture}
\end{document}

and generates this image:

---

Edit

I misunderstood the question before. The following should work, although it might not be the "best" solution. I define a coordinate (current) from which I draw the next segment. Then I define a coordinate (tmp) (using \path) where the next position is and then I redefine (current) to be (tmp).

\begin{tikzpicture}
    \begin{axis}[
        xmin=0,
        xmax=5,
        ymin=0,
        ymax=2,
        ]
\coordinate (current) at (axis cs: 0, 0);

\pgfplotsinvokeforeach{1, ..., 5} {
    \draw[mark=*] (current) -- ++(axis cs: 1, 0.1*#1);
    \path (current) ++(axis cs: 1, 0.1*#1) coordinate (tmp);
    \coordinate (current) at (tmp);
}
\end{axis}

\end{tikzpicture}

Alternatively you could use \coordinate (tmp) at ($(current)+(axis cs: 1, 0.1*#1)$); to define (tmp), though this requires \usetikzlibrary{calc} in the preamble. Sadly, apparently one needs to pass in xmin, ..., ymax manually, if addplot is never used (at least nothing is drawn for me, if I don't pass them in manually). This is the generated picture:

Answer 3

samples at already has a \foreach syntax, so there is no need to use \foreach.

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
  \begin{axis}
    \addplot[mark=*, samples at={0,...,5}] (\x, 0.1*\x);
  \end{axis}
\end{tikzpicture}
\end{document}

Edit:

Here is a solution, that does not use \addplot but \draw - also a solution that adds marks:

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\begin{document}
\begin{tikzpicture}
  \begin{axis}[xmin=-1, xmax=12, ymin=-1, ymax=10]
    \draw[thick] (0,0) \foreach \x in {1,...,5} { -- ++ (1,0.1*\x)};
    \draw[red] (0,0) \foreach \x in {1,...,5} { -- plot[mark=*] coordinates { ++(1,0.1*\x)}};
  \end{axis}
\end{tikzpicture}
\end{document}

This does not work right now because I used \foreach inside axis - it need to be rewritten with PGFPlots variants of \foreach.

Edit:

I found that it is not possible to do it like that with PGFPlots variants of \foreach. An alternative is to use a named coordinate as in the answer by @Simon, so that it can be drawn piecewise. -but with plot, so that marks can be made:

\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
\begin{axis}[xmin=0, xmax=5, ymin=0, ymax=2]
\coordinate (current) at (0, 0);  
\pgfplotsinvokeforeach{1, ..., 5} {
  \draw (current) -- plot[mark=*] coordinates {++(1, 0.1*#1)} coordinate (current);
}
\end{axis}
\end{tikzpicture}
\end{document}

For some reason, the entire plot changes when xmin is changed to e.g. -1. I can not explain this strange behaviour.