Scaling and trimming white space from a pgfplots picture

Question

In answering How do I create a combined figure with two imported curves and draw around it with Tikz?, I was able to make my own graph fill the space between two horizontal lines as seen here. However, when I tried to import a dat file, I ran into difficulties.

My first problem was scaling. I thought I could use the key height to fix the height of the image. But it's not behaving as I thought it would:

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\def\myimage#1{%%
    \begin{tikzpicture}%%[x=#1,y=#1]
      \begin{axis}[
        height=#1,
        hide axis,
        no markers,
      ]
      \addplot + table[x index=0, y index=1]{vp1.dat};
      \end{axis}
  \end{tikzpicture}}

\pagestyle{empty}
\begin{document}

\begin{tikzpicture}
  \draw (0,0) -- ++(6,0)
        (0,4) -- ++(6,0);
  \node[inner sep=0pt,draw,red] at (3,2) {\myimage{4cm}};
\end{tikzpicture}

\end{document}

I wanted it so that the red box's top and bottom should be flush with the black horizontal lines.

My second problem was getting rid of all the white space. I would like the bounding box for the graph to fit as tightly as possible when I've hidden the axes. In other words, the red border should be snug up against the blue of the graph.

Here's my vp1.dat file:

1 3
2 4
3 -5
4 6

Here's my vp2.dat file:

1 3
2 4
3 1
4 3

Update

I have partial solutions to my questions but no combined solution.

Solution to first problem

Regarding the first problem, I can get the pgfplot to fill the desired effect by using a combination of

scale only axis
height=#2

MWE:

\documentclass{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{tikz}
\usepackage{pgfplots}
\def\myimage#1#2{%%
    \begin{tikzpicture}
      \begin{axis}[
        scale only axis,
        height=#2,
        hide axis,
        no markers,
      ]
      \addplot + table[x index=0, y index=1]{#1};
      \end{axis}
  \end{tikzpicture}}

\pagestyle{empty}
\begin{document}

\begin{tikzpicture}
  \draw (0,0) -- ++(6,0)
        (0,4) -- ++(6,0);
  \node[anchor=south] at (3,4) {\texttt{height=4cm} passed to \texttt{pgfplots}};
  \node[inner sep=0pt,draw,red] at (3,2) {\myimage{vp1.dat}{4cm}};
  \draw[<->] (6.25,0) -- ++(0,4) node [midway,right]{4cm};
\end{tikzpicture}

\end{document}

which results in:

Solution to second problem

Regarding the second problem, I can get the pgfplot to trim the extra white space that I do not want by using both

clip bounding box=upper bound
hide axis

MWE:

\documentclass{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{tikz}
\usepackage{pgfplots}
\def\myimage#1#2{%%
    \begin{tikzpicture}
      \begin{axis}[
        clip bounding box=upper bound,
        hide axis,
        no markers,
      ]
      \addplot + table[x index=0, y index=1]{#1};
      \end{axis}
  \end{tikzpicture}}

\pagestyle{empty}
\begin{document}

\begin{tikzpicture}
  \node[anchor=south] at (3,4.35) {graph fits snuggly in its bounding box};
  \node[inner sep=0pt,draw,red] at (3,2) {\myimage{vp1.dat}{4cm}};
\end{tikzpicture}

\end{document}

which results in:

No solution for combined approach

But when I try to combine both methods, the height is not obeyed properly and I can't figure out how it's being calculated.

\documentclass{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{tikz}
\usepackage{pgfplots}
\def\myimage#1#2{%%
    \begin{tikzpicture}
      \begin{axis}[
        scale only axis,
        clip bounding box=upper bound,
        height=#2,
        hide axis,
        no markers,
      ]
      \addplot + table[x index=0, y index=1]{#1};
      \end{axis}
  \end{tikzpicture}}

\pagestyle{empty}
\begin{document}

\begin{tikzpicture}
  \draw (0,0) -- ++(6,0)
        (0,4) -- ++(6,0);
  \node[anchor=south] at (3,4) {combining \texttt{clipping} and \texttt{height}};
  \node[inner sep=0pt,draw,red] at (3,2) {\myimage{vp1.dat}{4cm}};
  \draw[<->] (6.25,0) -- ++(0,4) node [midway,right]{4cm};
\end{tikzpicture}
\end{document}

which results in:

Answer 1

You want enlargelimits=false combined with scale only axis and height. pgfplots adds some whitespace around the plot by default, enlargelimits=false removes that.

\documentclass{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{tikz}
\usepackage{pgfplots}
\def\myimage#1#2{%%
    \begin{tikzpicture}
      \begin{axis}[
        scale only axis,
        height=#2,
        hide axis,
        no markers,
        enlargelimits=false
      ]
      \addplot + table[x index=0, y index=1]{#1};
      \end{axis}
  \end{tikzpicture}}

\pagestyle{empty}
\begin{document}

\begin{tikzpicture}
  \draw (0,0) -- ++(6,0)
        (0,4) -- ++(6,0);
  \node[anchor=south] at (3,4) {\texttt{enlargelimits}, \texttt{scale only axis} and \texttt{height}};
  \node[inner sep=0pt,draw,red] at (3,2) {\myimage{vp1.dat}{4cm}};
  \draw[<->] (6.25,0) -- ++(0,4) node [midway,right]{4cm};
\end{tikzpicture}
\end{document}

Answer 2

I hope someone can come up with an answer which sticks entirely with tikz or pgfplots directives.

Here's a solution that lets me both clip the extra white space and set the box to the desired height.

My approach is to use pgfplots ability to clip the extra white space via

hide axis
clip bounding box=upper bound

Then I save the graph to a box (or, I could put it in its own standalone file). Then I scale according to the size of the saved box.

\documentclass{article}
\usepackage[margin=0.5in]{geometry}
\usepackage{tikz}
\usepackage{pgfplots}

\def\myimageSnug#1{%%
    \begin{tikzpicture}
      \begin{axis}[
        clip bounding box=upper bound,
        hide axis,
        hide axis,
        no markers,
      ]
      \addplot + table[x index=0, y index=1]{#1};
      \end{axis}
  \end{tikzpicture}}

\pagestyle{empty}
\begin{document}

\newsavebox{\myimagebox} 
\savebox{\myimagebox}{\myimageSnug{vp1.dat}}
\begin{tikzpicture}
  \draw (0,0) -- ++(6,0)
        (0,4) -- ++(6,0);
  \node[anchor=south] at (3,4.35) {\footnotesize graph fits snuggly in its bounding box \textbf{and} it's the correct height};

  \node[inner sep=0pt,draw,red,scale=4cm/\ht\myimagebox] at (3,2) {\usebox{\myimagebox}};
\end{tikzpicture}%%

\end{document}

resulting in

Alternatively, I could use a standalone file named graph_01:

\documentclass{standalone}
\usepackage{pgfplots}
\begin{document}

\begin{tikzpicture}
  \begin{axis}[
    clip bounding box=upper bound,
    hide axis,
    hide axis,
    no markers,
  ]
  \addplot + table[x index=0, y index=1]{vp1.dat};
  \end{axis}
\end{tikzpicture}

\end{document}

And then import it:

\documentclass{article}
\usepackage{graphicx}
\usepackage[margin=0.5in]{geometry}
\usepackage{tikz}
\usepackage{pgfplots}
\pagestyle{empty}
\begin{document}

\begin{tikzpicture}
  \draw (0,0) -- ++(6,0)
        (0,4) -- ++(6,0);
  \node[anchor=south] at (3,4.35) {\footnotesize graph fits snuggly in its bounding box \textbf{and} it's the correct height};

  \node[inner sep=0pt,draw,red] at (3,2) {\includegraphics[height=4cm]{graph_01}};
\end{tikzpicture}%%

\end{document}