Coordinates of intersection

Question

The code generates a strain-stress curve. How can the code be simplified? How can the code be make smarter?

Can I make the Bezier curve with one draw command? \ShowintersectionB prints just the coordinates of the intersection point. I don't know how to do this without the circle (0pt) command. Can I save the coordinates of the intersection point and print them later in the text?

I took some of the code from:

• Coordinates of intersections
• Can I mark ends of lines with a cross?
• Intersections in PGFplots

---

\documentclass[12pt]{standalone}

\usepackage[per-mode=symbol]{siunitx}

\usepackage{pgfplots}
\pgfplotsset{compat=1.11}

\usepackage{tikz}

\usetikzlibrary{intersections}
\usetikzlibrary{calc}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{shapes.misc}

\tikzset{
  crossp/.style={
    thick,
    draw=gray,
    cross out,
    inner sep=0pt,
    outer sep=0pt,
    minimum size=2*(#1-\pgflinewidth),
  },
}

\begin{document}

\makeatletter
\newcommand\transformxdimension[1]{
\pgfmathparse{((#1/\pgfplots@x@veclength)+\pgfplots@data@scale@trafo@SHIFT@x)/10^\pgfplots@data@scale@trafo@EXPONENT@x}
}

\newcommand\transformydimension[1]{
\pgfmathparse{((#1/\pgfplots@y@veclength)+\pgfplots@data@scale@trafo@SHIFT@y)/10^\pgfplots@data@scale@trafo@EXPONENT@y}
}
\makeatother

\newcommand*{\ShowIntersectionA}{
\fill 
  [name intersections={of=Hardening and Hooke, name=i, total=\t}] 
  [red, opacity=1, every node/.style={above left, black, opacity=1}] 
  \foreach \s in {1,...,\t}{(i-\s) circle (2pt)
    node [above left] {\s}};
}

\newcommand*{\ShowIntersectionB}{
\fill
  [name intersections={of=Hardening and Hooke, name=i, total=\t}] 
  [every node/.style={below right, black, opacity=1}] 
  \foreach \s in {1,...,\t}{(i-\s) circle (0pt)
    node [below right] { 
    \pgfgetlastxy{\macrox}{\macroy}
    \transformxdimension{\macrox}
    \pgfmathprintnumber{\pgfmathresult},%
    \transformydimension{\macroy}%
    \pgfmathprintnumber{\pgfmathresult}}};
}

\begin{tikzpicture}
\begin{axis}[
    x={(2cm,0)}, 
    y={(0,0.02cm)},
    compat=newest,
    axis y line=left,
    axis x line=left,
    axis line style=
        {-{Stealth[inset=1pt, angle=30:15pt]}, very thick},
    ymin=0,     % start the diagram at this y-coordinate
    ymax=500,   % end   the diagram at this y-coordinate
    xmin = 0,
    xmax = 7,
    ylabel style={rotate=-90},
    every axis y label/.style=
     {at={(ticklabel* cs:1.02)},anchor=south,},
    ylabel=$\sigma$ in \si{\mega\pascal},
    every axis x label/.style=
         {at={(ticklabel* cs:1.02)},below left = 8pt},
    every tick/.style={thick},
    ytick={0,100,...,400},
    xtick={0,1,...,6},
    yticklabels={0,100,200,300,400},
    xlabel=$\epsilon$ in \si{\percent},
    xticklabels={0,1,...,6},
    minor y tick num={1},
    minor x tick num={4},
    tick align=outside]

\addplot[thick, domain=0:1]{300*x};

\coordinate (O) at (0,0);
\coordinate (A) at (1,300);
\coordinate (B) at (4,450);
\coordinate (C) at (6,400);
\coordinate (P) at (0.2,0);
\coordinate (Q) at ($(2,{300*(2-0.2)})$);

\draw[name path global=Hooke] (P) -- +($2*($(A)-(O)$)$);
%\draw[red, name path global=GraphCurve] (P) -- (Q);

\node[crossp=5pt,rotate=130] at (C) {};
\node[right=4pt] at (C) {Break};

%\addplot[only marks] coordinates {(3,300) (25,450) (30,400)};

%\foreach \x in {A,B,C} 
%   {\edef\temp{\noexpand\fill [red] (\x) circle (0.1cm);} \temp}; 

\draw[blue, name path global=Hardening]
    (A) .. controls +(71.5651:1.637cm) and +(180:2cm) .. (B);

\ShowIntersectionA
\ShowIntersectionB

% This is not working
%\fill[yellow,name intersections={of=Hardening and Hooke}] circle (2pt); 

\draw[green] (B) .. controls +(0:2cm) and +(130:5mm) .. (C);
\end{axis}
\end{tikzpicture}

\end{document}

Answer 1

No doubt this could be simplified further. However, for a start:

• combine the \ShowIntersectionsA and \ShowIntersectionsB into \ShowIntersection;
• eliminate the definition and use of O;
• use a label to add 'Break' rather than a second node operation;
• don't declare 2 different, potentially conflicting, compatibility levels for pgfplots;
• opacity=1 is default - no need for this unless you have declared a different default;
• black is default (for most cases) so if you write fill=red rather than just red, then you don't need draw=black for all the label nodes;
• don't define Q as you don't use it.

One good way to find out what bits do what is to add a colour to the style specification or, even, comment it out and see if stuff breaks. If you leave comments for yourself about what does what, it is easier to cut unused code when you are done.

It is, however, not easy to draw the bezier curve in one step since you want it to be in two different colours. Simplicity probably dictates leaving well alone in that case!

\documentclass[12pt,tikz,border=5pt]{standalone}

\usepackage[per-mode=symbol]{siunitx}

\usepackage{pgfplots}
\pgfplotsset{compat=newest}


\usetikzlibrary{intersections}
\usetikzlibrary{calc}
\usetikzlibrary{arrows.meta}
\usetikzlibrary{shapes.misc}

\tikzset{
  crossp/.style={
    thick,
    draw=gray,
    cross out,
    inner sep=0pt,
    outer sep=0pt,
    minimum size=2*(#1-\pgflinewidth),
  },
}

\begin{document}

  \makeatletter
  \newcommand\transformxdimension[1]{
    \pgfmathparse{((#1/\pgfplots@x@veclength)+\pgfplots@data@scale@trafo@SHIFT@x)/10^\pgfplots@data@scale@trafo@EXPONENT@x}
  }

  \newcommand\transformydimension[1]{
    \pgfmathparse{((#1/\pgfplots@y@veclength)+\pgfplots@data@scale@trafo@SHIFT@y)/10^\pgfplots@data@scale@trafo@EXPONENT@y}
  }
  \makeatother

  \newcommand*{\ShowIntersection}{%
    \fill
    [
      name intersections={of=Hardening and Hooke, name=i, total=\t},
      fill=red
    ]
    \foreach \s in {1,...,\t}{(i-\s) circle (2pt)
      node [above left] {\s} (i-\s) node [below right] {%
        \pgfgetlastxy{\macrox}{\macroy}
        \transformxdimension{\macrox}
        \pgfmathprintnumber{\pgfmathresult},
        \transformydimension{\macroy}
        \pgfmathprintnumber{\pgfmathresult}}};}

  \begin{tikzpicture}
    \begin{axis}[
      x={(2cm,0)},
      y={(0,0.02cm)},
      axis y line=left,
      axis x line=left,
      axis line style=
      {-{Stealth[inset=1pt, angle=30:15pt]}, very thick},
      ymin=0,     % start the diagram at this y-coordinate
      ymax=500,   % end   the diagram at this y-coordinate
      xmin = 0,
      xmax = 7,
      ylabel style={rotate=-90},
      every axis y label/.style=
      {at={(ticklabel* cs:1.02)},anchor=south,},
      ylabel=$\sigma$ in \si{\mega\pascal},
      every axis x label/.style=
      {at={(ticklabel* cs:1.02)},below left = 8pt},
      every tick/.style={thick},
      ytick={0,100,...,400},
      xtick={0,1,...,6},
      yticklabels={0,100,200,300,400},
      xlabel=$\epsilon$ in \si{\percent},
      xticklabels={0,1,...,6},
      minor y tick num={1},
      minor x tick num={4},
      tick align=outside]

      \addplot[thick, domain=0:1]{300*x};

      \coordinate (A) at (1,300);
      \coordinate (B) at (4,450);
      \coordinate (C) at (6,400);
      \coordinate (P) at (0.2,0);

      \draw[name path global=Hooke] (P) -- +($2*(A)$);

      \node[crossp=5pt, rotate=130, label=-130:{Break}] at (C) {};

      \draw[blue, name path global=Hardening]
      (A) .. controls +(71.5651:1.637cm) and +(180:2cm) .. (B);

      \ShowIntersection

      \draw[green] (B) .. controls +(0:2cm) and +(130:5mm) .. (C);
    \end{axis}
  \end{tikzpicture}

\end{document}

Answer 2

First I want to mention that I totally agree with cfr's answer. That is why my answer bases on his answer.

The main change is that with the release of PGFPlots v1.16 it now is now possible to store (axis) coordinates with \pgfplotspointgetcoordinates in data point, which then can be called by \pgfkeysvalueof.

(Besides that I made some other (minor) changes to the code to improve it a bit.)

% PGFPlots v1.16
\documentclass[border=5pt]{standalone}
\usepackage[per-mode=symbol]{siunitx}
\usepackage{pgfplots}
    \usetikzlibrary{
        arrows.meta,
        calc,
        intersections,
        shapes.misc,
    }
    \tikzset{
        crossp/.style={
            thick,
            draw=gray,
            cross out,
            inner sep=0pt,
            outer sep=0pt,
            minimum size={2*(#1-\pgflinewidth)},
        },
    }
    \pgfplotsset{compat=1.11}
    \newcommand*{\ShowIntersection}{
        \fill [
            name intersections={
                of=Hardening and Hooke,
                name=i,
                total=\t,
            },
            fill=red,
        ] \foreach \s in {1,...,\t} {
            (i-\s) circle (2pt)
            node [above left] {\s} (i-\s)
            node [below right] {
                % -------------------------------------------------------------
                % using `\pgfplotspointgetcoordinates' stores the (axis)
                % coordinates in `data point' which then can be called by
                % `\pgfkeysvalueof'
                \pgfplotspointgetcoordinates{(i-\s)}
                $\pgfmathprintnumber{\pgfkeysvalueof{/data point/x}}$,
                $\pgfmathprintnumber{\pgfkeysvalueof{/data point/y}}$
                % -------------------------------------------------------------
            }
        };
    }
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
        x=2cm,      y=0.02cm,
        xmin=0,     xmax=6.99,
        ymin=0,     ymax=499,
        xlabel={$\epsilon$ in \si{\percent}},
        ylabel={$\sigma$ in \si{\mega\pascal}},
        axis lines=left,
        axis line style={
            -{Stealth[inset=1pt,angle=30:15pt]},
            very thick,
        },
        ylabel style={
            at={(ticklabel* cs:1.02)},
            anchor=south,
            rotate=-90,
        },
        xlabel style={
            at={(ticklabel* cs:1.02)},
            below left=8pt,
        },
        every tick/.style={
            thick,
        },
        xtick distance=1,
        ytick distance=100,
        minor y tick num={1},
        minor x tick num={4},
        tick align=outside,
    ]

        \addplot [thick,domain=0:1,samples=2] {300*x};

        \coordinate (A) at (1,300);
        \coordinate (B) at (4,450);
        \coordinate (C) at (6,400);
        \coordinate (P) at (0.2,0);

        \draw [name path global=Hooke] (P) -- +($2*(A)$);

        \node [crossp=5pt,rotate=40,label=-40:Break] at (C) {};

        \draw [blue, name path global=Hardening]
            (A) .. controls +(71.5651:1.637cm) and +(180:2cm) .. (B);

        \ShowIntersection

        \draw [green]
            (B) .. controls +(0:2cm) and +(130:5mm) .. (C);

    \end{axis}
\end{tikzpicture}
\end{document}