Dynamic Plotting, Plot Shift, Tikz Units

Question

I'm having multiple questions regarding the following:

\documentclass[
paper=A4,               
twoside=false,          
fontsize=12pt,          
parskip=half+,          
numbers=ddot,           
captions=tableheading,   
bibliography=totoc,   
listof=totoc            
]
{scrbook}  


\usepackage{tkz-euclide}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,positioning,intersections,shapes,decorations, arrows.meta, calc, plotmarks}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{arrows.meta}

%PGF
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\usetkzobj{all}
\usepackage{amsmath}
\usepackage{amssymb}

\newcommand*{\ShowIntersection}[2]{
    \fill 
    [name intersections={of=#1 and #2, name=j, total=\t}] 
    [black, opacity=1, every node/.style={black, opacity=1}] 
    \foreach \s in {1,...,\t}{(j-\s) circle (1pt)node [] {}
    %   (i-\s)--(i-\s|-{axis cs:0,0}) node[fill=white]{\tiny $\overline{x}_{\s}$}
        }; 
}

% see: https://tex.stackexchange.com/questions/256883/telling-tikz-to-continue-the-previously-drawn-path-with-a-line-to-operation
\tikzset{%
  from end of path/.style={
    insert path={
      \pgfextra{%
        \expandafter\pgfprocesspathextractpoints%
          \csname tikz@intersect@path@name@#1\endcsname%
        \pgfpointlastonpath%
        \pgfgetlastxy\lastx\lasty
      }
      (\lastx,\lasty)
}}}



\begin{document}
\begin{minipage}[t]{\pdfpagewidth} %Makes sure that the figure is in the middle of the page.

%%Tikzpicture
\begin{tikzpicture}[>=latex,x=1pt, y=1pt] 
\def\ymin{2};           %% pt
\def\xmax{20};          %% pt     

\begin{axis}[   
    axis lines=center,
    xtick=\empty, 
    ytick=\empty, 
    xlabel={$r$},         
    ylabel={},         
    xlabel style={below}, 
    ylabel style={left},  
    xmin=0,             %% cm
    xmax=\xmax,         %% cm
    ymin=-\ymin,        %% cm
    ymax=10,            %% cm
    axis equal image
]

%%Parameters %\xdef = global variables %\def = local variables
\xdef\gammaL{15};
\xdef\gammaD{1};
\xdef\k{0.5};
\xdef\kprime{\k*1.5}
\xdef\B{1.8};
\xdef\I{0.15};

%% Plot Functions
% Lineare
\addplot[color = black, mark=none, domain=0:\gammaL, name path global = linear_prime]{((1/(1-\kprime)*\I*(-x+\gammaL)} 
node[pos=0, right, xshift=5mm]{\footnotesize{\tiny$\frac{1}{1-k^\prime}I(\cdot+\gamma_L)$}};
\addplot[color = black, mark=none, domain=0:\gammaL, name path global = linear]{((1/(1-\k)*\I*(-x+\gammaL)}
node[pos=0, right, xshift=5mm]{\footnotesize{\tiny$\frac{1}{1-k}I(\cdot+\gamma_L)$}};
% Non-Linear
% Red
\def\axisshiftred{1.5};
\addplot[color=red, mark=none, domain=0:\axisshiftred]{(-\B)};
\addplot[color=red, mark=none, domain=\axisshiftred:\xmax, samples=500, name path global = red_kprime]{3*((x-\axisshiftred)*(1-\kprime)-\gammaD)^(1/2)-\B};
% Blue
\def\axisshiftblue{1};
\addplot[color=blue, mark=none, domain=0:\axisshiftblue]{(-\B)};
\addplot[color=blue, mark=none, domain=\axisshiftblue:\xmax, samples=300, name path global = blue_k]{3*((x-\axisshiftblue)*(1-\k)-\gammaD)^(1/2)-\B};

%% Intersections
% Shows Intersection between two plots, by marking it with a black point
\ShowIntersection{linear_prime}{red_kprime}; 
\ShowIntersection{linear}{blue_k};
% path to a point of intersection
\path [name intersections={of=linear and blue_k,by=interblue}]; 
\path [name intersections={of=linear_prime and red_kprime,by=interred}]; 

%% Dashed Lines
\draw[dashed] (0,\ymin*10) |- (interblue);
\draw[dashed] (0,\ymin*10) -| (interblue);
\draw[dashed] (0,\ymin*10) |- (interred);
\draw[dashed] (0,\ymin*10) -| (interred);

\end{axis}    
\end{tikzpicture}
\end{minipage}


\end{document}

which produces the following picture:

Could someone please explain:

How do the units work here? Within tikzpicture I defined the two "vectors" to be (1pt, 0) and (0, 1pt), right? Does this change in the axis-Environment? If \ymin is really in pt, why is there exactly a factor 10 when I am drawing the dashed lines?
Why do the constant and the Squareroot-Function not intersect, when all functions are shifted by axisshiftred or axisshiftblue and plotted accordingly?
Is there anything super-stupid, you find repulsive and unelegant?

I will be doing a million more of those figures, thats why I am keeping things "dynamic" and capsulate everything in a variable. Thank you again for your help. :-)

For second question: Your function (blue and red) is evaluating square root of negative number for some range. That range won't be plotted. Hence there is a gap between constant and this function. — nidhin, Nov 27 '18 at 13:34
pgfplots does its own rescalings such that in the end the plot will have the predefined width and height. That is, the units will be chosen such that the plots with the specified domains fill the picture. So the units you assign to x and y in the ambient tikzpicture won't have the effect you might be thinking of. Likewise for ymin. — , Nov 27 '18 at 14:01
20pt width will be too small to fit the a couple of characters. — nidhin, Nov 27 '18 at 14:48

score 4 · Accepted Answer · answered Dec 07 '18 at 15:07

For future references: this produces the figure in the intended manner (colors may vary ^.^):

   \documentclass[
    paper=A4,               
    twoside=false,          
    fontsize=12pt,          
    parskip=half+,          
    numbers=ddot,           
    captions=tableheading,   
    bibliography=totoc,   
    listof=totoc            
    ]
    {scrbook}  


\usepackage{tkz-euclide}
\usepackage{tikz}
\usetikzlibrary{shapes.geometric,positioning,intersections,shapes,decorations, arrows.meta, calc, plotmarks}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{arrows.meta}

%PGF
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\usetkzobj{all}
\usepackage{amsmath}
\usepackage{amssymb}

\newcommand*{\ShowIntersection}[2]{
    \fill 
    [name intersections={of=#1 and #2, name=j, total=\t}] 
    [black, opacity=1, every node/.style={black, opacity=1}] 
    \foreach \s in {1,...,\t}{(j-\s) circle (1pt)node [] {}
    %   (i-\s)--(i-\s|-{axis cs:0,0}) node[fill=white]{\tiny $\overline{x}_{\s}$}
        }; 
}

% see: https://tex.stackexchange.com/questions/256883/telling-tikz-to-continue-the-previously-drawn-path-with-a-line-to-operation
\tikzset{%
  from end of path/.style={
    insert path={
      \pgfextra{%
        \expandafter\pgfprocesspathextractpoints%
          \csname tikz@intersect@path@name@#1\endcsname%
        \pgfpointlastonpath%
        \pgfgetlastxy\lastx\lasty
      }
      (\lastx,\lasty)
}}}



\begin{minipage}[t]{\pdfpagewidth} %Makes sure that the figure is in the middle of the page.

%%Tikzpicture
\begin{tikzpicture}[>=latex,x=1pt, y=1pt] 
\def\ymin{2};           %% cm
\def\xmax{20};          %% cm    

\begin{axis}[   
    axis lines=center,
    xtick=\empty, 
    ytick=\empty, 
    xlabel={$r$},         
    ylabel={},         
    xlabel style={below}, 
    ylabel style={left},  
    xmin=0,             %% cm
    xmax=\xmax,         %% cm
    ymin=-\ymin,        %% cm
    ymax=10,            %% cm
    axis equal image
]

%%Parameters %\xdef = global variables %\def = local variables
\xdef\gammaL{15};
\xdef\gammaD{0};
\xdef\k{0.5};
\xdef\kprime{\k*1.5}
\xdef\B{1.8};
\xdef\I{0.15};

%% Plot Functions
% Lineare
\addplot[color = black, mark=none, domain=0:\gammaL, name path global = linear_prime]{((1/(1-\kprime)*\I*(-x+\gammaL)} 
node[pos=0, right, xshift=5mm]{\footnotesize{\tiny$\frac{1}{1-k^\prime}I(\cdot+\gamma_L)$}};
\addplot[color = black, mark=none, domain=0:\gammaL, name path global = linear]{((1/(1-\k)*\I*(-x+\gammaL)}
node[pos=0, right, xshift=5mm]{\footnotesize{\tiny$\frac{1}{1-k}I(\cdot+\gamma_L)$}};
% Non-Linear
% Red
\def\axisshiftred{3};
\addplot[color=red, mark=none, domain=0:\axisshiftred]{(-\B)};
\addplot[color=red, mark=none, domain=\axisshiftred:\xmax, samples=500, name path global = red_kprime]{3*((x-\axisshiftred)*(1-\kprime)-\gammaD)^(1/2)-\B};
% Blue
\def\axisshiftblue{1.5};
\addplot[color=blue, mark=none, domain=0:\axisshiftblue]{(-\B)};
\addplot[color=blue, mark=none, domain=\axisshiftblue:\xmax, samples=300, name path global = blue_k]{3*((x-\axisshiftblue)*(1-\k)-\gammaD)^(1/2)-\B};

%% Intersections
% Shows Intersection between two plots, by marking it with a black point
\ShowIntersection{linear_prime}{red_kprime}; 
\ShowIntersection{linear}{blue_k};
% path to a point of intersection
\path [name intersections={of=linear and blue_k,by=interblue}]; 
\path [name intersections={of=linear_prime and red_kprime,by=interred}]; 

%% Dashed Lines
\draw[dashed] (0,\ymin*10) |- (interblue);
\draw[dashed] (0,\ymin*10) -| (interblue);
\draw[dashed] (0,\ymin*10) |- (interred);
\draw[dashed] (0,\ymin*10) -| (interred);

\end{axis}

%% Labels (outside of Axsis-Environment, units is pt (Why? Also: is it? ¯\_(ツ)_/¯))
% 1mm = 2.84528 pt 
% 1pt = 0.35145925884mm

%%Label
%% At the End of a plotted Function
\node[color=blue, right, from end of path=blue_k] {{\footnotesize$S(\cdot (1-k) -\gamma_D)-B$}};
\node[color=red, right, from end of path=red_kprime] {{\footnotesize$S(\cdot (1-k^\prime) -\gamma_D)-B$}};

%% at a specific point
\node[color=black, left] () at (0,0) {$-B$};
\node[color=black, left] () at (0, 110) {$\frac{1}{1-k^\prime}I\gamma_L$};
\node[color=black, left] () at (0, 60) {$\frac{1}{1-k}I\gamma_L$};
%\node[color=black, left] () at (0,0) {\footnotesize{$-B$}};
%\node[color=red, left] () at (0,\yminpt-\Bprimept) {\footnotesize{$-B^\prime$}};
%\node[color=black, left] () at (0,\yminpt+30) {\footnotesize{$\frac{1}{1-k}I\gamma_L$}};

%% At the x-Axis-Projection of a point
%\node[color=black, below] () at (interb|-0,\yminpt) {$r^*$};
%\node[color=black, below] () at (interr|-0,\yminpt) {$r^{*\prime}$};

%% At the y-Axis-Projection of a point
%\node[color=black, left] () at (interblue-|0,0) {$-B$};


\end{tikzpicture}
\end{minipage}



\end{document}

To answer question 1), see https://tex.stackexchange.com/a/287299/173523 — Hiwi Makro, Dec 20 '18 at 14:28

Dynamic Plotting, Plot Shift, Tikz Units

1 Answers1