Problem with drawing a tangent on a graph with pgfplots

pgfplotstangenttikz-pgf

I need to draw a tangent to a graph at x=0, i found here a code it works perfectly with any x excepet for x=0 , i tried to find a solution but i didn't if any one can help i'll be very grateful . thanks in advance.

here is my code :

% used PGFPlots v1.13 and TikZ v3.0.1a
\documentclass[border=2mm]{standalone}
\usepackage{xcolor}
\colorlet{Curve}{red!75!black}
\colorlet{Tangent}{blue!75!black}
\usepackage{pgfplots}
\pgfplotsset{compat=1.10}
\usetikzlibrary{
    calc,
    intersections,
    math,
}
\makeatletter
\def\parsenode[#1]#2\pgf@nil{%
    \tikzset{label node/.style={#1}}
    \def\nodetext{#2}
}
\tikzset{
    % define style for the points
    Point/.style={
        shape=circle,
        inner sep=0pt,
        minimum size=3pt,
    },
    add node at x/.style 2 args={
        name path global=plot line,
        /pgfplots/execute at end plot visualization/.append={
            \begingroup
            \@ifnextchar[{\parsenode}{\parsenode[]}#2\pgf@nil
            \path [name path global = position line #1-1]
            ({axis cs:#1,0}|-{rel axis cs:0,0}) --
            ({axis cs:#1,0}|-{rel axis cs:0,1});
            \path [xshift=1pt, name path global = position line #1-2]
            ({axis cs:#1,0}|-{rel axis cs:0,0}) --
            ({axis cs:#1,0}|-{rel axis cs:0,1});
            \path [
            name intersections={
                of={plot line and position line #1-1},
                name=left intersection
            },
            name intersections={
                of={plot line and position line #1-2},
                name=right intersection
            },
            label node/.append style={pos=1}
            ] (left intersection-1) -- (right intersection-1)
            node [label node]{\nodetext};
            % ---------------------------------------------------------
            % draw the tangent line from a bit right of the point on
            % the curve to the intersection with the ordinate
            % and draw the corresponding points
            \draw [Tangent,line width=0.6pt, color=red] let
            \p1=($ (left intersection-1) - (right intersection-1) $),
            \p2=($ (left intersection-1)!sign(#1)*60mm!(right intersection-1) $),
            \p3=($ ({axis cs:0,0}) - (\p2) $),
            \n1={\x3/\x1}
            in
            (\p2) -- +($ {\n1}*(\x1,\y1) $)
            %                            node [Point,fill=Tangent] (origin intersection) {}
            %                            node [Point,fill=Curve] at (left intersection-1) {}
            ;
            %                    % ----------
            %                    % draw the horizontal line at the curve intersection point
            %                    % plus the label above/below the line
            %                    \tikzmath{
                %                        coordinate \c1;
                %                        \c1=(left intersection-1) - (right intersection-1);
                %                        \slope=\cy1/\cx1*sign(#1);
                %                    }
            %                    \pgfmathsetmacro{\AboveBelow}{ \slope>0 ? "above" : "below" }
            %                    \draw [dotted]
            %                        ([xshift=sign(#1)*2.5mm] left intersection-1) --
            %                        (left intersection-1) --
            %                            node [\AboveBelow,node font=\scriptsize] {$f(x)$}
            %                        (left intersection-1 -| origin intersection) --
            %                        +($ sign(#1)*(-2.5mm,0) $)
            %                            coordinate [pos=0.5] (a)
            %                    ;
            %                    % draw the horizontal line at the ordinate intersection point
            %                    \draw [dotted] (origin intersection)
            %                        +($ sign(#1)*(-2.5mm,0) $) --
            %                        (origin intersection);
            %                    % draw vertical line left/right of the ordinate
            %                    \pgfmathsetmacro{\LeftRight}{ #1<0 ? "right" : "left" }
            %                    \draw [stealth-stealth] (origin intersection)
            %                        +($ sign(#1)*(-1.25mm,0) $) -- (a)
            %                            node [midway,\LeftRight,node font=\scriptsize] {$p$}
            %                    ;
            %                    % ---------------------------------------------------------
            \endgroup
        },
    },
}
\makeatother
\begin{document}

        \begin{tikzpicture}[scale=1.2]
            
            \begin{axis}[legend style={at={(0.65,0.65)},anchor=north},scaled ticks=false,
                %   y tick label style={/pgf/number format/sci},
                every axis y label/.style={at={(ticklabel* cs:0.95)},anchor=west,},
                yticklabel style = {font=\scriptsize},
                xticklabel style = {font=\scriptsize},
                footnotesize,
                %xlabel=$t\ (s)$,
                %   ylabel=$\mathrm{\left[  {{I}_{2}} \right]  {{.10}^{-3}}\ mol/l}$
                x= 0.95cm,
                y=2.8 cm,
                xmin=0, xmax=10,
                ymin=0, ymax=2.2,
                xtick={0,1,...,10},
                ytick={0.5,1,...,2},
                %xtick distance=40
                minor xtick={0.5,1.5,...,9.5},
                minor ytick={0.1,0.2,...,2.2},
                %minor tick num=4,
                grid=both,
                %xlabel=$x$,
                %ylabel={$s(t)$ },
                domain=\pgfkeysvalueof{/pgfplots/xmin}:(\pgfkeysvalueof{/pgfplots/xmax},samples=300,
                tangent/.style={add node at x={#1}{},},scale only axis,]
                \addplot [thick,draw=Curve,line width =1.2pt,color=black,tangent=0.0001] {2*(1-exp(-x))};
                
                \addplot [line width =0.4pt,fill=blue, fill opacity=0.2]coordinates {
                    (0, 1.9) 
                    (0, 2.1)
                    (10, 2.1)
                    (10, 1.9)  };
                
                
                \addplot[mark=*] coordinates {(3,1.9)} ;
                \addplot[mark=*] coordinates {(1,1.26)} ;
            \end{axis}
        \end{tikzpicture}
        
\end{document}

Best Answer

Using the tzplot package:

\documentclass[tikz]{standalone}
    
\usepackage{tzplot}

\begin{document}

\begin{tikzpicture}[yscale=3]
\tzhelplines[xstep=.5,ystep=.1](10,2.2)
\tzaxes[-](10,2.2)
\tzticks{0,1,...,10}{0,0.5,...,2}
\tzticks*[gray](0:1.3pt){0.5,1,...,10}{0.1,0.2,...,2.2}
\def\Fx{2*(1-exp(-\x))}
\tzfn[thick]\Fx[-.00999:10] % name path = Fx
% tangent
\tztangentat[red,thick]{Fx}{0}[0:1]
\tztangentat[red,thick]{Fx}{1}[0:2]
\tztangentat[red,thick]{Fx}{3}[0:5]
\tzvXpointat*{Fx}{1}
\tzvXpointat*{Fx}{3}
\end{tikzpicture}

\end{document}

Related Solutions

[Tex/LaTex] How to access \xmin, \xmax, \ymin, \ymax from within PGFplots axis environment

You can access the values of xmin, xmax, etc. through \pgfkeysvalueof{/pgfplots/xmin}. This only works if they have been set explicitly in the axis options, though, so it is most likely not what you want. Instead, you should use the nodes current axis.above origin, current axis.below origin, current axis.left of origin and current axis.right of origin.

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

\begin{tikzpicture} 
\begin{axis}[] 

\addplot[mark=none, domain=-2.5:2.5, thick, red] ({x},{x*x-0.5});% 

\draw (current axis.above origin) -- (current axis.below origin);
\draw (current axis.left of origin) -- (current axis.right of origin);

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

enter image description here

[Tex/LaTex] How to draw tangent line of an arbitrary point on a path in TikZ

Here's an approach that uses the decorations.markings library to place support coordinates at a specified distance along a path, which can be used to set a local coordinate system at a later time to draw tangents or orthogonal lines.

You specify a tangent point by using tangent=<pos> in your first path. In a later path, you can then set use tangent to set a local coordinate system for that path: (0,0) is the tangent point itself, (1,0) is 1 unit along the tangent line, (0,1) is one unit along the orthogonal line.

You can specify tangent=<pos> multiple times in your original path. You can then specify which tangent point to use for a new path by calling use tangent=<count>, where the tangent points are numbered in the order they were specified in the original path.

Using these styles, the following code

\draw [
    tangent=0.4,
    tangent=0.56
] (0,0)
    to [out=20,in=120] (5,2)
    to [out=-60, in=110] (9,1);
\draw [blue, thick, use tangent] (-3,0) -- (3,0);
\draw [orange, thick, use tangent=2] (-2,0) -- (2,0) (0,0) -- (0,1);

would yield this

Here's the complete code:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations.markings}

\begin{document}

\begin{tikzpicture}[
    tangent/.style={
        decoration={
            markings,% switch on markings
            mark=
                at position #1
                with
                {
                    \coordinate (tangent point-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,0pt);
                    \coordinate (tangent unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (1,0pt);
                    \coordinate (tangent orthogonal unit vector-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}) at (0pt,1);
                }
        },
        postaction=decorate
    },
    use tangent/.style={
        shift=(tangent point-#1),
        x=(tangent unit vector-#1),
        y=(tangent orthogonal unit vector-#1)
    },
    use tangent/.default=1
]
\draw [
    tangent=0.4,
    tangent=0.56
] (0,0)
    to [out=20,in=120] (5,2)
    to [out=-60, in=110] (9,1);
\draw [blue, thick, use tangent] (-3,0) -- (3,0);
\draw [orange, thick, use tangent=2] (-2,0) -- (2,0) (0,0) -- (0,1);
\end{tikzpicture}
\end{document}

Best Answer

Related Solutions

[Tex/LaTex] How to access \xmin, \xmax, \ymin, \ymax from within PGFplots axis environment

[Tex/LaTex] How to draw tangent line of an arbitrary point on a path in TikZ

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