[Tex/LaTex] Tikz intersection of lines with unnamed points

intersectionspgfmathtikz-pgf

This works:

\draw (0,0) coordinate (A);
\draw (1,1) coordinate (B);
\draw (1,0) coordinate (C);
\draw (0,1) coordinate (D);
\coordinate (X) at (intersection of A--B and C--D);

but this doesn't:

\draw (0,0) coordinate (A);
\draw (1,1) coordinate (B);
\coordinate (X) at (intersection of A--B and (0,1)--(1,0));

I think it would be a great convenience to use points as in the second example, where they don't have to be named before being used as endpoints of lines.

Is there any way of coercing TiKZ to create intersections of lines given by endpoints, without naming those endpoints first?

Best Answer

With intersections library you don't need to name each coordinate but each path

\documentclass[border=10pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{intersections}
\begin{document}

\begin{tikzpicture}
\draw (0,0) coordinate (A);
\draw (1,1) coordinate (B);
\draw (1,0) coordinate (C);
\draw (0,1) coordinate (D);
\draw (A)--(B);\draw (C)--(D);  % added for `cross symbol` demonstration
\coordinate (X) at (intersection of A--B and C--D);

%

\begin{scope}[xshift=2cm]    % so that they won't overlap
\draw[name path=AB] (0,0)  -- (1,1);
\draw[name path=CD] (0,1) -- (1,0);
\draw [name intersections={of=AB and CD, by=x}] (x) circle (2pt)node[right] {$x$};
\end{scope}
\end{tikzpicture}

\end{document}

enter image description here

Related Solutions

[Tex/LaTex] Intersection of lines to draw a convex function

With only TikZ but with functions. Remark : I use samples=2 to draw the lines because two points are enough but for m we need enough points to find the correct min values. I use a part of the Jake's answer.

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[declare function={
    f(\t)=tan(60)*\t+1.7;
    g(\t)=tan(45)*\t+2.4;
    h(\t)=tan(30)*\t+3.7;
    i(\t)=tan(18)*\t+5.5;
    m(\t)=min(f(\t) ,g(\t) ,h(\t),i(\t));}] 

 \draw[very thin,color=gray] (-0.1,-0.1) grid (10.1,10);
 \draw[->] (-0.2,0) -- (10.2,0) node[right] {$x$};
 \draw[->] (0,-0.2) -- (0,10.2) node[above] {$y$};  

 \clip (-1,-1) rectangle (10,10);     
\foreach \func in {f,g,h,i}
\draw [blue, thin] plot [domain=0:10, samples=2] (\x,{\func(\x)});
\draw [red, thick] plot [domain=0:10, samples=100] (\x,{m(\x)}); 
\end{tikzpicture}

\end{document}

enter image description here

[Tex/LaTex] TikZ doesn’t find all intersections between plot and a line

I don’t know why PGF doesn’t find these intersections, it probably has do to something with how the path is built internally from the points of the table of values gnuplot creates.

It works if you either

set set samples 100 or
use—with the original samples setting—the smooth option.

All intersections are found now.

The of key (\tikz@intersect@path@names@parse) expects spaces around and which is obviously stripped if you use of=kurve \a and linie \a, so you will need to do of/.expanded=kurve \a\space and linie \a or of={kurve \a} and linie \a.

You also might introduce spurious spaces with \foreach in:

\foreach \p/\a in {%
    %% T = 0.27
    0.0231/a,
    %% T = 0.28
    0.02855/b,
    %% T = 0.29
    0.0338/c             % <- there’s a space!
}{

This space actually may help if you .expanded with the of key but is usually trouble so avoiding this is reccomended.

(That space is also present in the other \foreach loop but as it is used with an .expanded before PGFkeys processes it, it is stripped.)

Code

\documentclass[convert=false,tikz]{standalone}
\usetikzlibrary{intersections}
\begin{document}
\begin{tikzpicture}[point/.style={fill=blue,minimum size=1mm,inner sep=0pt,circle}]
    % Zoom (to prevent oveflow)
    \def\yzoom{100}
    % Plots
    \foreach \T/\xmin/\a in {
        0.27/1.538/a,
        0.28/1.590/b,
        0.29/1.649/c
    } {
        \draw [thin,smooth,name path global/.expanded={kurve \a}]
            plot [raw gnuplot] function {%
                set xrange [\xmin:10];
                set yrange [0:0.08*\yzoom];
                set samples 1000;
                f(x) = \yzoom*(\T/(x-1) - 1/(x**2));
                plot f(x);
            };
    }
    % Lines
    \foreach \p/\a in {%
        %% T = 0.27
        0.0231/a,
        %% T = 0.28
        0.02855/b,
        %% T = 0.29
        0.0338/c%
    }{
        \draw [red,thin,name path global/.expanded={linie \a}]
            (0,\p*\yzoom) -- (10,\p*\yzoom) node [fill=white,pos=0.1] {\a};
        \path [name intersections={of={kurve \a} and linie \a, total=\t}] \foreach \s in {1,...,\t} {(intersection-\s) node[point]{}};
    }
\end{tikzpicture}
\end{document}

Output

enter image description here

Best Answer

Related Solutions

[Tex/LaTex] Intersection of lines to draw a convex function

[Tex/LaTex] TikZ doesn’t find all intersections between plot and a line

Code

Output

Related Question