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Math Help - Line intersection with unit circle using TikZ/PGF

  1. #1
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    Post [Solved] Line intersection with unit circle using TikZ/PGF

    Update:
    I was able to track it down myself. I was missing the Everyshi package, included in the ms package (CTAN: directory: /tex-archive/macros/latex/contrib/ms). Now I can use the CVS version and not get "GUI framework cannot be initialized".
    The working code looks like this:
    Code:
    \begin{tikzpicture}
    [scale=1.5,line cap=round,
    % Styles
    axes/.style={thick},
    information text/.style={rounded corners,inner sep=1ex}]
    
    \usetikzlibrary{arrows,calc,intersections}
    
    % The graphic
    \draw[help lines,step=0.5cm] (-1.4,-1.4) grid (1.4,1.4);
    \draw[name path=unitcircle] (0,0) circle(1cm);
    
    \begin{scope}[axes]
    \draw[->] (-1.5,0) -- (1.5,0) node[right] {$x$} coordinate(x axis);
    \draw[->] (0,-1.5) -- (0,1.5) node[above] {$y$} coordinate(y axis);
    \foreach \x/\xtext in {-1, -.5/-\frac{1}{2}, .5/\frac{1}{2}, 1}
    \draw[xshift=\x cm] (0pt,1pt) -- (0pt,-1pt) node[below,fill=white,inner sep=0.2ex] {\tiny $\xtext$};
    \foreach \y/\ytext in {-1, -.5/-\frac{1}{2}, .5/\frac{1}{2}, 1}
    \draw[yshift=\y cm] (1pt,0pt) -- (-1pt,0pt) node[left,fill=white,inner sep=0.2ex] {\tiny $\ytext$};
    \end{scope}
    
    
    \foreach \t/\ttext in {-1,-0.5,...,1}
    {
    	\path[name path=myline] (1,0) -- (0,\t) node[sloped, near end, above=-2pt] {\tiny \color{blue}$\scriptscriptstyle -t = \ttext$} -- (-1,2*\t);
    	\path [name intersections={of=unitcircle and myline, by={C, C'}}];
    	\draw [name path=C--C',red] (C) -- (C');
    	\fill [red, name intersections={of=unitcircle and myline}]
    	    (intersection-1) circle (0.3mm)
    	    (intersection-2) circle (0.3mm);
    }
    
    \draw[yshift=-1.7cm] node[below,text width=2cm,information text] {Figure 1.1};
    
    \end{tikzpicture}
    I have been trying to fix this for many hours now and I cannot find any working solution. So if anyone can help, please do so.
    What I want to do is to find the intersection point (and add a dot/circle) between the line generated with this (see full TikZ code below):
    Code:
    \foreach \t/\ttext in {-1,-0.5,...,1}
    {
    \draw (1,0) -- (0,\t) node[sloped, near end, above] {\tiny $-t = \ttext$} -- (-1, 2*\t);
    }
    and a unit circle generated with
    Code:
    \draw (0,0) circle (1cm);
    or
    Code:
    \node (c1) at (0,0) [draw,circle,scale=9] {};
    I have tried several approaches but nothing seems to work. Tries include this "solution":
    Nabble - pgf-users - Intersection Line/Circle
    Nabble - pgf-users - Intersection Line/Circle (2)
    but it just generates errors of "Undefined control sequence. <recently read> \pgfsetpath" and various tries have easily reached 100+ errors.

    I'm using the latest CVS build of TikZ/PGF but slightly mixed with the 2.00 final build. The mixing is because I got "GUI framework cannot be initialized" at the file "pgfutil-latex.def" with just pure CVS. Perhaps it is causing problem, but if so, help to install it correctly is appreichiated.
    I also use TeXnicCenter 1.0 rc, as the working enviroment together with MiKTeX 2.8 basic. And I have tried to set install packages on the fly to Yes, but with no success.

    By the way: I know the intersection points are given by:
    <br />
(x,y) = (\frac{t^2-1}{t^2+1},\frac{2t}{t^2+1})<br />
    but it seems like I cannot use these expressions as coordinates (using \t instead of t) because it seems like the dividing is causing trouble.

    Full code (except \usepackage{tikz} and some document things):

    Code:
    \begin{tikzpicture}
    [scale=1.5,line cap=round,
    % Styles
    axes/.style={thick},
    information text/.style={rounded corners,inner sep=1ex}]
    
    \usetikzlibrary{arrows,calc,intersections}
    
    % Colors
    \colorlet{anglecolor}{green!50!black}
    % The graphic
    \draw[help lines,step=0.5cm] (-1.4,-1.4) grid (1.4,1.4);
    %\draw (0,0) circle (1cm);
    \node (c1) at (0,0) [draw,circle,scale=9] {};
    
    \begin{scope}[axes]
    \draw[->] (-1.5,0) -- (1.5,0) node[right] {$x$} coordinate(x axis);
    \draw[->] (0,-1.5) -- (0,1.5) node[above] {$y$} coordinate(y axis);
    \foreach \x/\xtext in {-1, -.5/-\frac{1}{2}, .5/\frac{1}{2}, 1}
    \draw[xshift=\x cm] (0pt,1pt) -- (0pt,-1pt) node[below,fill=white] {\tiny $\xtext$};
    \foreach \y/\ytext in {-1, -.5/-\frac{1}{2}, .5/\frac{1}{2}, 1}
    \draw[yshift=\y cm] (1pt,0pt) -- (-1pt,0pt) node[left,fill=white] {\tiny $\ytext$};
    \end{scope}
    
    \foreach \t/\ttext in {-1,-0.5,...,1}
    {
    \draw (1,0) -- (0,\t) node[sloped, near end, above] {\tiny $-t = \ttext$} -- (-1, 2*\t);
    %\draw[red] (intersection cs:
                    first line={(1,0)--(0,\t)},
                    second line={(-1,-2)--(-1,2)})
                    circle (5pt);
    %\draw[red] (intersection of (1,0)--(0,\t) and (-1,-2)--(-1,2)) circle (5pt);
    
    }
    \end{tikzpicture}
    Last edited by Hugzor; January 6th 2010 at 02:01 PM. Reason: Solved
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