[Tex/LaTex] Parallel lines on a grid and circle best practices

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I am a TeX/LaTeX noob, but I am learning rapidly. I am about to attempt to draw the following figure using LaTeX/TeX/TikZ I already have a, (I think) good working knowledge of how to draw circles, braces, lines, segments, and nodes, etc.

The last time I drew one though, I noticed that I spent a lot of time fine tuning parameters, making sure that lines intersected circles at the proper points, making sure lines were parallel, etc.

I need to draw the following figure, so I wanted first inquire if there is a fast/easy way, or anything I should keep in mind, when creating parallel lines (the red ones), as per the following figure:

enter image description here

The main time sinks I foresee are going to be the following:

Making sure the length of the purple lines are exactly correct, so as not to overshoot the red ones.
Making sure the red lines are all parallel to each other.
Making sure than I can draw nodes/dots where lines intersect each other and/or the circle.

Is there any particular way(s) that is recommended to make sure that the above points do not waste too much time? I would appreciate any advice/examples.

Thanks!

P.S. I am making good use of TikZ as well.

EDIT:

I am including a minimal example of my 'skill' set. As you can see, I painstakingly usually just have to fine tune co-ordinates, for where things intersect, etc. I also do not know how to not-waste-time if I wanted to make parallel lines, as shown in the red lines above. Here is my example code:

\documentclass[journal]{IEEEtran}
\usepackage{graphicx}
\usepackage{float}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{tikz}
\usetikzlibrary{matrix}
\usetikzlibrary{decorations.pathreplacing}
\usepackage{xspace} 
\usepackage{float}
\usepackage{capt-of}
\usepackage{cases}



\begin{document}

\newcommand{\var}{1.5}

\begin{tikzpicture}
%\begin{tikzpicture}

    \draw [help lines] (-4,-4) grid (4,4);

    % Draw the axes
    \draw [->,black, ] (-4,0) -- (4,0) ;
    \draw [->,black] (0,-4) -- (0,4) ;

    % Draw the circle
    \path [draw, ultra thick,  black] (0,0) circle (3);

    %Radial Lines    
    \draw[black](0:0)--(45:3);
    \draw[black](0:0)--(135:3);
    \draw[black](0:0)--(225:3);
    \draw[black](0:0)--(315:3);        

    %Wavefront normal
    \draw[blue](0:0)--(60:3);
    \draw[blue](0:0)--(240:3);

    \draw[blue](0,1) arc (90:60:1);
    \draw[blue] (0,0.95)arc(90:60:0.95);
    \node[] at (75:1.2)  {$\alpha$};

    \draw[blue] (0.7,1.2)arc(90:30:0.37);
    %\node[] at (50:2) {$\frac{pi}{4}-\alpha$};
    \draw[-latex](1.5,3)node[right]{$\frac{\pi}{4}-\alpha$}
        to[out=180,in=90] (50:1.5);

    %Points
    \path[fill, black](45:3) circle(0.1);
    \node[] at (45:3.3){1};
    \path[fill, black](135:3) circle(0.1);
    \node[] at (133:3.3){4};
    \path[fill,black](225:3) circle(0.1);
    \node[] at (225:3.3){3};
    \path[fill, black](315:3) circle(0.1);
    \node[] at (313:3.3){2};

    %Wavefronts
    \draw[blue, ultra thick](-.5,3.6347)--(3.5,1.3252);
    \draw[blue, ultra thick](-2.5,2.34)--(3.5,-1.1242);
    \draw[blue, ultra thick](-3.2,0.9509)--(2.8,-2.5132);
    \draw[blue, ultra thick](-3.2,-1.4985)--(0.2,-3.4615);

    %Right angle signs
    \draw[red](60:2.8)--(62:2.8)--(62:2.9);
    \draw[red](60:.68)--(68:.69)--(67:.79);




    % Done
\end{tikzpicture}


\end{document}

The above code is now giving me this:

enter image description here

Best Answer

The first TikZ picture shows a rather sloppy idea to draw the parallel lines. The second example shows a more automatic way of drawing secants (one could have used the \angle value directly but I want do show how I’d do it, if the direction of the vector is not known to the user.

The second example also shows that calc’s ($(<p1>)!(<p3>)!(<p2>)$) isn’t very exact for close (<p1>) and (<p2>). Of course, there isn’t even a line when <p1> = <p2>.

The intersections library might be more precise in finding points where the orthogonal line to the vector and the secants intersect.

Code

\documentclass[tikz,convert=false]{standalone}
\usetikzlibrary{calc,through}
\tikzset{
  m*/.style args={#1:#2}{
    insert path={node [fill=green!50!black, outer sep=+0pt, shape=circle, inner sep=0pt, minimum size=+4pt,#1,label={#2}] {}}
  },
  m/.style={insert path={coordinate (#1)}},
  parLines/.style={draw=red,,shorten <=+-.5cm,shorten >=-.5cm},
  vertLines/.style={draw=purple,shorten >=.5\pgflinewidth},
  @splitLine/.code args={#1 -- #2}{\def\tikztotargetA{#1}\def\tikztotargetB{#2}},
  vert on/.style={
    to path={
      [@splitLine/.expanded={\tikztotarget}]
      -- ($(\tikztotargetA)!(\tikztostart)!(\tikztotargetB)$) node[right angle node,rotate=90*#1] {}\tikztonodes
    }
  },
  vert on/.default=0,
  right angle node/.style={
    at end,sloped,above,allow upside down,
    anchor=south east,
    shape=rectangle,
    inner sep=0pt,
    minimum size=3pt,
    append after command={
      \pgfextra\pgfinterruptpath\draw[right angle node path] (\tikzlastnode.south west) -- (\tikzlastnode.north west) -- (\tikzlastnode.north east);\endpgfinterruptpath\endpgfextra
    }
  },
  right angle node path/.style={draw,thin,black,-,shorten >=.4pt},
  secant/.style={
    to path={
      let \p{@dir}=(\tikztotarget), \n{@dir}={atan2(\x{@dir},\y{@dir})} in
      (node cs: name=\tikztostart, anchor=#1) [m*={name=m#1}:#1] -- (node cs: name=\tikztostart, anchor={2*(\n{@dir}-90)-#1}) [m=m#1'] \tikztonodes
    }
  }
}
\begin{document}
\begin{tikzpicture}[thick]
\clip (-2.5,-2.5) rectangle (2.5,2.5);
\draw[thin, ->] (0,0) [m*={black,minimum size=+3pt,name=O}:] -- node [sloped,above,inner sep=+1pt,font=\scriptsize] {$\vec v$} ++(150:1) coordinate (d);

\draw[thin, ->] (0,0) -- ([rotate=90]d)  [shorten >=-1.3cm];
\draw[thin, ->] (0,0) -- ([rotate=-90]d) [shorten >=-1.3cm];

\node [draw=blue, circle through={(2,0)}] (c) {};

\draw[parLines] (c.50)  [m*={name=m1}:1] -- ++([scale=2] d)    [m=m1'];
\draw[parLines] (c.140) [m*={name=m2}:2] -- ++([scale=-4] d)   [m=m2'];
\draw[parLines] (c.-30) [m*={name=m3}:3] -- ++([scale=4.5] d)  [m=m3'];
\draw[parLines] (c.210) [m*={name=m4}:4] -- ++([scale=-2.5] d) [m=m4'];

\draw[vertLines] (c.center) to[vert on] (m1 -- m1');
\draw[vertLines] (c.center) to[vert on] (m4' -- m4);
\end{tikzpicture}

\foreach \angle in {0,10,...,359}{% Careful, 36 pages!
\begin{tikzpicture}[thick]
\clip (-2.5,-2.5) rectangle (2.5,2.5);
\draw[thin, ->] (0,0) [m*={black,minimum size=+3pt,name=O}:] -- node [sloped,above,inner sep=+1pt,font=\scriptsize] {$\vec v$} ++(\angle:1) coordinate (d);

\draw[thin, ->] (0,0) -- ([rotate=90]d)  [shorten >=-1.3cm];
\draw[thin, ->] (0,0) -- ([rotate=-90]d) [shorten >=-1.3cm];

\node [draw=blue, circle through={(2,0)}] (c) {};

\draw[parLines] (c) to[secant=30]  (d);
\draw[parLines] (c) to[secant=140] (d);
\draw[parLines] (c) to[secant=-30] (d);
\draw[parLines] (c) to[secant=210] (d);


\draw[vertLines] (c.center) to[vert on] (m30 -- m30');
\draw[vertLines] (c.center) to[vert on] (m210' -- m210);
\end{tikzpicture}%
}
\end{document}

Output

enter image description here

Related Solutions

[Tex/LaTex] Best practices references

The Essential Guide to LaTeX2ε Usage (l2tabu) explains some of the most common mistakes in LaTeX usage.

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

A solution which allows to draw intersection segments of any two intersections is available as tikz library fillbetween.

This library works as general purpose tikz library, but it is shipped with pgfplots and you need to load pgfplots in order to make it work:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}];

\end{tikzpicture}

\end{document}

enter image description here

The key intersection segments is described in all detail in the pgfplots reference manual section "5.6.6 Intersection Segment Recombination"; the key idea in this case is to

create a temporary path temp1 which is the first intersection segment of red and blue, more precisely, it is the first intersection segment in the Left argument in red and blue : red. This path is drawn as thin black path. Substitute its \draw statement by \path to make it invisible.
Compute the desired intersection segment by intersecting temp1 and green and use the correct intersection segment. By trial and error I figured that it is the third segment of path temp1 which is written as L3 (L = left argument in temp1 and green and 3 means third segment of that path).

The argument involves some trial and error because fillbetween is unaware of the fact that end and startpoint are connected -- and we as end users do not see start and end point.

Note that you can connect these path segments with other paths. If such an intersection segment should be the continuation of another path, use -- as before the first argument in sequence. This allows to fill paths segments:

\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usetikzlibrary{fillbetween}

\begin{document}

\begin{tikzpicture}

\draw [name path=red,red] (120:1.06) circle (1.9);
%\draw [name path=yellow,yellow] (0:1.06) circle (2.12);
\draw [name path=green,green!50!black] (0:0.77) circle (2.41);
\draw [name path=blue,blue] (0:0) circle (1.06);

% substitute this temp path by `\path` to make it invisible:
\draw[name path=temp1, intersection segments={of=red and blue,sequence=L1}];
\draw[red,fill=blue,-stealth,ultra thick, intersection segments={of=temp1 and green,sequence=L3}]  
    [intersection segments={of=temp1 and green, sequence={--R2}}]
;

\end{tikzpicture}

\end{document}

enter image description here

Best Answer

Code

Output

Related Solutions

[Tex/LaTex] Best practices references

[Tex/LaTex] TikZ: Drawing an arc from an intersection to an intersection

Related Question