[Tex/LaTex] Tikz: Avoiding line segments in snake path

diagramsfeynmangraphicspgf-decorationstikz-pgf

I am using tikz to draw Feynman diagrams, and I learned how to draw a curved snake path.

The problem is that in general line segments are present (I'd like to avoid them).

I found a couple of post with could help to solve the problem, but none of them is working properly for me. The post are:

The second method results in the figure below,

Diagram generated with the code below

\documentclass{beamer}


\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing,decorations.markings,snakes}
\newif\ifstartcompletesineup
\newif\ifendcompletesineup
\pgfkeys{
    /pgf/decoration/.cd,
    start up/.is if=startcompletesineup,
    start up=true,
    start up/.default=true,
    start down/.style={/pgf/decoration/start up=false},
    end up/.is if=endcompletesineup,
    end up=true,
    end up/.default=true,
    end down/.style={/pgf/decoration/end up=false}
}
\pgfdeclaredecoration{complete sines}{initial}
{
    \state{initial}[
        width=+0pt,
        next state=upsine,
        persistent precomputation={
            \ifstartcompletesineup
                \pgfkeys{/pgf/decoration automaton/next state=upsine}
                \ifendcompletesineup
                    \pgfmathsetmacro\matchinglength{
                        0.5*\pgfdecoratedinputsegmentlength / (ceil(0.5* \pgfdecoratedinputsegmentlength / \pgfdecorationsegmentlength) )
                    }
                \else
                    \pgfmathsetmacro\matchinglength{
                        0.5 * \pgfdecoratedinputsegmentlength / (ceil(0.5 * \pgfdecoratedinputsegmentlength / \pgfdecorationsegmentlength ) - 0.499)
                    }
                \fi
            \else
                \pgfkeys{/pgf/decoration automaton/next state=downsine}
                \ifendcompletesineup
                    \pgfmathsetmacro\matchinglength{
                        0.5* \pgfdecoratedinputsegmentlength / (ceil(0.5 * \pgfdecoratedinputsegmentlength / \pgfdecorationsegmentlength ) - 0.4999)
                    }
                \else
                    \pgfmathsetmacro\matchinglength{
                        0.5 * \pgfdecoratedinputsegmentlength / (ceil(0.5 * \pgfdecoratedinputsegmentlength / \pgfdecorationsegmentlength ) )
                    }
                \fi
            \fi
            \setlength{\pgfdecorationsegmentlength}{\matchinglength pt}
        }] {}
    \state{downsine}[width=\pgfdecorationsegmentlength,next state=upsine]{
        \pgfpathsine{\pgfpoint{0.5\pgfdecorationsegmentlength}{0.5\pgfdecorationsegmentamplitude}}
        \pgfpathcosine{\pgfpoint{0.5\pgfdecorationsegmentlength}{-0.5\pgfdecorationsegmentamplitude}}
    }
    \state{upsine}[width=\pgfdecorationsegmentlength,next state=downsine]{
        \pgfpathsine{\pgfpoint{0.5\pgfdecorationsegmentlength}{-0.5\pgfdecorationsegmentamplitude}}
        \pgfpathcosine{\pgfpoint{0.5\pgfdecorationsegmentlength}{0.5\pgfdecorationsegmentamplitude}}
}
    \state{final}{}
}
\tikzset{
  % style to apply some styles to each segment of a path
  on each segment/.style={
    decorate,
    decoration={
      show path construction,
      moveto code={},
      lineto code={
        \path [#1]
        (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast);
      },
      curveto code={
        \path [#1] (\tikzinputsegmentfirst)
        .. controls
        (\tikzinputsegmentsupporta) and (\tikzinputsegmentsupportb)
        ..
        (\tikzinputsegmentlast);
      },
      closepath code={
        \path [#1]
        (\tikzinputsegmentfirst) -- (\tikzinputsegmentlast);
      },
    },
  },
  % style to add an arrow in the middle of a path
  mid arrow/.style={postaction={decorate,decoration={
        markings,
        mark=at position .5 with {\arrow[#1]{stealth}}
      }}},
}

\begin{document}
\begin{frame}
  \frametitle{Field and Mass Renormalization}
\begin{center}
      \begin{tikzpicture}[thick,scale=.6]
        \path [draw=blue,postaction={on each segment={mid arrow=blue}}]
        (-4,0) -- (-2,0) -- (2,0) -- (4,0);
        \draw[draw=blue,decorate, decoration=complete sines] (2,0) arc (0:180:2cm);
      \end{tikzpicture}
    \end{center}
\end{frame}
\end{document}

Any fresh ideas on this respect?

Best Answer

Here's a different approach that does not use a decoration, but rather a to path together with a plot statement that connects two points using a semicircle with a superimposed sine wave.

The number of complete periods to be drawn is specified using the key wave count. Another half period is added to this number so that the wave starts and ends on the outside (I think this looks better than starting on the inside or asymmetrically).

The amplitude of the wave is set using wave amplitude, and the semicircle can be flipped to the opposite side of the path using mirror semicircle=true.

This approach could reasonably easily be adapted to allow for circle sectors different from 180° (I don't know if that's ever needed in Feynman diagrams, though).

\documentclass[border=5mm]{standalone}


\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing,calc}

\newif\ifmirrorsemicircle

\tikzset{
    wave amplitude/.initial=0.2cm,
    wave count/.initial=8,
    mirror semicircle/.is if=mirrorsemicircle,
    mirror semicircle=false,
    wavy semicircle/.style={
        to path={
            let \p1 = (\tikztostart),
            \p2 = (\tikztotarget),
            \n1 = {veclen(\y2-\y1,\x2-\x1)},
            \n2 = {atan2(\y2-\y1,\x2-\x1))} in
            plot [
                smooth,
                samples=(\pgfkeysvalueof{/tikz/wave count}+0.5)*8+1, % Calculate the number of samples needed, so the samples are in sync with the wave and fall on the extrema
                domain=0:1,
                shift={($(\p1)!0.5!(\p2)$)}
            ] ({ % Polar coordinates: Angle...
                (\x*180-\n2 + 180 + \ifmirrorsemicircle 1 \else -1 \fi * 90%
            }:{ % ... and radius
                (%
                    \n1/2+\pgfkeysvalueof{/tikz/wave amplitude} * %
                    sin(
                        \x * 360 * (\pgfkeysvalueof{/tikz/wave count} + 0.5%
                    )%
                )%
            })
        } (\tikztotarget)
    }
}

\begin{document}
      \begin{tikzpicture}[thick,scale=.6]
        \draw [blue] (-4,0) -- (-2,0) -- (2,-1) -- (4,-2);
        \draw [red] (-2,0) to [wavy semicircle] (2,-1)
                to [
                    wavy semicircle,
                    wave amplitude=0.1cm,
                    wave count=15,
                    mirror semicircle
                ] (4,-2);
      \end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] Draw only some segments of a path in TikZ

This is a reworking of Jan's code to make it a little more TikZ-like. It still does the same thing: repeats the path, once as a fill and once as a draw, but with certain parts of the path removed for the draw stage. The main modification is that (hopefully) it now looks exactly like a standard TikZ command.

\documentclass{article}

\usepackage{tikz}
\makeatletter
\long\def\my@drawfill#1#2;{%
\@skipfalse
\fill[#1,draw=none] #2;
\@skiptrue
\draw[#1,fill=none] #2;
}

\newif\if@skip

\newcommand{\skipit}[1]{%
\if@skip
\else
#1
\fi
}

\newcommand{\drawfill}[1][]{%
  \my@drawfill{#1}}
\makeatother



\begin{document}
\begin{tikzpicture}
  \drawfill[fill=green,draw=blue,ultra thick] (0,0) -- (0,1) \skipit{--} (1,1) -- (1,0) \skipit{.. controls +(0,-1) and +(0,-1) ..} (0,0);
\end{tikzpicture}
\end{document}

This produces:

alt text

I'm sure that there are additional improvements to be made, which is one reason why I'm making this community wiki (the other being that it is really Jan's answer). In particular:

I couldn't make the \skipit command take an optional argument and still work. I think that it doesn't get expanded properly before the genuine TikZ commands see it and they don't like having macros as part of their path specification.
The assignment of key-value pairs is a bit of a hack: basically, we turn off the drawing on the fill command and turn off the filling on the draw command. It might be useful to be able to specify a set of keys that only get put on the draw command and a set for the fill command, so something like \drawfill[options for both, fillopt={options for fill}, drawopt={options for draw}] but I don't know enough (anything) about pgfkeys so don't have a clue how to go about that.

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

The source of the difficulty is that ellipses are constructed in a particular way in TikZ. They are paths that start from the x-axis and proceed counter-clockwise around their centre. The vast majority of the time, the exact parametrisation doesn't matter. You appear to have found the one situation where it does!

In the actual question, you only want to be able to mirror the ellipse, and so draw it starting from the negative x-axis (the title of the question suggests a more flexible approach). That's actually not too hard since we can exploit the symmetry of the ellipse. The key is to provide it with a negative x-radius, since then it will start from the negative x-axis (and proceed clockwise, but we could correct for that by negating the y-radius as well). To do this, we interrupt the call from the node shape to the drawing command and flip the sign of the x-radius. The simplest way to do this is to redefine the \pgfpathellipse macro to do the negation and then call the original macro. The following code does this.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations,shapes,decorations.markings}
\makeatletter
\let\origpgfpathellipse=\pgfpathellipse
\def\revpgfpathellipse#1#2#3{%
  #2%
  \pgf@xa=-\pgf@x
  \origpgfpathellipse{#1}{\pgfqpoint{\pgf@xa}{0pt}}{#3}}
\makeatother

\tikzset{
  reversed ellipse/.style={
    ellipse,
    reverse the ellipse%
  },
  reverse the ellipse/.code={
    \let\pgfpathellipse=\revpgfpathellipse
  }
}
\begin{document}
\begin{tikzpicture}
\node[ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,0) {hello world};

\node[reversed ellipse,
  draw,
  postaction={
    decorate,
    decoration={
      markings,
      mark=at position 1 with {
        \arrow[line width=5pt,blue]{>}
      }
    }
  }
] at (0,-2) {hello world};
\end{tikzpicture}

\end{document}

Here's the result:

rotated ellipse

(the arrow got clipped, but you can see where it lies)

Best Answer

Related Solutions

[Tex/LaTex] Draw only some segments of a path in TikZ

[Tex/LaTex] Rotate a node but not its content: the case of the ellipse decoration

Related Question