[Tex/LaTex] Custom decoration along curved paths

tikz-pgf

The problem that I started out with were those straight lines at the end of paths decorated with snake or coil, which I wanted to get rid of. I found a very nice solution here for the wavy line:
https://tex.stackexchange.com/a/29645/36900

The problem that I am facing now, however, is when I apply this decoration to curved paths:

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

\pgfdeclaredecoration{complete sines}{initial}
{
    \state{initial}[
        width=+0pt,
        next state=sine,
        persistent precomputation={\pgfmathsetmacro\matchinglength{
            \pgfdecoratedinputsegmentlength / round(\pgfdecoratedinputsegmentlength/\pgfdecorationsegmentlength)}
            \setlength{\pgfdecorationsegmentlength}{\matchinglength pt}
        }] {}
    \state{sine}[width=\pgfdecorationsegmentlength]{
        \pgfpathsine{\pgfpoint{0.25\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}}
        \pgfpathcosine{\pgfpoint{0.25\pgfdecorationsegmentlength}{-\pgfdecorationsegmentamplitude}}
        \pgfpathsine{\pgfpoint{0.25\pgfdecorationsegmentlength}{-\pgfdecorationsegmentamplitude}}
        \pgfpathcosine{\pgfpoint{0.25\pgfdecorationsegmentlength}{\pgfdecorationsegmentamplitude}}
}
    \state{final}{}
}

\begin{document}

\begin{tikzpicture}[line width=1. pt]

        \draw[decorate, decoration={snake}] 
        (3,-3) arc (180:-90:1);
        \draw[line width=0.3pt]
        (3,-3) arc (180:-90:1);

        \draw[decorate,decoration={complete sines}] 
        (4,1) arc (180:-90:1);
        \draw[line width=0.3pt]
        (4,1) arc (180:-90:1);

      \end{tikzpicture}

\end{document}

enter image description here

One clearly sees how these "decoration segments" are simply rotated and put behind one another resulting in a finite displacement with respect to the initial path, due the finite width of the pattern that is repeated.

I was wondering if there is the possibility to decorate a path "continuously". If I could specify the xy-displacement (x showing tangential to the initial path) of each point along the initial path like this

{0.}{\amplitude * sin(2*pi/\wavelength * \x)}

where \wavelength could be computed at the beginning as in the example above, and \x denotes the actual position along the initial path.

Superimposing an oscillation along the y-coordinate should also allow me to produce coils.

I guess one could define a decoration with segments of width 1pt but I thought that there must be a simpler solution.

Best Answer

Not sure it's exactly what is required and it certainly has the risk of being quite slow. But the approach taken here is to essentially plot the sine function along the path.

There is a high possibility of some inaccuracies/ugliness at the very end of the path, due to the low accuracy of TeX. Some ugliness will also occur along paths with acute angles.

\documentclass[border=5pt]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations}

\tikzset{/pgf/decoration/.cd,
    number of sines/.initial=10,
    angle step/.initial=20,
}
\newdimen\tmpdimen
\pgfdeclaredecoration{complete sines}{initial}
{
    \state{initial}[
        width=+0pt,
        next state=move,
        persistent precomputation={
            \pgfmathparse{\pgfkeysvalueof{/pgf/decoration/angle step}}%
            \let\anglestep=\pgfmathresult%
            \let\currentangle=\pgfmathresult%
            \pgfmathsetlengthmacro{\pointsperanglestep}%
                {(\pgfdecoratedremainingdistance/\pgfkeysvalueof{/pgf/decoration/number of sines})/360*\anglestep}%
        }] {}
    \state{move}[width=+\pointsperanglestep, next state=draw]{
        \pgfpathmoveto{\pgfpointorigin}
    }
    \state{draw}[width=+\pointsperanglestep, switch if less than=1.25*\pointsperanglestep to final, % <- bit of a hack
        persistent postcomputation={
        \pgfmathparse{mod(\currentangle+\anglestep, 360)}%
        \let\currentangle=\pgfmathresult%
    }]{%
        \pgfmathsin{+\currentangle}%
        \tmpdimen=\pgfdecorationsegmentamplitude%
        \tmpdimen=\pgfmathresult\tmpdimen%
        \divide\tmpdimen by2\relax%
        \pgfpathlineto{\pgfqpoint{0pt}{\tmpdimen}}%
    }
    \state{final}{
        \ifdim\pgfdecoratedremainingdistance>0pt\relax
            \pgfpathlineto{\pgfpointdecoratedpathlast}
        \fi
   }
}

\begin{document}

\begin{tikzpicture}[
    sines/.style={
        very thick,
        line join=round, 
        draw=black, 
        decorate, 
        decoration={complete sines, number of sines=15, amplitude=5pt}
    }
]

  \draw [red, postaction={sines}] 
      (0,0) .. controls +(-1,1) and +(1,-1) .. (2,2);

  \draw [red, postaction={sines}] 
        (1,3) circle [radius=1];

\end{tikzpicture}

\end{document}

enter image description here

Related Solutions

[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)

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

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}

Best Answer

Related Solutions

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

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

Related Question