[Tex/LaTex] Truncate tikz snake decoration without changing frequency

decorationstikz-decorationstikz-pgf

I would like to draw a diagram of a wave penetrating a body, well several bodies. Or in some cases appear to go through a hollow cylinder. Since all of this is projected onto a 2d plane, this effect is drawn practically as just stopping the drawing of the wave at a certain point.

I've been using the snake decoration to do this, but it seems that if distance between the two points that I want to draw between is not and integer number times the frequency of the wave, a straight segment appears at the end of the snake.

There have been several questions and solutions about this problem, but all of the given solutions involve changing the frequency of the wave to stretch or squish the wave so that $n$ cycles of wave fit in the gap. (here, here, here, and here, for example.)

Technically, the wave I'm drawing should have a constant frequency throughout, so what I'd really like is a way of truncating the wave regardless of the point in the cycle the wave ends at. I've tried to illustrate this below:

% straight line at end of snake
\draw [decorate, decoration=snake] (0,0) -- (1.2,0);
% changing the frequency to fit wave path length:
\draw [decorate, decoration=snake, segment length=13] (0,-1) -- (1.2,-1); 
% the effect I'm after, truncated snake at any amplitude:
\draw [decorate, decoration=snake] (0,-2) -- (2,-2);
\fill [white] (1.2,-2.2) rectangle (2.1,-1.8);

I hope I've made myself clear, please ask for further clarification if needed.

Best Answer

You can actually plot a wave as sine function that it is. Then you can set the exact function you want to display and plot it. A wave can be described as

y(x) = A*sin(w*x + b)

So you plot it like \draw[domain=C:D] plot (\x,{A*sin(w*\x r + br)});, where the r's stand for radians. Heck, you can even make a command for that, which translates everything to radians out of the box:

\newcommand{\sinewave}[4][]{\draw[#1]  plot (\x,{#2*sin((#4*pi/180)r + 2*pi*#3*\x r)})}

Here you get a cmd like \sinewave[tikz options]{Amplitude}{Frequency, in Hz}{Phase angle, in degrees}. The domain option set the start and end of the sine wave and samples sets the 'smoothness' of the wave.

Here's a complete MWE:

\documentclass[tikz,border=5mm]{standalone}

\newcommand{\sinewave}[4][]{\draw[#1]  plot (\x,{#2*sin((#4*pi/180)r + 2*pi*#3*\x r)})}

\begin{document}
\begin{tikzpicture}[domain=0:1.2, samples=120]
\draw plot (\x,{0.1*sin(10*\x r)});
\draw[yshift=-1cm] plot (\x,{0.15*sin(13*\x r)});
\sinewave[yshift=-2cm]{0.2}{4}{90};
\end{tikzpicture}
\end{document}

Related Solutions

[Tex/LaTex] How to animate a path or how to draw starting fraction of a complex but linear path

Here's the decoration Caramdir came up with, adapted to draw only the first fraction of an arbitrary path:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{decorations}

% A simple empty decoration, that is used to ignore the last bit of the path
\pgfdeclaredecoration{ignore}{final}
{
\state{final}{}
}

% Declare the actual decoration.
\pgfdeclaremetadecoration{middle}{initial}{
    \state{initial}[
        width={0pt},
        next state=middle
    ]
    {\decoration{moveto}}

    \state{middle}[
        width={\pgfdecorationsegmentlength*\pgfmetadecoratedpathlength},
        next state=final
    ]
    {\decoration{curveto}}

    \state{final}
    {\decoration{ignore}}
}

% Create a key for easy access to the decoration
\tikzset{middle segment/.style={decoration={middle},decorate, segment length=#1}}

\begin{document}\noindent
\foreach \step in {0.2,0.4,...,1} {%
\begin{tikzpicture}
    \draw[middle segment=\step,ultra thick,red,->] (0,0) to[out=30,in=150] (3,0) -- (7,1) -- (8,0);
\end{tikzpicture}\\
}
\end{document}

[Tex/LaTex] Coil path decoration without straight segment

Edit 2: Adapted code using \makeatletter and \makeatother to avoid the bad practice of midifying a package's file.

Edit: Changed code to make the coils end at the middle of the line.

If I understand correctly, you can get the result you are looking for by changing the predefined coil decoration. Although, the solution I propose is not prefect. The problem is that you need to change the segment length value a little bit to avoid too much (or too little) space at the end of the coil. Here are some examples, the blue coils correspond to the modified decoration:

enter image description here

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{decorations.pathmorphing}

\makeatletter

% gluon decoration (based on the original coil decoration)

\pgfdeclaredecoration{gluon}{coil}
{
  \state{coil}[switch if less than=%
    0.5\pgfdecorationsegmentlength+%>
    \pgfdecorationsegmentaspect\pgfdecorationsegmentamplitude+%
    \pgfdecorationsegmentaspect\pgfdecorationsegmentamplitude to last,
               width=+\pgfdecorationsegmentlength]
  {
    \pgfpathcurveto
    {\pgfpoint@oncoil{0    }{ 0.555}{1}}
    {\pgfpoint@oncoil{0.445}{ 1    }{2}}
    {\pgfpoint@oncoil{1    }{ 1    }{3}}
    \pgfpathcurveto
    {\pgfpoint@oncoil{1.555}{ 1    }{4}}
    {\pgfpoint@oncoil{2    }{ 0.555}{5}}
    {\pgfpoint@oncoil{2    }{ 0    }{6}}
    \pgfpathcurveto
    {\pgfpoint@oncoil{2    }{-0.555}{7}}
    {\pgfpoint@oncoil{1.555}{-1    }{8}}
    {\pgfpoint@oncoil{1    }{-1    }{9}}
    \pgfpathcurveto
    {\pgfpoint@oncoil{0.445}{-1    }{10}}
    {\pgfpoint@oncoil{0    }{-0.555}{11}}
    {\pgfpoint@oncoil{0    }{ 0    }{12}}
  }
  \state{last}[next state=final]
  {
    \pgfpathcurveto
    {\pgfpoint@oncoil{0    }{ 0.555}{1}}
    {\pgfpoint@oncoil{0.445}{ 1    }{2}}
    {\pgfpoint@oncoil{1    }{ 1    }{3}}
    \pgfpathcurveto
    {\pgfpoint@oncoil{1.555}{ 1    }{4}}
    {\pgfpoint@oncoil{2    }{ 0.555}{5}}
    {\pgfpoint@oncoil{2    }{ 0    }{6}}
  }
  \state{final}{}
}

\def\pgfpoint@oncoil#1#2#3{%
  \pgf@x=#1\pgfdecorationsegmentamplitude%
  \pgf@x=\pgfdecorationsegmentaspect\pgf@x%
  \pgf@y=#2\pgfdecorationsegmentamplitude%
  \pgf@xa=0.083333333333\pgfdecorationsegmentlength%
  \advance\pgf@x by#3\pgf@xa%
}

\makeatother

\begin{document}

\begin{tikzpicture}
  \node (a) at (0,0) {A};
  \node (b) at (2,0) {B};
  \path (a) edge[decorate,decoration={coil, amplitude=4pt,
    segment length=5pt}] (b);
\end{tikzpicture}

\begin{tikzpicture}
  \node (a) at (0,0) {A};
  \node (b) at (2,0) {B};
  \path (a) edge[color=blue,decorate,decoration={gluon, amplitude=4pt,
    segment length=5.25pt}] (b);
\end{tikzpicture}

\begin{tikzpicture}
  \node (a) at (0,0) {A};
  \node (b) at (2,0) {B};
  \path (a) edge[decorate,decoration={coil, amplitude=4pt,
    segment length=5pt, aspect=0}] (b);
\end{tikzpicture}

\begin{tikzpicture}
  \node (a) at (0,0) {A};
  \node (b) at (2,0) {B};
  \path (a) edge[color=blue,decorate,decoration={gluon, amplitude=4pt,
    segment length=5.2pt, aspect=0}] (b);
\end{tikzpicture}

\begin{tikzpicture}
  \node (a) at (0,0) {A};
  \node (b) at (3.5,0) {B};
  \path (a) edge[decorate,decoration={coil, amplitude=4pt,
    segment length=5pt}] (b);
\end{tikzpicture}

\begin{tikzpicture}
  \node (a) at (0,0) {A};
  \node (b) at (3.5,0) {B};
  \path (a) edge[color=blue,decorate,decoration={gluon, amplitude=4pt,
    segment length=5.25pt}] (b);
\end{tikzpicture}

\begin{tikzpicture}
  \node (a) at (0,0) {A};
  \node (b) at (3.5,0) {B};
  \path (a) edge[decorate,decoration={coil, amplitude=4pt,
    segment length=5pt, aspect=0}] (b);
\end{tikzpicture}

\begin{tikzpicture}
  \node (a) at (0,0) {A};
  \node (b) at (3.5,0) {B};
  \path (a) edge[color=blue,decorate,decoration={gluon, amplitude=4pt,
    segment length=4.9pt, aspect=0}] (b);
\end{tikzpicture}

\end{document}

Best Answer

Related Solutions

[Tex/LaTex] How to animate a path or how to draw starting fraction of a complex but linear path

[Tex/LaTex] Coil path decoration without straight segment

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