TikZ: Decorated paths without straight segment

Question

When a path is decorated in TikZ a straight segment might be added at the end, depending on the length of the path. This is undesirable in some cases, and a resolution for the snake decoration has appeared in this question.

I would like to get an integer or half-integer number of wavelengths in a path for a snake and a coil decoration, with the wavelength calculated automatically so that there is no straight segment at the end. I would also like a switch for each of the endpoints that allows me to choose if the path at that endpoint points in one or the other direction.

Answer 1

Here's an extended version of the complete sines decoration, which can now be controlled using start up/start down and end up/end down.

\documentclass[a4paper,12pt]{article}
\usepackage{tikz}
\usetikzlibrary{decorations}
\begin{document}

\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}{}
}

\begin{tikzpicture}

\draw [gray!30] (0,-7) grid [step=0.5] (2.5,0);
\node at (1.25cm,0) [align=center,anchor=south] {\texttt{start up}\\\texttt{end up}};
\begin{scope}[
    every path/.style={
        decoration={
            complete sines,
            segment length=0.5cm,
            amplitude=0.5cm,
            mirror,
            start up,
            end up
        },
        decorate,
        thick
    }]
\foreach \length [count=\n] in {1,1.25,...,2.5}
    \draw [yshift=-\n cm + 0.5cm] (0,0) node [anchor=east] {\length cm} -- (\length cm,0);
\end{scope}

\begin{scope}[xshift=3cm]
\draw [gray!30] (0,-7) grid [step=0.5] (2.5,0);
\node at (1.25cm,0) [align=center,anchor=south] {\texttt{start up}\\\texttt{end down}};
\begin{scope}[
    every path/.style={
        decoration={
            complete sines,
            segment length=0.5cm,
            amplitude=0.5cm,
            mirror,
            start up,
            end down
        },
        decorate,
        thick
    }]
\foreach \length [count=\n] in {1,1.25,...,2.5}
    \draw [yshift=-\n cm + 0.5cm] (0,0) -- (\length cm,0);
\end{scope}
\end{scope}

\begin{scope}[xshift=9cm]
\draw [gray!30] (0,-7) grid [step=0.5] (2.5,0);
\node at (1.25cm,0) [align=center,anchor=south] {\texttt{start down}\\\texttt{end up}};
\begin{scope}[
    every path/.style={
        decoration={
            complete sines,
            segment length=0.5cm,
            amplitude=0.5cm,
            mirror,
            start down,
            end up
        },
        decorate,
        thick
    }]
\foreach \length [count=\n] in {1,1.25,...,2.5}
    \draw [yshift=-\n cm + 0.5cm] (0,0) -- (\length cm,0);
\end{scope}
\end{scope}

\begin{scope}[xshift=6cm]
\draw [gray!30] (0,-7) grid [step=0.5] (2.5,0);
\node at (1.25cm,0) [align=center,anchor=south] {\texttt{start down}\\\texttt{end down}};
\begin{scope}[
    every path/.style={
        decoration={
            complete sines,
            segment length=0.5cm,
            amplitude=0.5cm,
            mirror,
            start down,
            end down
        },
        decorate,
        thick
    }]
\foreach \length [count=\n] in {1,1.25,...,2.5}
    \draw [yshift=-\n cm + 0.5cm] (0,0) -- (\length cm,0);
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document}