装饰一个圆圈结束装饰“exaclty”

Question

我想以一种方式装饰一个圆圈，使装饰的起点和终点重合一个好方法。当然，它们总是重合的，但我希望装饰元素重复整数次。有没有简单的方法来实现它？当然，调整装饰的amplitude和/或segment length可以有所帮助，但它需要手动微调，我想避免这种情况。

我看了pgf手动的，特别是第 24 章，但我没有找到答案。顺便说一句，第 24.3 节包含我的部分代码，它们有同样的“问题”，而第 24.4 节（调整装饰）或 48.2 节（路径变形装饰）对我来说毫无用处。

\documentclass[tikz, border=3mm]{standalone}
\usetikzlibrary{decorations.pathmorphing}

\begin{document}
    \begin{tikzpicture}
        \draw[decorate, decoration=zigzag] (0,0) circle (1cm);
        \draw[decorate, decoration=bumps]   (3,0) circle (1cm);
        \draw[red, thick] (1,0) circle (3mm) (4,0) circle (3mm); % <- Just to stress the problem
    \end{tikzpicture}
\end{document}

Answer 1

一个临时建议是将线段长度设置为 pi 毫米（对于半径为 1 厘米的圆）。

\documentclass[tikz, border=3mm]{standalone}
\usetikzlibrary{decorations.pathmorphing}

\begin{document}
    \begin{tikzpicture}
        \draw[decorate, decoration={zigzag,segment length=3.14mm}] (0,0) circle (1cm);
        \draw[decorate, decoration={bumps,segment length=3.14mm}]   (3,0) circle (1cm);
        \draw[red, thick] (1,0) circle (3mm) (4,0) circle (3mm); % <- Just to stress the problem
    \end{tikzpicture}
\end{document}

更新：更完整的锯齿形解决方案。

\documentclass[tikz, border=3mm]{standalone}
\usetikzlibrary{decorations,decorations.pathmorphing}
\pgfkeys{/tikz/.cd,
    pattern repetition/.store in=\PatternRepetition,
    pattern repetition=20
}

\pgfdeclaremetadecoration{closing zigzag}{initial}{%
 \state{initial}[width=0pt, next state=zigzag] {
    \pgfmathdivide{\pgfmetadecoratedpathlength}{\PatternRepetition}
    \let\pgfmetadecorationsegmentlength\pgfmathresult
    \pgfset{/pgf/decoration/segment length=\pgfmathresult pt}
  }
\state{zigzag}[width=\pgfmetadecorationsegmentlength, next state=zigzag] {
\decoration{zigzag}
}
\state{final}
  {
    \pgfpathlineto{\pgfpointdecoratedpathlast}
  }
}

% does not quite work yet 
\pgfdeclaremetadecoration{closing bumps}{initial}{%
 \state{initial}[width=0pt, next state=bumps] {
    \pgfmathdivide{\pgfmetadecoratedpathlength}{\PatternRepetition}
    \pgfset{/pgf/decoration/segment length=\pgfmathresult pt}
    \pgfmathdivide{\pgfmetadecoratedpathlength}{\PatternRepetition}
    \let\pgfmetadecorationsegmentlength\pgfmathresult
  }
\state{bumps}[width=\pgfmetadecorationsegmentlength, next state=bumps] {
\decoration{bumps}
}
\state{final}
  {
    \pgfpathlineto{\pgfpointdecoratedpathlast}
  }
}

\newlength{\totallength}
\begin{document}
    \begin{tikzpicture}
    \draw[decorate, decoration={closing zigzag}] (0,0) circle (1cm);
    \tikzset{pattern repetition=55}
    \draw[decorate, decoration={closing zigzag}]   (3,0) circle (1cm and 2cm);
    \draw[red, thick] (1,0) circle (3mm) (4,0) circle (3mm); % <- Just to stress the problem
    \end{tikzpicture}
\end{document}