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TikZ-decoration：沿曲線控制裝飾幅度

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TikZ-decoration：沿曲線控制裝飾幅度

使用基於的路徑裝飾這個解決方案由土撥鼠提供，我正在尋找改變圖形上裝飾幅度的可能性。

有這個情節

在此輸入影像描述

應用上述裝飾給出

在此輸入影像描述

這正是裝飾該做的事。

事實上，所需的曲線應該如下所示：

在此輸入影像描述

最後的輸出是透過手動搜尋正確的位置來操縱幅度創建的，這是一種「試錯」方法。改變尺寸tikzpicture將會給出錯誤的結果 fx

在此輸入影像描述

現在的基本想法是提供一個單獨的路徑（可以在開發過程中使其可見）來控制沿著原始（藍色）曲線的裝飾幅度。在這種情況下，控制路徑（紅色）將非常簡單：

在此輸入影像描述

控制路徑可以解釋為可通過 設定的裝飾幅度的一個因素decoration={amplitude=}。

假設這種方法會非常方便，我有點驚訝它不可用TikZ- 或者我是否監督過它？如果不是：如何獲得\state{step}裝飾定義部分內控製曲線的 y 值？

MWE 產生上述所有圖表（即使在效率和結構美方面沒有很好地編碼）：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.pathmorphing}

\newcounter{randymark}
\newcommand{\amplitudesetter}{}
\pgfdeclaredecoration{mark random y steps}{start}
{%
  \state{start}[width=+0pt,next state=step,persistent precomputation={\pgfdecoratepathhascornerstrue\setcounter{randymark}{0}}]
    {\stepcounter{randymark}
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpoint{0pt}{0pt}}
    }%
  \state{step}[auto end on length=1.5\pgfdecorationsegmentlength,
               auto corner on length=1.5\pgfdecorationsegmentlength,
               width=+\pgfdecorationsegmentlength]
    {\stepcounter{randymark}\amplitudesetter
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpoint{\pgfdecorationsegmentlength}{rand*\pgfdecorationsegmentamplitude}}
    }%
  \state{final}
    {\stepcounter{randymark}
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpointdecoratedpathlast}%
    }%
}%

\begin{document}
\begin{tikzpicture}[x=5mm,y=5mm,decoration={mark random y steps,segment length=1.5mm,amplitude=0.75mm}]% original curve
  \draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
  \pgfmathsetseed{2}
  \draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
\end{tikzpicture}

\vspace{2ex}

\begin{tikzpicture}[x=5mm,y=5mm,decoration={mark random y steps,segment length=1.5mm,amplitude=0.75mm}]% original curve
  \draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
  \pgfmathsetseed{2}
  \draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \draw[blue!80!black,thick] plot[variable=\x,samples at={1,...,\arabic{randymark}},smooth] (randymark\x);
\end{tikzpicture}

\vspace{2ex}

\begin{tikzpicture}[x=5mm,y=5mm,decoration={mark random y steps,segment length=1.5mm,amplitude=0.75mm}]% original curve
  \draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
  \pgfmathsetseed{2}
  \renewcommand{\amplitudesetter}{%
    \pgfdecorationsegmentamplitude=0.75mm
    \ifnum\value{randymark}<48\pgfdecorationsegmentamplitude=0.7mm\fi%
    \ifnum\value{randymark}<46\pgfdecorationsegmentamplitude=0.6mm\fi%
    \ifnum\value{randymark}<44\pgfdecorationsegmentamplitude=0.5mm\fi%
    \ifnum\value{randymark}<42\pgfdecorationsegmentamplitude=0.4mm\fi%
    \ifnum\value{randymark}<40\pgfdecorationsegmentamplitude=0.3mm\fi%
    \ifnum\value{randymark}<38\pgfdecorationsegmentamplitude=0.2mm\fi%
    \ifnum\value{randymark}<36\pgfdecorationsegmentamplitude=0.1mm\fi%
    \ifnum\value{randymark}<34\pgfdecorationsegmentamplitude=0mm\fi%
    \ifnum\value{randymark}<8\pgfdecorationsegmentamplitude=0.75mm\fi%
    }
  \draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \draw[blue!80!black,thick] plot[variable=\x,samples at={1,...,\arabic{randymark}},smooth] (randymark\x);
\end{tikzpicture}

\vspace{2ex}

\begin{tikzpicture}[x=2.5mm,y=2.5mm,decoration={mark random y steps,segment length=1.5mm,amplitude=0.75mm}]% original curve
  \draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
  \pgfmathsetseed{2}
  \renewcommand{\amplitudesetter}{%
    \pgfdecorationsegmentamplitude=0.75mm
    \ifnum\value{randymark}<48\pgfdecorationsegmentamplitude=0.7mm\fi%
    \ifnum\value{randymark}<46\pgfdecorationsegmentamplitude=0.6mm\fi%
    \ifnum\value{randymark}<44\pgfdecorationsegmentamplitude=0.5mm\fi%
    \ifnum\value{randymark}<42\pgfdecorationsegmentamplitude=0.4mm\fi%
    \ifnum\value{randymark}<40\pgfdecorationsegmentamplitude=0.3mm\fi%
    \ifnum\value{randymark}<38\pgfdecorationsegmentamplitude=0.2mm\fi%
    \ifnum\value{randymark}<36\pgfdecorationsegmentamplitude=0.1mm\fi%
    \ifnum\value{randymark}<34\pgfdecorationsegmentamplitude=0mm\fi%
    \ifnum\value{randymark}<8\pgfdecorationsegmentamplitude=0.75mm\fi%
    }
  \draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \draw[blue!80!black,thick] plot[variable=\x,samples at={1,...,\arabic{randymark}},smooth] (randymark\x);
\end{tikzpicture}

\vspace{2ex}

\begin{tikzpicture}[x=5mm,y=5mm,decoration={mark random y steps,segment length=1.5mm,amplitude=0.75mm}]
  \draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
  \pgfmathsetseed{2}
  \draw [red,thick,name=amplitudecontrol] (0,1) -- (2,1) -- (2,0) -- (7,0) -- (12,1) -- (25,1);
  \draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
\end{tikzpicture}

\end{document}

答案1

首先我要說的是，我真的很喜歡這個問題，並且對你所取得的成就印象深刻。這是解決可擴展性的提案。定義一個控制幅度的函數，

varyingamp(x) = whatever you like

其中x是修飾路徑的分數（為了確保可擴展性）。 （這樣的功能已經被使用過這裡為了具有可變的線寬。如果我以前使用過類似的東西，我一點也不會感到驚訝。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,decorations.pathmorphing}

\newcounter{randymark}
%\newcommand{\amplitudesetter}{}
\pgfdeclaredecoration{mark random y steps}{start}
{%
  \state{start}[width=+0pt,next state=step,persistent precomputation={
  \pgfdecoratepathhascornerstrue\setcounter{randymark}{0}}]
    {\stepcounter{randymark}
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpoint{0pt}{0pt}}
    }%
  \state{step}[auto end on length=1.5\pgfdecorationsegmentlength,
               auto corner on length=1.5\pgfdecorationsegmentlength,
               width=+\pgfdecorationsegmentlength]
    {\stepcounter{randymark}%\amplitudesetter
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpoint{\pgfdecorationsegmentlength}{rand*\pgfdecorationsegmentamplitude}}
    }%
  \state{final}
    {\stepcounter{randymark}
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpointdecoratedpathlast}%
    }%
}%

\pgfdeclaredecoration{mark varying random y steps}{start}
{%
  \state{start}[width=+0pt,next state=step,persistent precomputation={
  \pgfdecoratepathhascornerstrue\setcounter{randymark}{0}}]
    {\stepcounter{randymark}
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpoint{0pt}{0pt}}
    }%
  \state{step}[auto end on length=1.5\pgfdecorationsegmentlength,
               auto corner on length=1.5\pgfdecorationsegmentlength,
               width=+\pgfdecorationsegmentlength]
    {\stepcounter{randymark}
     \pgfmathsetmacro{\myfraction}{\the\pgfdecorationsegmentlength*\value{randymark}/\pgfdecoratedpathlength}
     \pgfmathsetmacro{\myamplitude}{varyingamp(\myfraction)}
     %\typeout{\myfraction,\myamplitude}
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpoint{\pgfdecorationsegmentlength}{rand*\myamplitude*\pgfdecorationsegmentamplitude}}
    }%
  \state{final}
    {\stepcounter{randymark}
     \pgfcoordinate{randymark\arabic{randymark}}{\pgfpointdecoratedpathlast}%
    }%
}%



\begin{document}
\begin{tikzpicture}[x=5mm,y=5mm,decoration={mark random y steps,segment length=1.5mm,amplitude=0.75mm}]% original curve
  \draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
  \pgfmathsetseed{2}
  \draw[blue!80!black,thick] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
\end{tikzpicture}

\vspace{2ex}

\begin{tikzpicture}[x=5mm,y=5mm,decoration={mark varying random y steps,segment
length=1.5mm,amplitude=0.75mm},declare function={
varyingamp(\x)=ifthenelse(\x<0.08,1,ifthenelse(\x<0.28,0,ifthenelse(\x<0.48,5*(\x-0.28),1)));}]% 
  \draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
  \draw[red,thick] plot[variable=\x,domain=0:25,samples=101] ({\x},{varyingamp(\x/25)});
  \pgfmathsetseed{2}
  \draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \draw[blue!80!black,thick] plot[variable=\x,samples at={1,...,\arabic{randymark}},smooth] (randymark\x);
\end{tikzpicture}

\vspace{2ex}

\begin{tikzpicture}[x=2.5mm,y=2.5mm,decoration={mark varying random y
steps,segment length=0.75mm,amplitude=0.75mm},declare function={
varyingamp(\x)=ifthenelse(\x<0.08,1,ifthenelse(\x<0.28,0,ifthenelse(\x<0.48,5*(\x-0.28),1)));}]
  \draw[style=help lines] (0,-4) grid[step=5mm] (25,1);
  \pgfmathsetseed{2}
  \draw[black] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \path[decorate] (0,0) -- (2,0) to [out=0,in=180](4,-3.5) to [out=0,in=225](6,-1.75) to [out=45,in=180](11,0) -- (24.25,0);
  \draw[blue!80!black,thick] plot[variable=\x,samples at={1,...,\arabic{randymark}},smooth] (randymark\x);
\end{tikzpicture}
\end{document}

在此輸入影像描述

函數在第二張圖中以紅色顯示。第三張圖顯示了可擴展性。 （當然，您還需要重新調整段長度。另請注意，此裝飾具有離散步驟，因此如果您有一個強烈變化的函數但只有幾個步驟，則該函數可能不會被完全“欣賞”，因為它只被評估在幾個點上。

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