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TikZ 中的振动曲线

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TikZ 中的振动曲线

我为 TikZ 中的一张图片编写了以下代码。这是一篇声学文章的插图。它应该给人一种边界曲线在振动的印象。我将非常感激有关如何实现这一点的建议。谢谢。

\begin{tikzpicture}
  \coordinate (omega-center) at (4.5,1.3);
  \coordinate (omega0) at ($(omega-center)+(0:2.5cm)$);
  \coordinate (omega1) at ($(omega-center)+(40:2cm)$);
  \coordinate (omega2) at ($(omega-center)+(80:2.5cm)$);
  \coordinate (omega3) at ($(omega-center)+(120:2.5cm)$);
  \coordinate (omega4) at ($(omega-center)+(160:2.5cm)$);
  \coordinate (omega5) at ($(omega-center)+(200:2.5cm)$);
  \coordinate (omega6) at ($(omega-center)+(240:2cm)$);
  \coordinate (omega7) at ($(omega-center)+(280:2cm)$);
  \coordinate (omega8) at ($(omega-center)+(320:2cm)$);

  \coordinate (omega0-out) at (90:1cm);
  \coordinate (omega0-in) at (270:1cm);
  \coordinate (omega1-out) at (90:1cm);
  \coordinate (omega1-in) at (270:1cm);
  \coordinate (omega2-out) at (90:1cm);
  \coordinate (omega2-in) at (270:1cm);
  \coordinate (omega3-out) at (250:1cm);
  \coordinate (omega3-in) at (70:1cm);
  \coordinate (omega4-out) at (200:1.5cm);
  \coordinate (omega4-in) at (20:1cm);
  \coordinate (omega5-out) at (20:1cm);
  \coordinate (omega5-in) at (200:1cm);
  \coordinate (omega6-out) at (60:1cm);
  \coordinate (omega6-in) at (240:1cm);
  \coordinate (omega7-out) at (70:1cm);
  \coordinate (omega7-in) at (250:1cm);
  \coordinate (omega8-out) at (90:1cm);
  \coordinate (omega8-in) at (270:1cm);

  \draw[black, very thick, fill=blue!10]
    (omega0) .. controls +(omega0-out) and +(omega1-in) .. (omega1)
             .. controls +(omega1-out) and +(omega2-in) .. (omega2)
             .. controls +(omega2-out) and +(omega3-in) .. (omega3)
             .. controls +(omega3-out) and +(omega4-in) .. (omega4)
             .. controls +(omega4-out) and +(omega5-in) .. (omega5)
             .. controls +(omega5-out) and +(omega6-in) .. (omega6)
             .. controls +(omega6-out) and +(omega7-in) .. (omega7)
             .. controls +(omega7-out) and +(omega8-in) .. (omega8)
             .. controls +(omega8-out) and +(omega0-in) .. (omega0);
\end{tikzpicture}

在此处输入图片描述

答案1

这里有一个想法。在原始形状上方绘制略微旋转且透明的相同形状：

\usetikzlibrary{calc}
\begin{tikzpicture}
  \coordinate (omega-center) at (4.5,1.3);
  \coordinate (omega0) at ($(omega-center)+(0:2.5cm)$);
  \coordinate (omega1) at ($(omega-center)+(40:2cm)$);
  \coordinate (omega2) at ($(omega-center)+(80:2.5cm)$);
  \coordinate (omega3) at ($(omega-center)+(120:2.5cm)$);
  \coordinate (omega4) at ($(omega-center)+(160:2.5cm)$);
  \coordinate (omega5) at ($(omega-center)+(200:2.5cm)$);
  \coordinate (omega6) at ($(omega-center)+(240:2cm)$);
  \coordinate (omega7) at ($(omega-center)+(280:2cm)$);
  \coordinate (omega8) at ($(omega-center)+(320:2cm)$);

  \coordinate (omega0-out) at (90:1cm);
  \coordinate (omega0-in) at (270:1cm);
  \coordinate (omega1-out) at (90:1cm);
  \coordinate (omega1-in) at (270:1cm);
  \coordinate (omega2-out) at (90:1cm);
  \coordinate (omega2-in) at (270:1cm);
  \coordinate (omega3-out) at (250:1cm);
  \coordinate (omega3-in) at (70:1cm);
  \coordinate (omega4-out) at (200:1.5cm);
  \coordinate (omega4-in) at (20:1cm);
  \coordinate (omega5-out) at (20:1cm);
  \coordinate (omega5-in) at (200:1cm);
  \coordinate (omega6-out) at (60:1cm);
  \coordinate (omega6-in) at (240:1cm);
  \coordinate (omega7-out) at (70:1cm);
  \coordinate (omega7-in) at (250:1cm);
  \coordinate (omega8-out) at (90:1cm);
  \coordinate (omega8-in) at (270:1cm);

  \def\myshape{
    (omega0) .. controls +(omega0-out) and +(omega1-in) .. (omega1)
             .. controls +(omega1-out) and +(omega2-in) .. (omega2)
             .. controls +(omega2-out) and +(omega3-in) .. (omega3)
             .. controls +(omega3-out) and +(omega4-in) .. (omega4)
             .. controls +(omega4-out) and +(omega5-in) .. (omega5)
             .. controls +(omega5-out) and +(omega6-in) .. (omega6)
             .. controls +(omega6-out) and +(omega7-in) .. (omega7)
             .. controls +(omega7-out) and +(omega8-in) .. (omega8)
             .. controls +(omega8-out) and +(omega0-in) .. (omega0)
  }

  \draw[black, very thick, fill=blue!10] \myshape;
  \begin{scope}[transform canvas={rotate around={3:(omega-center)}}]
     \draw[black, very thick, draw opacity=0.3] \myshape;
  \end{scope}
  \begin{scope}[transform canvas={rotate around={-3:(omega-center)}}]
     \draw[black, very thick, draw opacity=0.3]  \myshape;
  \end{scope}
\end{tikzpicture}

结果

根据 Dan H. 在评论中给出的想法，可以通过添加更多层来增加“更多振动”。我认为在这种情况下，附加层应该比主层更薄。例如：

  % Ommited all the initialization of coordinates, which is the same
  \draw[black, very thick, fill=blue!10] \myshape;
  \begin{scope}[transform canvas={rotate around={2:(omega-center)}}]
     \draw[black, thick, draw opacity=0.3] \myshape;
  \end{scope}
  \begin{scope}[transform canvas={rotate around={-2:(omega-center)}}]
     \draw[black, thick, draw opacity=0.3]  \myshape;
  \end{scope}
  \begin{scope}[transform canvas={rotate around={4:(omega-center)}}]
     \draw[black, thick, draw opacity=0.1] \myshape;
  \end{scope}
  \begin{scope}[transform canvas={rotate around={-4:(omega-center)}}]
     \draw[black, thick, draw opacity=0.1]  \myshape;
  \end{scope}

结果：

结果

答案2

为了记录，我还发布了我的最终版本。我没有像 JLDiaz 建议的那样旋转附加层，而是决定缩放它们。结果如下。 在此处输入图片描述

代码：

\begin{tikzpicture}[scale=.5]
  \coordinate (origin) at (-4.5,-1.3);
  \coordinate (observer) at (-3,2.7);
  \coordinate (x) at ($(origin) + (1,0,0)$);
  \coordinate (y) at ($(origin) + (0,1,0)$);
  \coordinate (z) at ($(origin) + (0,0,1)$);
  \coordinate (sphere-center) at (-.5,.7);

  \coordinate (bounded-label) at (.5,4.5);
  \coordinate (unbounded-label) at (1.5,5.4);

  \coordinate (omega-center) at (0,0);
  \coordinate (omega0) at ($(omega-center)+(0:2.5cm)$);
  \coordinate (omega1) at ($(omega-center)+(40:2cm)$);
  \coordinate (omega2) at ($(omega-center)+(80:2.5cm)$);
  \coordinate (omega3) at ($(omega-center)+(120:2.5cm)$);
  \coordinate (omega4) at ($(omega-center)+(160:2.5cm)$);
  \coordinate (omega5) at ($(omega-center)+(200:2.5cm)$);
  \coordinate (omega6) at ($(omega-center)+(240:2cm)$);
  \coordinate (omega7) at ($(omega-center)+(280:2cm)$);
  \coordinate (omega8) at ($(omega-center)+(320:2cm)$);

  \coordinate (omega0-out) at (90:1cm);
  \coordinate (omega0-in) at (270:1cm);
  \coordinate (omega1-out) at (90:1cm);
  \coordinate (omega1-in) at (270:1cm);
  \coordinate (omega2-out) at (90:1cm);
  \coordinate (omega2-in) at (270:1cm);
  \coordinate (omega3-out) at (250:1cm);
  \coordinate (omega3-in) at (70:1cm);
  \coordinate (omega4-out) at (200:1.5cm);
  \coordinate (omega4-in) at (20:1cm);
  \coordinate (omega5-out) at (20:1cm);
  \coordinate (omega5-in) at (200:1cm);
  \coordinate (omega6-out) at (60:1cm);
  \coordinate (omega6-in) at (240:1cm);
  \coordinate (omega7-out) at (70:1cm);
  \coordinate (omega7-in) at (250:1cm);
  \coordinate (omega8-out) at (90:1cm);
  \coordinate (omega8-in) at (270:1cm);

  \coordinate (normal) at (290:.8cm);

  \shade[inner color=blue!50!white,outer color=white] (sphere-center) circle [x radius=6.5cm, y radius=5.5cm];
  \draw[blue, dashed] (sphere-center) circle [x radius=6cm, y radius=5cm];

  % Domain Omega
  \def\myshape{
    (omega0) .. controls +(omega0-out) and +(omega1-in) .. (omega1)
             .. controls +(omega1-out) and +(omega2-in) .. (omega2)
             .. controls +(omega2-out) and +(omega3-in) .. (omega3)
             .. controls +(omega3-out) and +(omega4-in) .. (omega4)
             .. controls +(omega4-out) and +(omega5-in) .. (omega5)
             .. controls +(omega5-out) and +(omega6-in) .. (omega6)
             .. controls +(omega6-out) and +(omega7-in) .. (omega7)
             .. controls +(omega7-out) and +(omega8-in) .. (omega8)
             .. controls +(omega8-out) and +(omega0-in) .. (omega0)
  }

  \shade[inner color=black!50!white,outer color=gray!50!white] \myshape;

  \tikzset{
    vibrate/.style = {red,
                      thick}
  }
  \begin{scope}[transform canvas={scale = 1.06}]
    \draw[vibrate, draw opacity=0.1] \myshape;
  \end{scope}
  \begin{scope}[transform canvas={scale = 1.04}]
    \draw[vibrate, draw opacity=0.3] \myshape;
  \end{scope}
  \begin{scope}[transform canvas={scale = 1.02}]
    \draw[vibrate, draw opacity=0.5] \myshape;
  \end{scope}

  \draw[red, thick] \myshape;

  \begin{scope}[transform canvas={scale = 0.98}]
    \draw[vibrate, draw opacity=0.5] \myshape;
  \end{scope}
  \begin{scope}[transform canvas={scale = 0.96}]
    \draw[vibrate, draw opacity=0.3] \myshape;
  \end{scope}
  \begin{scope}[transform canvas={scale = 0.94}]
    \draw[vibrate, draw opacity=0.1] \myshape;
  \end{scope}

  % Normal vector
  \draw[-latex,label=$\mathbf{n}$] (omega4) -- node[pos=0.4, right] {\scriptsize $\ve{n}$} +(normal);

  % Coordinate system
  \fill (origin) circle (1pt);

  \node[right] at (x) {\scriptsize $x$};
  \node[above] at (y) {\scriptsize $y$};
  \node[below] at (z) {\scriptsize $z$};

  \draw[-latex] (origin) -- (x);
  \draw[-latex] (origin) -- (y);
  \draw[-latex] (origin) -- (z);

  % Observer
  \node[above right] at (observer) {\scriptsize $\vr$};
  \fill (observer) circle (1pt);
  \draw[-latex] (origin) -- (observer);

  % Domain labels
  \node at (omega-center) {$\Omega_+$};
  \node[above right] at (omega1) {$\Gamma_v$};

  \node[above] at (unbounded-label) {$\Omega_U$};
  \node[above] at (bounded-label) {$\Omega_B$};
\end{tikzpicture}

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