绘制恒定随机扭曲的圆圈

Question

我正在尝试绘制一个特殊且矛盾的情节：一个带有随机扭曲的圆圈，无论我构建文档多少次，它都必须保持不变。

下面是我想要实现的一个示例

该图由以下代码生成

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


\begin{document}
    \begin{tikzpicture}
        % axes
        \draw[ultra thin] (-2.5, 0) -- (2.5, 0);
        \draw[ultra thin] (0, -2.5) -- (0, 2.5);
        % undistorted sphere
        \draw[ultra thin, dashed] (0, 0) circle (2.25cm);
        \draw[ultra thin, dashed, ->] (0:0) -- (125:2.25);
        \node at (-1, 1) {$R$};
        % distrorted sphere
        \draw[very thick] plot[domain=0:350,smooth cycle ] (\x:2+rnd*0.5);
        \draw[very thick, ->] (0:0) -- (45:2.1);
        \draw[ultra thin, ->] (1, 0) arc (0:45:1);
        \node at (1.2, 0.4) {$\theta$};
        \node at (0.7, 1.25) {$R(\theta)$};
    \end{tikzpicture}
\end{document}

代码的问题在于，每当我对其进行更改并重建文档时，“扭曲”的圆圈都会具有不同的形状，因为我正在使用该rnd函数。我想要一个恒定随机形状的原因是因为我想以角度 θ 表示其半径，因此它必须接触圆的轮廓。

有什么想法可以实现这样的事情吗？

Answer 1

用户回答JPG，矢量R不与随机曲线相交。为了实现两条路径的相交，我们必须使用库intersections。添加到 JPG 的答案：

\documentclass{standalone}
\usepackage{tikz}   
\usetikzlibrary{decorations.pathmorphing,intersections}

    \begin{document}
       \begin{tikzpicture}[>=latex]
            \pgfmathsetseed{1} % choose a number which give a good shape to your circle
            % axes
            \draw[ultra thin] (-2.5, 0) -- (2.5, 0);
            \draw[ultra thin] (0, -2.5) -- (0, 2.5);
            % undistorted sphere
            \draw[ultra thin, dashed] (0, 0) circle (2.25cm);
            \draw[ultra thin, dashed, ->] (0:0) -- (125:2.25);
            \node at (-1, 1) {$R$};
            % distrorted sphere
            \path[draw,very thick, name path=curve] plot[domain=0:350,smooth cycle ] (\x:2+rnd*0.5);
            \path[very thick, name path=line] (0:0) -- (45:2.5);
            \draw [name intersections={of=curve and  line, by=x}];
            \draw [very thick, ->] (0,0)--(x);
            \draw[ultra thin, ->] (1, 0) arc (0:45:1);
            \node at (1.2, 0.4) {$\theta$};
            \node at (0.7, 1.25) {$R(\theta)$};
        \end{tikzpicture}
    \end{document}

Answer 2

用于\pgfmathsetseed初始化随机数生成的种子：

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


\begin{document}
   \begin{tikzpicture}
        \pgfmathsetseed{1} % choose a number which give a good shape to your circle
        % axes
        \draw[ultra thin] (-2.5, 0) -- (2.5, 0);
        \draw[ultra thin] (0, -2.5) -- (0, 2.5);
        % undistorted sphere
        \draw[ultra thin, dashed] (0, 0) circle (2.25cm);
        \draw[ultra thin, dashed, ->] (0:0) -- (125:2.25);
        \node at (-1, 1) {$R$};
        % distrorted sphere
        \draw[very thick] plot[domain=0:350,smooth cycle ] (\x:2+rnd*0.5);
        \draw[very thick, ->] (0:0) -- (45:2.1);
        \draw[ultra thin, ->] (1, 0) arc (0:45:1);
        \node at (1.2, 0.4) {$\theta$};
        \node at (0.7, 1.25) {$R(\theta)$};
    \end{tikzpicture}
\end{document}

编辑：如果你想自动计算箭头的长度

然后，您可以在绘图之前生成箭头的长度，并使用此长度来获得所需的精确角度。由于您不知道绘图将以哪些角度计算，因此您应该从要绘制箭头的角度开始绘图：

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


\begin{document}
    \begin{tikzpicture}
        \pgfmathsetseed{1}
        % axes
        \draw[ultra thin] (-2.5, 0) -- (2.5, 0);
        \draw[ultra thin] (0, -2.5) -- (0, 2.5);
        % undistorted sphere
        \draw[ultra thin, dashed] (0, 0) circle (2.25cm);
        \draw[ultra thin, dashed, ->] (0:0) -- (125:2.25);
        \node at (-1, 1) {$R$};
        % distrorted sphere
        \pgfmathsetmacro\RR{2+rnd*0.5}
        \draw[very thick] plot[domain=45:395,smooth cycle ] (\x:{ifthenelse(\x==45,\RR,2+rnd*0.5)});
        \draw[very thick, ->] (0:0) -- (45:\RR);
        \draw[ultra thin, ->] (1, 0) arc (0:45:1);
        \node at (1.2, 0.4) {$\theta$};
        \node at (0.7, 1.25) {$R(\theta)$};
    \end{tikzpicture}
\end{document}