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如何阻止随机生成的不同圆圈之间的重叠

tag-icon • tag-icon tikz-pgf
如何阻止随机生成的不同圆圈之间的重叠

这个问题和这个问题类似tikz：均匀随机分布圆圈（这也是我获得这张 TiKz 图片的部分代码的地方）但有所不同。我希望绘制多个不重叠的圆圈，但其中一些圆圈不同。目前这是我的代码：

\documentclass{article}
\usepackage{tikz}
\usepackage[margin=0.5in]{geometry}
\newcommand{\fillrandomly}[5]{
    \xdef\xlist{4}
    \xdef\ylist{4}
    \pgfmathsetmacro\diametersqr{(#3*2)^2}
    \foreach \i in {1,...,#4}{
        \foreach \k in {1,...,20}{
            \pgfmathsetmacro\x{rnd*#1}
            \pgfmathsetmacro\y{rnd*#2}
            \xdef\collision{0}
            \foreach \element [count=\i] in \xlist{
                \pgfmathtruncatemacro\j{\i-1}
                \pgfmathsetmacro\checkdistancesqr{ ( ({\xlist}[\j]-(\x))^2 + ({\ylist}[\j]-(\y))^2 ) }
                \ifdim\checkdistancesqr pt<\diametersqr pt
                    \xdef\collision{1}
                    \breakforeach
                \fi
            }
            \ifnum\collision=0
                \xdef\xlist{\xlist,\x}
                \xdef\ylist{\ylist,\y}
                \draw (\x,\y) circle [radius=#3] node[anchor=center] {#5};
                \breakforeach
            \fi 
        }
    }
}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{scope}[xshift=0.2cm,yshift=0.2cm]
\fillrandomly{3.6}{3.8}{0.15}{12}{$-$}
\fillrandomly{3.6}{3.8}{0.15}{12}{$+$}
\end{scope}
        \draw (0,5) -- (0,1);
\draw (0,1) .. controls (0,0) and (0,0) .. (1,0);
\draw (1,0) -- (3,0);
\draw (3,0) .. controls (4,0) and (4,0) .. (4,1);
\draw (4,1) -- (4,5);
\draw[densely dashed] (0,5) .. controls (0,4.5) and (0,4.5) .. (0.5,4.5);
\draw[densely dashed] (0.5,4.5) -- (3.5,4.5);
\draw[densely dashed] (3.5,4.5) .. controls (4,4.5) and (4,4.5) .. (4,5);
\node[anchor=center] at (2,-0.5) {concentrated strong acid};

    \begin{scope}[xshift=5cm]
                \foreach \X in {1,...,3}
            {\draw (2+1.8*rand,2+1.9*rand) circle (0.15) node[anchor=center] {$+$};
            \draw (2+1.8*rand,2+1.9*rand) circle (0.15) node[anchor=center] {$-$};}
        \draw (0,5) -- (0,1);
\draw (0,1) .. controls (0,0) and (0,0) .. (1,0);
\draw (1,0) -- (3,0);
\draw (3,0) .. controls (4,0) and (4,0) .. (4,1);
\draw (4,1) -- (4,5);
\draw[densely dashed] (0,5) .. controls (0,4.5) and (0,4.5) .. (0.5,4.5);
\draw[densely dashed] (0.5,4.5) -- (3.5,4.5);
\draw[densely dashed] (3.5,4.5) .. controls (4,4.5) and (4,4.5) .. (4,5);
\node[anchor=center] at (2,-0.5) {dilute strong acid};
\end{scope}
    \begin{scope}[xshift=10cm]
\begin{scope}[xshift=0.2cm,yshift=0.2cm]
\fillrandomly{3.6}{3.8}{0.15}{8}{$-$}
\fillrandomly{3.6}{3.8}{0.15}{8}{$+$}
\end{scope}
\foreach \X in {1,...,8}
{
            \draw[fill=black!10]  (2+1.8*rand,2+1.9*rand) circle (0.15);
            }
        \draw (0,5) -- (0,1);
\draw (0,1) .. controls (0,0) and (0,0) .. (1,0);
\draw (1,0) -- (3,0);
\draw (3,0) .. controls (4,0) and (4,0) .. (4,1);
\draw (4,1) -- (4,5);
\draw[densely dashed] (0,5) .. controls (0,4.5) and (0,4.5) .. (0.5,4.5);
\draw[densely dashed] (0.5,4.5) -- (3.5,4.5);
\draw[densely dashed] (3.5,4.5) .. controls (4,4.5) and (4,4.5) .. (4,5);
\node[anchor=center] at (2,-0.5) {concentrated weak acid};
\end{scope}
        \begin{scope}[xshift=15cm]
                \foreach \X in {1,...,2}
            {\draw (2+1.8*rand,2+1.9*rand) circle (0.15) node[anchor=center] {$+$};
            \draw (2+1.8*rand,2+1.9*rand) circle (0.15) node[anchor=center] {$-$};}
            \draw[fill=black!10]  (2+1.8*rand,2+1.9*rand) circle (0.15);
        \draw (0,5) -- (0,1);
\draw (0,1) .. controls (0,0) and (0,0) .. (1,0);
\draw (1,0) -- (3,0);
\draw (3,0) .. controls (4,0) and (4,0) .. (4,1);
\draw (4,1) -- (4,5);
\draw[densely dashed] (0,5) .. controls (0,4.5) and (0,4.5) .. (0.5,4.5);
\draw[densely dashed] (0.5,4.5) -- (3.5,4.5);
\draw[densely dashed] (3.5,4.5) .. controls (4,4.5) and (4,4.5) .. (4,5);
\node[anchor=center] at (2,-0.5) {dilute weak acid};
\end{scope}
\draw[fill=black!10] (0,-1) circle (0.15) node[right=0.1cm] {Unionised};
\draw (0,-1.5) circle (0.15) node[anchor=center] {$+$} node[right=0.1cm] {Positive Ion};
\draw (0,-2) circle (0.15) node[anchor=center] {$-$} node[right=0.1cm] {Negative Ion}; 
\end{tikzpicture}
\vspace{-2cm}
\caption{Concentrated and dilute solutions of weak and strong acids}
\end{figure}
\end{document}

生成如下图像： enter image description here 我不确定如何停止三种不同类型的圆圈之间的重叠，尤其是从左边数的第一个和第三个烧杯。请 XeLaTeX 回答

答案1

发生这种情况的原因很明显：你抽取两个或更多个独立样本，因此如果你说

\fillrandomly{3.6}{3.8}{0.15}{12}{$-$} 
\fillrandomly{3.6}{3.8}{0.15}{12}{$+$}

+ 离子不知道 - 离子。但修复它非常简单。只需将碰撞列表的重置设为不属于 的一部分\fillrandomly，但每当您开始新组时都执行此操作。也就是说，我重新定义了它，使其不会重置碰撞列表，并添加了发出重置的\fillrandomly命令。我还定义了一种在过程中会发生变化的样式，以便可以添加已填充的离子。\resetlistsion

\documentclass{article}
\usepackage{tikz}
\usepackage[margin=0.5in]{geometry}
\newcommand{\resetlists}{\xdef\xlist{4}\xdef\ylist{4}}
\newcommand{\fillrandomly}[5]{
    \pgfmathsetmacro\diametersqr{(#3*2)^2}
    \foreach \i in {1,...,#4}{
        \foreach \k in {1,...,20}{
            \pgfmathsetmacro\x{rnd*#1}
            \pgfmathsetmacro\y{rnd*#2}
            \xdef\collision{0}
            \foreach \element [count=\i] in \xlist{
                \pgfmathtruncatemacro\j{\i-1}
                \pgfmathsetmacro\checkdistancesqr{ ( ({\xlist}[\j]-(\x))^2 + ({\ylist}[\j]-(\y))^2 ) }
                \ifdim\checkdistancesqr pt<\diametersqr pt
                    \xdef\collision{1}
                    \breakforeach
                \fi
            }
            \ifnum\collision=0
                \xdef\xlist{\xlist,\x}
                \xdef\ylist{\ylist,\y}
                \draw[ion] (\x,\y) circle [radius=#3] node[anchor=center] {#5};
                \breakforeach
            \fi 
        }
    }
}
\begin{document}
\begin{figure}
\begin{tikzpicture}
\begin{scope}[xshift=0.2cm,yshift=0.2cm]
\resetlists
\tikzset{ion/.style={}}
\fillrandomly{3.6}{3.8}{0.15}{12}{$-$}
\fillrandomly{3.6}{3.8}{0.15}{12}{$+$}
\end{scope}
        \draw (0,5) -- (0,1);
\draw (0,1) .. controls (0,0) and (0,0) .. (1,0);
\draw (1,0) -- (3,0);
\draw (3,0) .. controls (4,0) and (4,0) .. (4,1);
\draw (4,1) -- (4,5);
\draw[densely dashed] (0,5) .. controls (0,4.5) and (0,4.5) .. (0.5,4.5);
\draw[densely dashed] (0.5,4.5) -- (3.5,4.5);
\draw[densely dashed] (3.5,4.5) .. controls (4,4.5) and (4,4.5) .. (4,5);
\node[anchor=center] at (2,-0.5) {concentrated strong acid};

% 2
\begin{scope}[xshift=5cm]
            \foreach \X in {1,...,3}
        {\draw (2+1.8*rand,2+1.9*rand) circle (0.15) node[anchor=center] {$+$};
        \draw (2+1.8*rand,2+1.9*rand) circle (0.15) node[anchor=center] {$-$};}
    \draw (0,5) -- (0,1);
\draw (0,1) .. controls (0,0) and (0,0) .. (1,0);
\draw (1,0) -- (3,0);
\draw (3,0) .. controls (4,0) and (4,0) .. (4,1);
\draw (4,1) -- (4,5);
\draw[densely dashed] (0,5) .. controls (0,4.5) and (0,4.5) .. (0.5,4.5);
\draw[densely dashed] (0.5,4.5) -- (3.5,4.5);
\draw[densely dashed] (3.5,4.5) .. controls (4,4.5) and (4,4.5) .. (4,5);
\node[anchor=center] at (2,-0.5) {dilute strong acid};
\end{scope}

% 3
\begin{scope}[xshift=10cm]
\begin{scope}[xshift=0.2cm,yshift=0.2cm]
\resetlists
\tikzset{ion/.style={}}
\fillrandomly{3.6}{3.8}{0.15}{8}{$-$}
\fillrandomly{3.6}{3.8}{0.15}{8}{$+$}
\tikzset{ion/.style={fill=black!10}}
\fillrandomly{3.6}{3.8}{0.15}{8}{}
\end{scope}
\draw (0,5) -- (0,1);
\draw (0,1) .. controls (0,0) and (0,0) .. (1,0);
\draw (1,0) -- (3,0);
\draw (3,0) .. controls (4,0) and (4,0) .. (4,1);
\draw (4,1) -- (4,5);
\draw[densely dashed] (0,5) .. controls (0,4.5) and (0,4.5) .. (0.5,4.5);
\draw[densely dashed] (0.5,4.5) -- (3.5,4.5);
\draw[densely dashed] (3.5,4.5) .. controls (4,4.5) and (4,4.5) .. (4,5);
\node[anchor=center] at (2,-0.5) {concentrated weak acid};
\end{scope}

%4
\begin{scope}[xshift=15cm]
\begin{scope}[xshift=0.2cm,yshift=0.2cm]
\resetlists
\tikzset{ion/.style={}}
\fillrandomly{3.6}{3.8}{0.15}{2}{$-$}
\fillrandomly{3.6}{3.8}{0.15}{2}{$+$}
\tikzset{ion/.style={fill=black!10}}
\fillrandomly{3.6}{3.8}{0.15}{1}{}
\end{scope}
\draw (0,5) -- (0,1);
\draw (0,1) .. controls (0,0) and (0,0) .. (1,0);
\draw (1,0) -- (3,0);
\draw (3,0) .. controls (4,0) and (4,0) .. (4,1);
\draw (4,1) -- (4,5);
\draw[densely dashed] (0,5) .. controls (0,4.5) and (0,4.5) .. (0.5,4.5);
\draw[densely dashed] (0.5,4.5) -- (3.5,4.5);
\draw[densely dashed] (3.5,4.5) .. controls (4,4.5) and (4,4.5) .. (4,5);
\node[anchor=center] at (2,-0.5) {dilute weak acid};
\end{scope}
\draw[fill=black!10] (0,-1) circle (0.15) node[right=0.1cm] {Unionised};
\draw (0,-1.5) circle (0.15) node[anchor=center] {$+$} node[right=0.1cm] {Positive Ion};
\draw (0,-2) circle (0.15) node[anchor=center] {$-$} node[right=0.1cm] {Negative Ion}; 
\end{tikzpicture}
\vspace{-2cm}
\caption{Concentrated and dilute solutions of weak and strong acids}
\end{figure}
\end{document}

enter image description here

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