使用 tikz 绘制点来生成阴影

Question

我想用 tikz 画出类似这样的希格斯势场。我不知道如何画出构成势“阴影”的点，有人知道如何帮助我吗？

[编辑：我并不是要求提供绘制电位的整个代码，因为我知道如何做到这一点，但我只想知道如何生成阴影]

[编辑：到目前为止我有这个代码：

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
\usepackage{tikz}
\usepackage{tzplot}


\begin{document}
    \begin{tikzpicture}
        \tzaxes(-2.5,-1.5)(2.5,5){$x$}{$y$}
        \tzfn[thick]{(-1.2*(\x)^2 +0.4*(\x)^4)}[-2.3:2.3]{$V(x)$}[ar]
        \tzfn[black, ->]{(\x)}[2:-2]{$z$}[ar]
        \draw[thick, dashed] (1.25,-0.9) arc (0:360:1.25cm and 0.2cm);
        \draw[thick] (2.15,3) arc (0:360:2.15cm and 0.5cm);
    \end{tikzpicture}
\end{document}

输出结果如下： 。我需要帮助来添加虚线，以便给出阴影的概念]

谢谢！

Answer 1

您可以使用fillbetweenPGFPlots 提供的库：

\documentclass[border=5mm]{standalone}
\usepackage{tzplot, pgfplots}
\pgfplotsset{compat=1.18}
\usepgfplotslibrary{fillbetween}

\begin{document}
    \begin{tikzpicture}
        \tzaxes(-2.5,-1.5)(2.5,5){$x$}{$y$}
        \tzfn[thick, name path=curve]{(-1.2*(\x)^2+0.4*(\x)^4)}[-2.3:2.3]{$V(x)$}[ar]
        \tzfn[black, ->]{(\x)}[2:-2]{$z$}[ar]
        \draw[thick, dashed, name path=bottom] (1.25,-0.9) 
            arc[start angle=0, end angle=360, x radius=1.25cm, y radius=0.2cm];
        \draw[thick, name path=top] (2.15,3) 
            arc[start angle=0, end angle=360, x radius=2.15cm, y radius=0.5cm];

        \path[name path=clipped curve, intersection segments={of=top and curve, sequence={R2}}];
        \fill[gray, opacity=0.2, intersection segments={of=clipped curve and bottom, sequence={L1}}] 
            to[out=100, in=180] (0,2.5) 
            arc[start angle=270, end angle=180, x radius=2.15cm, y radius=0.5cm] -- cycle;
        \fill[gray, opacity=0.2, intersection segments={of=clipped curve and bottom, sequence={L5[reverse]}}]
            to[out=80, in=0] (0,2.5) 
            arc[start angle=270, end angle=360, x radius=2.15cm, y radius=0.5cm];
        \fill[gray, opacity=0.4, intersection segments={of=clipped curve and bottom, sequence={L3 -- R3}}] -- cycle;
    \end{tikzpicture}
\end{document}

---

正如评论中所建议的，使用图案的变化来模仿点状阴影：

\documentclass[border=5mm]{standalone}
\usepackage{tzplot, pgfplots}
\pgfplotsset{compat=1.18}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{patterns.meta}

\begin{document}
    \begin{tikzpicture}
        \tzaxes(-2.5,-1.5)(2.5,5){$x$}{$y$}
        \tzfn[thick, name path=curve]{(-1.2*(\x)^2+0.4*(\x)^4)}[-2.3:2.3]{$V(x)$}[ar]
        \tzfn[black, ->]{(\x)}[2:-2]{$z$}[ar]
        \draw[thick, dashed, name path=bottom] (1.25,-0.9) 
            arc[start angle=0, end angle=360, x radius=1.25cm, y radius=0.2cm];
        \draw[thick, name path=top] (2.15,3) 
            arc[start angle=0, end angle=360, x radius=2.15cm, y radius=0.5cm];

        \path[name path=clipped curve, intersection segments={of=top and curve, sequence={R2}}];
        \fill[
            pattern={
                Dots[radius=0.4pt, angle=45, distance={2pt/sqrt(2)}]
            }, 
            intersection segments={
                of={clipped curve and bottom}, 
                sequence={L1}
            }
        ] to[out=100, in=180] (0,2.5) 
            arc[start angle=270, end angle=180, x radius=2.15cm, y radius=0.5cm] -- cycle;
        \fill[
            pattern={
                Dots[radius=0.4pt, angle=45, distance={2pt/sqrt(2)}]
            }, 
            intersection segments={
                of={clipped curve and bottom}, 
                sequence={L5[reverse]}
            }
        ] to[out=80, in=0] (0,2.5) 
            arc[start angle=270, end angle=360, x radius=2.15cm, y radius=0.5cm];
        \fill[
            pattern={
                Dots[radius=0.7pt, angle=45, distance={2pt/sqrt(2)}]
            }, 
            intersection segments={
                of={clipped curve and bottom}, 
                sequence={L3 -- R3}
            }
        ] -- cycle;
    \end{tikzpicture}
\end{document}