pgfplots：找到两条曲线的交点并确定交点的 y 值

2024-5-26 • tag-icon

感谢您阅读我的问题！

介绍

现在我想画一幅图，其中我需要计算路口两条曲线的交点，并确定交点的 y 值是否为零。如果不为零，我需要画一条通过该点垂直于 x 轴的直线。
我将使用循环（foreach ) 来完成操作，但现在我在获取循环总数时遇到了问题。总数循环应该是总数，intersections但现在看来，总数intersections没有正确复制到宏中\t。

这是我的代码： 我的环境是 VSCode + TexLive + LaTeX Workshop

\documentclass[tikz]{standalone}
\usepackage{pgfplots,pgf,tikz}
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\pgfplotsset{compat=1.18}
\usetikzlibrary{intersections}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
    \def\sigmarayleigh{1}
    \def\gaussmean{4}
    \def\gaussvar{1.5}
    \def\xmin{0}
    \def\xmax{8}
    \def\ymin{0}
    \def\ymax{0.7}
    \begin{axis}[title = Fig1,xlabel = $Voltage$,ylabel = $Probability Density$,xmin = \xmin, xmax = \xmax, ymin = \ymin, ymax = \ymax, grid = both, legend pos = north east]
        \coordinate (O) at (\xmin,\ymin);
        \coordinate (X) at (\xmax,\ymin);
        \coordinate (Y) at (\xmin,\ymax);
        \addplot[name path = rayleigh, domain = 0:8, samples = 100, color = black, dashed, line width = 1pt]{x*exp(-x^2/(2*\sigmarayleigh^2))/(\sigmarayleigh^2)};
        \addplot[name path = gauss, domain = 0:8, samples = 100, color = black, line width = 1pt]{1/(sqrt(2*pi*\gaussvar))*exp(-(x-\gaussmean)^2/(2*\gaussvar))};
        \path [name intersections={of=rayleigh and gauss, name = ii, total=\t}];
        \foreach \s in {1,...,\t}{
            \typeout{Total intersections: \s};
        };
    \end{axis}
\end{tikzpicture}
\end{document}

我将测试我的循环是否有效，但此代码无法成功编译。
以下是编译日志：

然后我对我的代码做了简单的修改，把替换成\t固定的数字9，然后这段代码就能成功运行了，修改后的代码如下：

\documentclass[tikz]{standalone}
\usepackage{pgfplots,pgf,tikz}
\usepackage{amsmath,amssymb,amsfonts,amsthm}
\pgfplotsset{compat=1.18}
\usetikzlibrary{intersections}
\usetikzlibrary{calc}
\begin{document}
\begin{tikzpicture}
    \def\sigmarayleigh{1}
    \def\gaussmean{4}
    \def\gaussvar{1.5}
    \def\xmin{0}
    \def\xmax{8}
    \def\ymin{0}
    \def\ymax{0.7}
    \begin{axis}[title = Fig1,xlabel = $Voltage$,ylabel = $Probability Density$,xmin = \xmin, xmax = \xmax, ymin = \ymin, ymax = \ymax, grid = both, legend pos = north east]
        \coordinate (O) at (\xmin,\ymin);
        \coordinate (X) at (\xmax,\ymin);
        \coordinate (Y) at (\xmin,\ymax);
        \addplot[name path = rayleigh, domain = 0:8, samples = 100, color = black, dashed, line width = 1pt]{x*exp(-x^2/(2*\sigmarayleigh^2))/(\sigmarayleigh^2)};
        \addplot[name path = gauss, domain = 0:8, samples = 100, color = black, line width = 1pt]{1/(sqrt(2*pi*\gaussvar))*exp(-(x-\gaussmean)^2/(2*\gaussvar))};
        \path [name intersections={of=rayleigh and gauss, name = ii, total=\t}];
        \foreach \s in {1,...,9}{
            \typeout{Total intersections: \s};
        };
    \end{axis}
\end{tikzpicture}
\end{document}

以下是编译日志：看起来\t在我的代码中没有赋值。
我的使用有问题吗intersections？

感谢您阅读我的问题！

介绍

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