用颜色填充区域

Question

我想用蓝色填充这个区域，有人可以帮帮我吗？（我是初学者）

多谢

\usepackage{tikz}
\usetikzlibrary{decorations,arrows, intersections, through}
\usetikzlibrary{decorations.markings}
\usetikzlibrary{calc}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\usetikzlibrary{quotes,angles}
\begin{tikzpicture}
\begin{axis} [xtick distance=1,legend pos=outer north east,xmin=-3,xmax=3,ymin=-8,ymax=8] 
  \addplot +[no markers,
  raw gnuplot,
  very thick,
  empty line = jump % not strictly necessary, as this is the default behaviour in the development version of PGFPlots
  , dotted, name path = A] gnuplot {
  set contour base;
  set cntrparam levels discrete 0.003;
  unset surface;
  set view map;
  set isosamples 500;
  set samples 500;
  splot x + 0.25*y^2 - 1;
};
\addlegendentry{$\mathfrak{Re}(z^2)= 1 - \frac{1}{4} (\mathfrak{Im}(z^2))^2$}
\addplot +[no markers,
  raw gnuplot,
  very thick,
  empty line = jump % not strictly necessary, as this is the default behaviour in the development version of PGFPlots
  , dotted] gnuplot {
  set contour base;
  set cntrparam levels discrete 0.003;
  unset surface;
  set view map;
  set isosamples 500;
  set samples 500;
  splot x - 1;
};
\addlegendentry{$\mathfrak{Re}(z)= 1$}
\end{axis}
\end{tikzpicture}

Answer 1

如果要使用路径绘制区域，则需要确保它是连续的。因此，您需要确保用于绘制此路径的函数也是以连续方式计算的。在我们填充它时可以看到，您当前的设置并非如此：

\documentclass[border=10pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}
\begin{tikzpicture}
\begin{axis} [
    xtick distance = 1, 
    legend pos = outer north east,
    xmin = -3, xmax = 3, ymin = -8, ymax = 8
  ] 
  \addplot +[no markers,
    raw gnuplot,
    very thick, 
    dotted, 
    fill = cyan!50
  ] gnuplot {
    set contour base;
    set cntrparam levels discrete 0.003;
    unset surface;
    set view map;
    set isosamples 500;
    set samples 500;
    splot x + 0.25*y^2 - 1;
  };
\end{axis}
\end{tikzpicture}
\end{document}

显然，该函数是逐步绘制的，并且具有正和负的部分是值可能以交替方式绘制，无论如何，绘制时都会产生不错的效果，但遗憾的是，我们无法使用任何设置来创建可填充区域。您需要尝试各种设置才能得出gnuplot一些有用的结果。

但是，我建议您不要使用gnuplots 来绘制函数，因为它们都相对简单。此外，您可能应该将函数拆分为曲线，以便获得上分支和下分支：

\documentclass[border=10pt]{standalone}
\usepackage{amssymb}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{backgrounds}

\begin{document}
\begin{tikzpicture}
\begin{axis} [
    xtick distance = 1, 
    legend pos = outer north east,
    xmin = -3, xmax = 3, ymin = -8, ymax = 8
  ] 
  \addplot+[
    no markers,
    very thick,
    dotted, 
    smooth,
    samples = 101,
    name path = A upper
  ] { sqrt( 4 - 4*x ) };
  \addlegendentry{$\mathfrak{Re}(z^2) = 1 - \frac{1}{4} (\mathfrak{Im}(z^2))^2$}
  \addplot+[
    no markers,
    very thick,
    dotted, 
    blue,
    forget plot,
    smooth,
    samples = 101,
    name path = A lower
  ] { -1 * sqrt( 4 - 4*x ) };
  \addplot+[
    no markers,
    very thick,
    dotted
  ] coordinates {
    (1,\pgfkeysvalueof{/pgfplots/ymin}) (1,\pgfkeysvalueof{/pgfplots/ymax})
  };
  \addlegendentry{$\mathfrak{Re}(z) = 1$}

  \begin{scope}[on background layer]
    \path[name path = plot box upper]  
      (\pgfkeysvalueof{/pgfplots/xmin},0) rectangle
      (\pgfkeysvalueof{/pgfplots/xmax},\pgfkeysvalueof{/pgfplots/ymax});
    \path[name path = plot box lower]  
      (\pgfkeysvalueof{/pgfplots/xmin},0) rectangle
      (\pgfkeysvalueof{/pgfplots/xmax},\pgfkeysvalueof{/pgfplots/ymin});
    
    \fill[cyan!50, intersection segments = {
      of = {A upper and plot box upper},
      sequence = {L*[reverse] -- R2}
    }] -- cycle; 
    \fill[cyan!50, intersection segments = {
      of = {A lower and plot box lower},
      sequence = {L*[reverse] -- R2}
    }] -- cycle; 
  \end{scope}
\end{axis}
\end{tikzpicture}
\end{document}