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与 gnuplot 的风格相同，与 TikZ 的普通图表的风格相同

tag-icon • tag-icon tikz-pgf gnuplot gnuplottex
与 gnuplot 的风格相同，与 TikZ 的普通图表的风格相同

我正在学习如何gnuplot使用TikZ。

我想绘制一些代数曲线的相邻图形。我从可以不使用 gnuplot 绘制的图形开始（它们不是隐式的）。我想在它们旁边绘制一条具有相同样式的隐式曲线（相同轴、居中和）ultra thick。

以下是我迄今为止所取得的成就。

\documentclass{standalone}

\usepackage{tikz}
\usepackage{gnuplot-lua-tikz}
\usepackage[shell]{gnuplottex}
\thispagestyle{empty}

\begin{document}

\begin{tikzpicture}
\def\sizeGraph{1.3}

  \draw[domain=-0.91:0.91, smooth, variable=\x, red, ultra thick] plot ({\x}, {sqrt(1-\x*\x)});
  \draw[domain=-1:-0.9, smooth, variable=\x, red, ultra thick] plot ({\x}, {sqrt(1-\x*\x)});
  \draw[domain=0.9:1, smooth, variable=\x, red, ultra thick] plot ({\x}, {sqrt(1-\x*\x)});

  \draw[domain=-0.91:0.91, smooth, variable=\x, red, ultra thick] plot ({\x}, {-sqrt(1-\x*\x)});
  \draw[domain=-1:-0.9, smooth, variable=\x, red, ultra thick] plot ({\x}, {-sqrt(1-\x*\x)});
  \draw[domain=0.9:1, smooth, variable=\x, red, ultra thick] plot ({\x}, {-sqrt(1-\x*\x)});

  \draw[->] (-\sizeGraph,0) -- (\sizeGraph,0) node[right] {$x$};
  \draw[->] (0,-\sizeGraph) -- (0,\sizeGraph) node[above] {$y$};
  
  \node [below=1.5cm, align=flush center]
        {
            $V(X^2+Y^2-1)$
        };
\end{tikzpicture}
\qquad
\begin{tikzpicture}
\def\sizeGraph{1.3}

    \draw[samples=1000, domain=-\sizeGraph:\sizeGraph, smooth, variable=\x, blue, ultra thick] plot ({\x}, {\x*\x});
    \draw[->] (-\sizeGraph,0) -- (\sizeGraph,0) node[right] {$x$};
    \draw[->] (0,-1.3) -- (0,1.3) node[above] {$y$};
    
      \node [below=1.5cm, align=flush center]
        {
            $V(Y-X^2)$
        };
\end{tikzpicture}
\qquad
\begin{tikzpicture}
\def\sizeGraph{1.3}

    \draw[samples=1000, domain=-\sizeGraph:\sizeGraph, smooth, variable=\x, orange!60!black, ultra thick] plot ({\x}, {\x});
    \draw[samples=1000, domain=-\sizeGraph:\sizeGraph, smooth, variable=\x, orange!60!black, ultra thick] plot ({\x}, {-\x});
    \draw[->] (-\sizeGraph,0) -- (\sizeGraph,0) node[right] {$x$};
    \draw[->] (0,-1.3) -- (0,1.3) node[above] {$y$};
    
      \node [below=1.5cm, align=flush center]
        {
            $V(Y^2-X^2)$
        };
\end{tikzpicture}
\quad
\begin{tikzpicture}
\def\sizeGraph{1.3}
    
    \draw[->] (-\sizeGraph,0) -- (\sizeGraph,0) node[right] {$x$};
    \draw[->] (0,-1.3) -- (0,1.3) node[above] {$y$};
    
    \begin{gnuplot}[terminal=tikz,terminaloptions={size 8,8}]
      set contour
      set cntrparam levels incremental 0.0001, 0.0001, 0.0001
      set view map
      set view equal
      unset surface
      unset key
      unset tics
      unset border
      set lmargin at screen 0
      set rmargin at screen 1
      set bmargin at screen 0
      set tmargin at screen 1
      set isosamples 1000,1000
      set xrange [-3.5:3.5]
      set yrange [-3.5:3.5]
      set view 0,0
      set cont base
      splot x**3 + y**3 - 6*x*y
    \end{gnuplot}
  \end{tikzpicture}

\end{document}

在此处输入图片描述

你能帮助我吗？

答案1

我提出以下不使用的解决方案gnuplot。我希望你不会无条件地爱上它。

在此处输入图片描述

它仅使用 TikZ 和奇异立方的参数化。

参数化是通过将曲线从原点投影到直线上获得的x+y=1.我们得到 （x，y）= 6t/(1+t^3)（1，t）。

在绘画过程中我们必须做出一些选择，因为吨不同于-1。这就是四个命令的原因\draw。不过它们可能会变成两个。

您的轴对于系数来说太小6在三次方程中。因此，我缩小了曲线以使有趣的部分适合所需的矩形。

\documentclass[11pt, border=.5cm]{standalone}

\usepackage{tikz}
\usetikzlibrary{calc, math}

\begin{document}

\tikzmath{%
  real \sizeGraph;
  \sizeGraph = 1.4;
}
\begin{tikzpicture}  
  \draw[domain=-0.91:0.91, smooth, variable=\x, red, ultra thick]
  plot ({\x}, {sqrt(1-\x*\x)});
  \draw[domain=-1:-0.9, smooth, variable=\x, red, ultra thick]
  plot ({\x}, {sqrt(1-\x*\x)});
  \draw[domain=0.9:1, smooth, variable=\x, red, ultra thick]
  plot ({\x}, {sqrt(1-\x*\x)});

  \draw[domain=-0.91:0.91, smooth, variable=\x, red, ultra thick]
  plot ({\x}, {-sqrt(1-\x*\x)});
  \draw[domain=-1:-0.9, smooth, variable=\x, red, ultra thick]
  plot ({\x}, {-sqrt(1-\x*\x)});
  \draw[domain=0.9:1, smooth, variable=\x, red, ultra thick]
  plot ({\x}, {-sqrt(1-\x*\x)});
  \draw[->] (-\sizeGraph,0) -- (\sizeGraph,0) node[right] {$x$};
  \draw[->] (0,-\sizeGraph) -- (0,\sizeGraph) node[above] {$y$};
  
  \node[below=1.5cm, align=flush center] {$V(X^2+Y^2-1)$};
\end{tikzpicture}
\qquad
\begin{tikzpicture}
  \draw[samples=1000, domain=-\sizeGraph:\sizeGraph, smooth,
  variable=\x, blue, ultra thick] plot ({\x}, {\x*\x});
  \draw[->] (-\sizeGraph,0) -- (\sizeGraph,0) node[right] {$x$};
  \draw[->] (0,-\sizeGraph) -- (0,\sizeGraph) node[above] {$y$};
    
  \node [below=1.5cm, align=flush center]{$V(Y-X^2)$};
\end{tikzpicture}
\qquad
\begin{tikzpicture}
  \draw[samples=1000, domain=-\sizeGraph:\sizeGraph, smooth,
  variable=\x, orange!60!black, ultra thick] plot ({\x}, {\x});
  \draw[samples=1000, domain=-\sizeGraph:\sizeGraph, smooth,
  variable=\x, orange!60!black, ultra thick] plot ({\x}, {-\x});
  \draw[->] (-\sizeGraph,0) -- (\sizeGraph,0) node[right] {$x$};
  \draw[->] (0,-\sizeGraph) -- (0,\sizeGraph) node[above] {$y$};
  
  \node [below=1.5cm, align=flush center] {$V(Y^2-X^2)$};
\end{tikzpicture}
\quad
\tikzmath{%
  integer \N{-}, \N{+}, \j;
  \N{-} = 21;
  \N{+} = 22;
}
\begin{tikzpicture}
  \begin{scope}[red, ultra thick, scale=.4]
    \draw (0, 0)
    \foreach \i [evaluate=\i as \j using \i/20] in {1, ..., \N{+}}{%
      -- (${1/(1+\j^3)*(6*\j)}*(1, \j)$)
    };
    \draw (0, 0)
    \foreach \i [evaluate=\i as \j using -\i/40] in {1, ..., \N{-}}{%
      -- (${6*\j/(1+\j^3)}*(1, \j)$)
    };
    
    \draw (0, 0)
    \foreach \i [evaluate=\i as \j using \i/20] in {1, ..., \N{+}}{%
      -- (${1/(1+\j^3)*(6*\j)}*(\j, 1)$)
    };
    \draw (0, 0)
    \foreach \i [evaluate=\i as \j using -\i/40] in {1, ..., \N{-}}{%
      -- (${6*\j/(1+\j^3)}*(\j, 1)$)
    };  
  \end{scope}
    \draw[->] (-\sizeGraph,0) -- (\sizeGraph,0) node[right] {$x$};
  \draw[->] (0,-\sizeGraph) -- (0,\sizeGraph) node[above] {$y$};

  \node [below=1.5cm, align=flush center] {$V(X^3+Y^3-6XY)$};
\end{tikzpicture}

\end{document}

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