简单的 Tikz 双曲线

Question

我想重新创建图片中的双曲线。到目前为止，我已经有了开始，按照在TikZ中绘制一定偏心率的双曲线和如何绘制椭圆？， 尤其cmhughes'，上一个问题的评论中的建议，但顶部椭圆缺少其上半部分。

我该如何修复此问题？我可以使用 来修复吗\addplot3？

\begin{tikzpicture}
\def\xm{5}
\def\ym{6.5}
\def\dom{2}

%\def\ecc{1.44022}
\def\ecc{2.3}
\def\a{1}
\def\b{(\a*sqrt((\ecc)^2-1)} 


\begin{axis}[scale=.8,
    hide axis,
    xmin=-\xm,xmax=\xm,
    ymin=-\ym,ymax=\ym]
    \addplot [domain=-\dom:\dom] ({\a*cosh(\x)},{\b*sinh(\x)});
    \addplot [domain=-\dom:\dom] ({-\a*cosh(\x)},{\b*sinh(\x)});

    \draw (0,0) ellipse (.55cm and .25cm);
    \draw (0,6) ellipse (1.3cm and .3cm);
%    \draw (0,-4) ellipse (1.8cm and .3cm);
\end{axis}
\end{tikzpicture}

Answer 1

这是一个\addplot3你可以尝试的例子

\documentclass[border=9,tikz]{standalone}
\usepackage{pgfplots}
\begin{document}
    \begin{tikzpicture}
        \begin{axis}[hide axis,axis equal]
            \addplot3[surf,domain=0:360,y domain=-2:2]
                ({cosh(y)*cos(x)},{cosh(y)*sin(x)},{sinh(y)});
        \end{axis}
    \end{tikzpicture}
\end{document}

Answer 2

我尝试了建议的优秀方法，但我对我的 3D 结果并不满意（到目前为止）。所以我想添加我想到的内容。

\documentclass[12pt,a4paper]{article}

\usepackage[fleqn]{amsmath}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}

\definecolor{whitesmokedark}{RGB}{235,235,235}
\definecolor{gainsboro}{RGB}{220,220,220}

\begin{document}

\begin{tikzpicture}
\def\xm{5}
\def\ym{10}
\def\df{3}
\def\dom{2}

%\def\ecc{1.44022}
\def\ecc{2.3}
\def\a{1}
\def\b{(\a*sqrt((\ecc)^2-1)} 

\begin{axis}[scale=.8,
    hide axis,
    xmin=-\xm,xmax=\xm,
    ymin=-\ym,ymax=\ym]

    \fill[gainsboro] (0,0) ellipse (.55cm and .2cm);
    \fill[whitesmokedark] (0,7.5) ellipse (2.1cm and .3cm);
    \fill[gainsboro] (0,-7.4) ellipse (2.05cm and .3cm);

    \addplot [domain=-\dom:\dom] ({\a*cosh(\x)},{\b*sinh(\x)});
    \addplot [domain=-\dom:\dom] ({-\a*cosh(\x)},{\b*sinh(\x)});

\end{axis}

\def\xax{2.7}
\draw[dotted] (\xax,\xax - 0.4) -- (\xax,\xax + 1);
\draw[solid, ->] (\xax,\xax + 1) -- (\xax,\xax + 1.7);
\draw[solid, ->] (\xax,\xax - 0.4) -- (1.5,2);
\draw[solid, ->] (\xax,\xax - 0.4) -- (4.5,2);

\node (x) at ( \xax -0.1,\xax + 1.3) [label=right:$x$] {};
\node (y) at (1.6,1.9) [label=above:$y$] {};
\node (z) at (4.5,1.9) [label=above:$z$] {};

\end{tikzpicture}

\end{document}

如下图所示。（欢迎批评指正。）

编辑3D解决方案：

\documentclass[12pt,a4paper]{article}

\usepackage[fleqn]{amsmath}
\usepackage[usenames, dvipsnames]{color}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.13}

\definecolor{mediumgreen}{RGB}{0,153,0}

\begin{document}
\begin{tikzpicture}[scale=1.5]
    \begin{axis}[
    shader=interp,
    opacity=0.7,
    fill opacity=0.7,
    axis lines = none,
    ticks=none,
    axis equal
    ]

    \draw[thick,->,black] (0,0,0) -- (4,0,0) node[anchor=north east]{$z$};
    \draw[thick,->] (0,0,0) -- (-1,-6,1) node[anchor=north east]{$y$};
    \draw[thick,->] (0,0,0) -- (0,0,4.3) node[anchor=east]{$x$};

    \addplot3[%
        shader=interp,
        opacity = 0.6,
        fill opacity=0.6,
        surf,
        colormap = {whiteblack}{color(0cm)  = (mediumgreen);color(1cm) =      (black)},
        variable = \u,
        variable y = \v,
        domain = 0:180,
        y domain = 0:360,
    ]
    ({cos(u)*sin(v)}, {sin(u)*sin(v)}, {.1*cos(v)});

    \addplot3[surf,domain=0:360,y domain=-1.5:1.5]
         ({cosh(y)*cos(x)},{cosh(y)*sin(x)},{sinh(y)});

    \end{axis}

\end{tikzpicture}

\end{document}