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磁盘上的双曲路径

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磁盘上的双曲路径

我想使用 Tikz 重现以下图片： 在此处输入图片描述

除了两条双曲线路径，我什么都能做。任何帮助我都感激不尽。

我有部分图片，这是我的代码：

\begin{figure}[h]
\centering
\begin{tikzpicture}
    \draw (0,0) circle (2.5);
    \draw (0,0) -- ({2.5*cos(45)},{2.5*sin(45)});
    \draw (0,0) -- (2.5,0);
    \draw ({2.5*cos(45)},-{2.5*sin(45)}) -- (-{2.5*cos(45)},{2.5*sin(45)});
    \draw (0.5,0) arc (0:45:0.5);
    \node[below left] at (0,0) {$O$};
    \node[above left] at (-{2.5*cos(45)},{2.5*sin(45)}) {$D$};
    \node[above right] at ({2.5*cos(45)},{2.5*sin(45)}) {$B$};
    \node[below right] at ({2.5*cos(45)},-{2.5*sin(45)}) {$C$};
    \node[right] at (2.5,0) {$\theta=0$};
    \node[below left] at ({1.25*cos(45)},-{1.25*sin(45)}) {$r^0=\frac{\omega}{c}$};
    \node[right] at ({0.5*cos(22.5)},{0.5*sin(45)}) {$\theta_B$};
\end{tikzpicture}
\end{figure}

答案1

嗯，变成了完全重写代码。无论如何，你仍然可以找出缺失部分所需的几位。我看到了 Przemysław Scherwentke 的评论，所以那些缺失的线被画成了圆段。

对绘图进行了一些参数化，并添加了一些注释。

在此处输入图片描述

\documentclass[tikz, border=3mm]{standalone}
\usetikzlibrary{calc,intersections,quotes,angles}
\begin{document}
\begin{tikzpicture}
% set up a few macros
\newcommand\circlerad{2.5cm}
\pgfmathsetmacro\Bangle{45}
\pgfmathsetmacro\Dangle{\Bangle-90}
\pgfmathsetmacro\Cangle{\Bangle+90}

% draw circle
\node [circle,draw,minimum size=2*\circlerad,name path=circ] (A) {};

% draw line to B and add named coordinate with label
\draw (A.center) coordinate[label=below left:$O$] (O)
   -- (A.\Bangle) coordinate[label=above right:$B$] (b);

% ditto for horizontal line from origin
\draw [name path=h1] (O) -- (A.0) coordinate[label=right:{$\theta=0$}] (e);

% draw line from D to C, add labels and r^0 node
\draw (A.\Dangle) coordinate[label=below right:$D$] (d) 
       -- (A.\Cangle) coordinate[label=above left:$C$] (c)
          node[below left,pos=0.25] {$r^0=\frac{\omega}{c}$};

% draw angle arc
\pic ["$\theta_B$",angle eccentricity=1.7,draw] {angle=e--O--b};

% draw hyperbolic arcs
\draw [name path=hypish] (d) arc[start angle=\Dangle-90,delta angle=-90,radius=\circlerad];
\draw (c) arc[start angle=\Cangle+90,delta angle=90,radius=\circlerad];

%find intersection of hyperbole and horizontal line, name coordinate i-1, and draw invisible
% verticle line from this point upwards
\path [name intersections={of=hypish and h1,name=i},overlay,name path=dashing] (i-1) -- ++(0,2*\circlerad);

% find intersection of invisible path and circle, draw line from to A
\draw [densely dashed,name intersections={of=dashing and circ,name=j}] (i-1) -- (j-1);

% label A
\node [below right,font=\footnotesize] at (i-1) {$A:(r_0,0)$};
\end{tikzpicture}
\end{document}

答案2

为了比较元帖子，包裹在luamplib. 用 编译lualatex。

在此处输入图片描述

\RequirePackage{luatex85}
\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
beginfig(1);
path c, r[], h[];
pair A,B,C,D;

c = fullcircle scaled 160;

t = 45*8/360; % the diagram should work for values other than 45°
B = point t of c;
C = point t-2 of c;
D = point t+2 of c;

r0 = origin -- point 0 of c;
r1 = origin -- B;
r2 = origin -- C;
r3 = origin -- D;

h1 = B{-B} .. C{C};
h2 = B{-B} .. D{D};

A = r0 intersectionpoint h1;

draw r0; draw r1; draw r2; draw r3;
draw h1; draw h2;

draw c withcolor .67 blue;
draw fullcircle scaled 16 cutafter r1 withcolor .67 blue;

draw A -- A shifted 1000 up cutafter c 
     dashed evenly scaled 2/3 
     withcolor .53 red;

label.llft("$O$", origin);
label.rt("$\vartheta=0$", point 0 of c);
label("$\vartheta_B$", 16 right rotated 20);
label.lrt("$A:(r_0,0)$", A);
label.llft("$r^0=c/\omega$", 1/2 C);

label("$B$", 1.08 B);
label("$D$", 1.08 D);
label("$C$", 1.08 C);

endfig;
\end{mplibcode}
\end{document}

笔记：在几个地方，MP 代码取决于以原点为中心的圆。

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