Can one draw a hyperbola with arguments in TikZ?

Question

I'm using TikZ to draw some conic-section graphs. There is a built-in ellipse command (semiaxes as two arguments) and a rudimentary parabola command (with a vertical axis, but one can rotate), but to draw a hyperbola I had to fake it with a spline and externally compute the control points. I don't want to plot a sequence of pixels, I'd prefer something parametric that can be easily modified. Is there a short-cut to draw a hyperbola just from the semiaxes and the centre location, within TikZ?

I'm not unhappy with spline approximations, they work fine for, say, cardioids, but is there some simpler way to get a hyperbola with TikZ?

pgf plot doesn't plot pixels, but connects the points where it evaluates by lines or by some smoothed lines (I don't know what it does, but for sufficiently well-behaved functions it looks quite nicely). Thus I usually draw hyperbolas by plotting something like 1/x. — Caramdir, Feb 01 '11 at 03:20
You can check How to plot hyperbola giving the foci and the fixed differene distance using TikZ and Drawing a hyperbola of a certain eccentricity in TikZ. — Kpym, Mar 04 '19 at 20:53
@Caramdir plot use lines to connect the points (you can check this by setting samples to a small number). The problem with plot is that it use something like 25 or more objects to draw the parabola, where a singe cubic Bézier curve is enough. Less objects means smaller PDF. — Kpym, Mar 04 '19 at 21:00

score 7 · Accepted Answer · answered Feb 01 '11 at 03:28

Look at sections 19.5 and 19.6 in the pgf manual. You can plot curves given by simple parametric equations, such as

 \draw[scale=0.5,domain=-3.141:3.141,smooth,variable=\t] plot ({\t*sin(\t r)},{\t*cos(\t r)});

So if you van find parametric equations of your hyperbola, you should be able to plot it.

score 5 · Answer 2 · answered Mar 04 '19 at 13:51

Here, take this hyperbola drawing sample to play with. The machinery is

%
% #1 optional parameters for \draw
% #2 angle of rotation in degrees
% #3 offset of center as (pointx, pointy) or (name-o-coordinate)
% #4 length of plus (semi)axis, that is axis which hyperbola crosses
% #5 length of minus (semi)axis
% #6 how much of hyperbola to draw in degrees, with 90 you’d reach infinity
%
\newcommand\tikzhyperbola[6][thick]{%
    \draw [#1, rotate around={#2: (0, 0)}, shift=#3]
        plot [variable = \t, samples=1000, domain=-#6:#6] ({#4 / cos( \t )}, {#5 * tan( \t )});
    \draw [#1, rotate around={#2: (0, 0)}, shift=#3]
        plot [variable = \t, samples=1000, domain=-#6:#6] ({-#4 / cos( \t )}, {#5 * tan( \t )});
}

\documentclass[tikz, margin=10]{standalone}

\usepackage{bm}

\usepackage{tikz}
\usetikzlibrary{shapes.geometric} % for shape=ellipse
\usetikzlibrary{calc}

\begin{document}

\def\tikzscale{0.8}
\begin{tikzpicture}[scale=\tikzscale]

\tikzset{
    elli/.style args={#1:#2and#3}{
        draw,
        shape=ellipse,
        rotate=#1,
        minimum width=2*#2,
        minimum height=2*#3,
        outer sep=0pt,
    }
}

%
% #1 optional parameters for \draw
% #2 angle of rotation in degrees
% #3 offset of center as (pointx, pointy) or (name-o-coordinate)
% #4 length of plus (semi)axis, that is axis which hyperbola crosses
% #5 length of minus (semi)axis
% #6 how much of hyperbola to draw in degrees, with 90 you’d reach infinity
%
\newcommand\tikzhyperbola[6][thick]{%
    \draw [#1, rotate around={#2: (0, 0)}, shift=#3]
        plot [variable = \t, samples=1000, domain=-#6:#6] ({#4 / cos( \t )}, {#5 * tan( \t )});
    \draw [#1, rotate around={#2: (0, 0)}, shift=#3]
        plot [variable = \t, samples=1000, domain=-#6:#6] ({-#4 / cos( \t )}, {#5 * tan( \t )});
}

\def\angle{33}
\def\bigaxis{3.2cm}
\def\smallaxis{1.5cm}

\draw [color=blue, line width = 0.4pt, dotted] (-7, 0) -- (7, 0) node [right] {$x_{1}$};
\draw [color=blue, line width = 0.4pt, dotted] (0, -5) -- (0, 5) node [above] {$x_{2}$};

\coordinate (center) at (-6, 2);

\node [scale=\tikzscale, elli=\angle:\bigaxis and \smallaxis, line width = 1.2pt, color=black, dotted] at (center) (e) {};

\draw [-{stealth}, line width = 1.2pt, color = orange] ([shift={(\angle:-12)}] e.center) -- ([shift={(\angle:12)}] e.center) node [above right] {$\bm{a}_1$};
\draw [-{stealth}, line width = 1.2pt, color = orange] ([shift={(90+\angle:-8)}] e.center) -- ([shift={(90+\angle:8)}] e.center) node [above left]  {$\bm{a}_2$};

\tikzhyperbola[line width = 1.2pt, color=blue!80!black]{\angle}{(center)}{\bigaxis}{\smallaxis}{77}

\pgfmathsetmacro\axisratio{\smallaxis / \bigaxis}

% asymptotes
\def\lengthofasymptote{15}
\draw [color=black!40, line width = 0.4pt, rotate around={\angle + atan( \axisratio ): (center)}]
    ($ (-\lengthofasymptote, 0) + (center) $) -- ++(2*\lengthofasymptote, 0) ;
\draw [color=black!40, line width = 0.4pt, rotate around={\angle - atan( \axisratio ): (center)}]
    ($ (-\lengthofasymptote, 0) + (center) $) -- ++(2*\lengthofasymptote, 0) ;

\tikzhyperbola[line width = 1.2pt, color=red!80!black]{90+\angle}{(center)}{\smallaxis}{\bigaxis}{76}

\end{tikzpicture}

\end{document}

What a superb and thoughtful example of TikZ coding! – jvarilly May 03 '20 at 02:51 — jvarilly, May 03 '20 at 02:51

score 4 · Answer 3 · answered Feb 01 '11 at 08:21

4

This should do the trick

\draw plot[variable=\t,samples=1000,domain=-35:35] ({sec(\t)},{tan(\t)});

answered Feb 01 '11 at 08:21

romeovs

9,102

Can one draw a hyperbola with arguments in TikZ?

3 Answers3

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