Is there a fastest way to draw staircase functions with tikz?

Question

I've been working on a graph for a staircase function, but my code is a mess. Is there a way to make it easier to plot this kind of function?

\documentclass[border=1 cm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \draw[-latex,thick] (-4, 0) -- (5, 0) node[right] {$x$};
  \draw[-latex,thick] (0, -4) -- (0, 4) node[above] {$y$};
  \draw[domain=0:1, smooth, variable=\x] plot ({\x}, {0});
  \draw[domain=1:2, smooth, variable=\x] plot ({\x}, {1});
  \draw[domain=2:3, smooth, variable=\x] plot ({\x}, {2});
  \draw[domain=3:4, smooth, variable=\x] plot ({\x}, {3});
  \draw[domain=0:-1, smooth, variable=\x] plot ({\x}, {-1});
  \draw[domain=-1:-2, smooth, variable=\x] plot ({\x}, {-2});
  \draw[domain=-2:-3, smooth, variable=\x] plot ({\x}, {-3});
  \foreach \x in {-3,-2,-1,1,2,3,4} 
  \draw[shift={(\x,0)},color=black] node[below] {$\x$};
  \foreach \y in {1,2,3} 
  \draw[shift={(0,\y)},color=black] node[left] {$\y$};
  \foreach \y in {-3,-2,-1} 
  \draw[shift={(0,\y)},color=black] node[right] {$\y$};
  \draw[color=black,fill] (-3,-3) circle (1.5pt);
  \draw[color=black,fill] (-2,-2) circle (1.5pt);
  \draw[color=black,fill] (-1,-1) circle (1.5pt);
  \draw[color=black,fill] (0,0) circle (1.5pt);
  \draw[color=black,fill] (3,3) circle (1.5pt);
  \draw[color=black,fill] (2,2) circle (1.5pt);
  \draw[color=black,fill] (1,1) circle (1.5pt);
  \draw[color=black,fill=white] (-2,-3) circle (1.5pt);
  \draw[color=black,fill=white] (-1,-2) circle (1.5pt);
  \draw[color=black,fill=white] (0,-1) circle (1.5pt);
  \draw[color=black,fill=white] (1,0) circle (1.5pt);
  \draw[color=black,fill=white] (2,1) circle (1.5pt);
  \draw[color=black,fill=white] (3,2) circle (1.5pt);
  \draw[color=black,fill=white] (4,3) circle (1.5pt);
\end{tikzpicture}
\end{document}

And this is my result:

Do you use LuaTeX? In this case the simple solution is to write Lua code to generate these things — user202729, Nov 29 '21 at 05:32
There's https://tex.stackexchange.com/questions/571392/graphing-a-discontinuous-function etc. — user202729, Nov 29 '21 at 05:33
Also there's a "more specific" way to draw the hollow and solid dots, see https://tex.stackexchange.com/questions/76418/plot-non-continuous-function-with-tikz — user202729, Nov 29 '21 at 05:35

Zarko · Accepted Answer · 2021-11-29T06:48:33.557

6

hm, fastest way? No, but a but shorter code if you use loops:

\documentclass[border=3mm]{standalone}
\usepackage{tikz}
\begin{document}
    \begin{tikzpicture}
% axis
\draw[-latex] (-3.5, 0) -- (4.5, 0) node[right] {$x$};
\draw[-latex] (0, -3.5) -- (0, 3.5) node[above] {$y$};
\foreach \x in {-3,-2,-1,1,2,3,4}
  \draw (\x,1mm) -- ++ (0,-2mm) node[below] {$\x$};
\foreach \y in {-3,-2,-1,1,2,3}
{
\ifnum\y<0

    \draw (-1mm,\y) -- ++ (2mm,0) node[right] {$\y$} 
\else

    \draw (1mm,\y) -- ++ (-2mm,0) node[left]  {$\y$}
\fi;
}
% staircases
\foreach \i in {-3,...,3}
{
  \filldraw[thick]  (\i,\i) circle[radius=0.5mm] -- ++ (1,0);
  \draw[thick, fill=white]  (\i+1,\i) circle[radius=0.5mm];
}
\end{tikzpicture}
\end{document}

Edit: You may use @Symbol1 suggestion and in above MWE replace

\foreach \y in {-3,-2,-1,1,2,3}
{
\ifnum\y<0  
    \draw (-1mm,\y) -- ++ (2mm,0) node[right] {$\y$} 
\else   
    \draw (1mm,\y) -- ++ (-2mm,0) node[left]  {$\y$}
\fi;
}

with shorter code

\foreach \y in {-3,-2,-1,1,2,3}
    \draw (0,\y) node[inner xsep=2mm, anchor=-90+90*sign(\y)] {$\y$} -- + (-1mm,0) -- + (1mm,0);

edited Nov 29 '21 at 06:48

answered Nov 29 '21 at 06:18

Zarko

296,517

node[right] {$\y$} can be replaced with node[anchor = 90 + 90*sign(\y)] {$\y$}. That saves the\ifnum – Symbol 1 Nov 29 '21 at 06:32
@Symbol1, interesting idea but for nice placing of tick labels the code is a bit more complex: \draw (0,\y) node[inner xsep=2mm, anchor = -90+90*sign(\y)] {$\y$} -- + (-1mm,0) -- + (1mm,0); – Zarko Nov 29 '21 at 06:45
Changed my mind, \draw({sign(\y)*0.5}, \y)node{$\y$} (-1mm,\y)--(1mm,\y); is also good alongside the interesting xsep. – Symbol 1 Nov 29 '21 at 07:00
1

@Symbol1, shorter: yes, but better? Labels positioning is wrong, correcting them by ({sign(-\y)*0.5} gives bad looking result :-( – Zarko Nov 29 '21 at 07:06

Roland · Answer 2 · 2021-11-30T00:09:10.533

A suggestion in pgfplots with jump mark left you can make this:

\documentclass{article}
\usepackage{pgfplots}
\begin{document}
\pgfplotsset{
    axissytle/.style={
        every axis x label/.style={at={(current axis.right of origin)},anchor=east,xshift=0.5cm},
        every axis y label/.style={at={(current axis.above origin)},anchor=north,yshift=0.5cm}
    }
}

\begin{tikzpicture}
    \begin{axis}[
        xmin=-5,
        xmax=5,
        ymin=-5,
        ymax=5,
        xtick={-4,...,4},
        ytick={0,1,...,4},
        axis lines=middle,
        label style={font=\tiny},
        tick label style={font=\tiny},
        axissytle,
        xlabel=$x$,
        ylabel=$y$,
        xtick distance={1},
        ytick distance={1},
        extra y ticks={-4,-3,-2,-1},
        extra y tick style={yticklabel style={xshift=0.5ex, anchor=west}}
        ]

        \addplot[jump mark left,mark=*,thick,black]coordinates{(-3,-3)(-2,-2)(-1,-1)(0,0)(1,1)(2,2)};
        \addplot[only marks,mark=*,thick,fill=white,draw=black] coordinates{(-2,-3)(-1,-2)(0,-1)(1,0)(2,1)(3,2)};
        \addplot[mark=o,thick]coordinates{(2,2) (3,2)};
    \end{axis}
\end{tikzpicture}


\end{document}

Is there a fastest way to draw staircase functions with tikz?

2 Answers2