How to improve this (added hatching)

Question

\documentclass[12pt,a4paper,openany]{book}

\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{amsmath,amssymb,amsthm}
%%%%%%%%%%%%%%%%%%%
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{patterns,shapes.geometric}
\begin{document}

\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
\begin{axis}[unbounded coords=jump,
x=1cm,y=1cm,
axis lines=middle,
xmin=-8,
xmax=8,
ymin=-5,
ymax=5,
ytick=\empty,
xtick=\empty]
\addplot[line width=2pt,color=blue,smooth,samples=51,domain=-8:-0.1,name
path=left] {(1/x)} node[pos=0.1,below=40mm]{$(A_3)$}node[pos=0.1,below=20mm,right=40mm]{$(\mathcal{C}_1)$};
\addplot[line width=2pt,color=blue,smooth,samples=51,domain=0.1:8,name
path=right] {(1/x)} node[pos=0.95,above=20mm]{$(A_1)$}node[pos=0.95,above=20mm,left=50mm]{$(\mathcal{C}_1)$};
\addplot[line width=2pt,color=red,smooth,samples=51,domain=0.1:8,name
path=right] {-(1/x)} node[pos=0.95,below=40mm]{$(A_4)$}node[pos=0.95,below=20mm,left=50mm]{$(\mathcal{C}_2) $};
\addplot[line width=2pt,color=red,smooth,samples=51,domain=-8:-0.1,name
path=left] {-(1/x)} node[pos=0.1,above=30mm]{$(A_4)$}node[pos=0.1,above=20mm,right=40mm]{$(\mathcal{C}_2) $};
\end{axis}
\end{tikzpicture}
\end{document}

I want to obtain something like this

This can be done with TikZ using reverse clip as defined in the answers to this question How can I invert a 'clip' selection within TikZ? as well as fillbetween from pgfplots. — AndréC, Jul 18 '20 at 17:55

LaTeXdraw.com · Accepted Answer · 2020-07-18T18:09:34.693

For hatching, I didn't use patterns as it is hard to customize. In this attempt, I used:

rotated grid to create the hatching (you can play on the distance between parallel lines by changing the ystep parameter)
\clip to specify the filling area

Here is the corresponding code:

\documentclass[12pt,a4paper,openany]{book}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{amsmath,amssymb,amsthm}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
\begin{axis}[unbounded coords=jump,
  x=1cm,y=1cm,
  axis lines=middle,
  xmin=-8,
  xmax=8,
  ymin=-5,
  ymax=5,
  ytick=\empty,
  xtick=\empty,
  axis on top]
% A3 hatch
\begin{scope}
  \clip plot[samples=51,domain=-8:-0.1] (\x, {1/\x}) -| (-8,-1/8) --cycle;
  \draw[blue!20,xstep=0cm,ystep=0.5cm,rotate=45] (-15,-15) grid (15,15);
\end{scope}
% A1 hatch
\begin{scope}
  \clip plot[samples=51,domain=0.1:8] (\x, {1/\x}) |- (0.1,1/0.1) --cycle;
  \draw[blue!20,xstep=0cm,ystep=0.5cm,rotate=45] (-15,-15) grid (15,15);
\end{scope}
% A4 hatch
\begin{scope}
  \clip plot[samples=51,domain=-8:-0.1] (\x, {-1/\x}) -| (-8,1/8) --cycle;
  \draw[red!20,xstep=0cm,ystep=0.5cm,rotate=-45] (-25,-25) grid (15,15);
\end{scope}
% A2 hatch
\begin{scope}
  \clip plot[samples=51,domain=0.1:8] (\x, {-1/\x}) |- (0.1,-1/0.1) --cycle;
  \draw[red!20,xstep=0cm,ystep=0.5cm,rotate=-45] (-25,-25) grid (15,15);
\end{scope}
% Fill between 
\begin{scope}
  \fill[yellow!10,opacity=] plot[samples=51,domain=0.1:8] (\x, {-1/\x}) -- plot[samples=51,domain=8:0.1] (\x, {1/\x}) -- plot[samples=51,domain=-0.1:-8] (\x, {-1/\x}) -- plot[samples=51,domain=-8:-0.1] (\x, {1/\x}) -- cycle ; 
\end{scope}
% Your code (I removed path names)
\addplot[line width=2pt,color=blue,smooth,samples=51,domain=-8:-0.1] {(1/x)};
\addplot[line width=2pt,color=blue,smooth,samples=51,domain=-8:-0.1] {(1/x)} node[pos=0.1,below=40mm]{$(A_3)$}node[pos=0.1,below=20mm,right=40mm]{$(\mathcal{C}_1)$};
\addplot[line width=2pt,color=blue,smooth,samples=51,domain=0.1:8] {(1/x)} node[pos=0.95,above=20mm]{$(A_1)$}node[pos=0.95,above=20mm,left=50mm]{$(\mathcal{C}_1)$};
\addplot[line width=2pt,color=red,smooth,samples=51,domain=0.1:8] {-(1/x)} node[pos=0.95,below=40mm]{$(A_4)$}node[pos=0.95,below=20mm,left=50mm]{$(\mathcal{C}_2) $};
\addplot[line width=2pt,color=red,smooth,samples=51,domain=-8:-0.1] {-(1/x)} node[pos=0.1,above=30mm]{$(A_4)$}node[pos=0.1,above=20mm,right=40mm]{$(\mathcal{C}_2) $};
\end{axis}
\end{tikzpicture}
\end{document}

yields:

For hatching the middle region, here is the corresponding code:

\documentclass[12pt,a4paper,openany]{book}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{amsmath,amssymb,amsthm}
%%%%%%%%%%%%%%%%%%%
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round,x=1cm,y=1cm]
\begin{axis}[unbounded coords=jump,
  x=1cm,y=1cm,
  axis lines=middle,
  xmin=-8,
  xmax=8,
  ymin=-5,
  ymax=5,
  ytick=\empty,
  xtick=\empty,
  axis on top]
% A3 hatch
\begin{scope}
  \clip plot[samples=51,domain=-8:-0.1] (\x, {1/\x}) -| (-8,-1/8) --cycle;
  \draw[blue!20,xstep=0cm,ystep=0.5cm,rotate=45] (-15,-15) grid (15,15);
\end{scope}
% A1 hatch
\begin{scope}
  \clip plot[samples=51,domain=0.1:8] (\x, {1/\x}) |- (0.1,1/0.1) --cycle;
  \draw[blue!20,xstep=0cm,ystep=0.5cm,rotate=45] (-15,-15) grid (15,15);
\end{scope}
% A4 hatch
\begin{scope}
  \clip plot[samples=51,domain=-8:-0.1] (\x, {-1/\x}) -| (-8,1/8) --cycle;
  \draw[red!20,xstep=0cm,ystep=0.5cm,rotate=-45] (-25,-25) grid (15,15);
\end{scope}
% A2 hatch
\begin{scope}
  \clip plot[samples=51,domain=0.1:8] (\x, {-1/\x}) |- (0.1,-1/0.1) --cycle;
  \draw[red!20,xstep=0cm,ystep=0.5cm,rotate=-45] (-25,-25) grid (15,15);
\end{scope}
% Fill between 
\begin{scope}
  \clip plot[samples=51,domain=0.1:8] (\x, {-1/\x}) -- plot[samples=51,domain=8:0.1] (\x, {1/\x}) -- plot[samples=51,domain=-0.1:-8] (\x, {-1/\x}) -- plot[samples=51,domain=-8:-0.1] (\x, {1/\x}) -- cycle ;
\draw[orange!40,xstep=0cm,ystep=0.5cm,rotate=-45] (-25,-25) grid (15,15);
  \draw[orange!40,xstep=0cm,ystep=0.5cm,rotate=45] (-25,-25) grid (15,15);
  \node[above right] at (0,0){$(A_5)$};
\end{scope}
\addplot[line width=2pt,color=blue,smooth,samples=51,domain=-8:-0.1] {(1/x)};
\addplot[line width=2pt,color=blue,smooth,samples=51,domain=-8:-0.1] {(1/x)} node[pos=0.1,below=40mm]{$(A_3)$}node[pos=0.1,below=20mm,right=40mm]{$(\mathcal{C}_1)$};
\addplot[line width=2pt,color=blue,smooth,samples=51,domain=0.1:8] {(1/x)} node[pos=0.95,above=20mm]{$(A_1)$}node[pos=0.95,above=20mm,left=50mm]{$(\mathcal{C}_1)$};
\addplot[line width=2pt,color=red,smooth,samples=51,domain=0.1:8] {-(1/x)} node[pos=0.95,below=40mm]{$(A_4)$}node[pos=0.95,below=20mm,left=50mm]{$(\mathcal{C}_2) $};
\addplot[line width=2pt,color=red,smooth,samples=51,domain=-8:-0.1] {-(1/x)} node[pos=0.1,above=30mm]{$(A_4)$}node[pos=0.1,above=20mm,right=40mm]{$(\mathcal{C}_2) $};
\end{axis}
\end{tikzpicture}
\end{document}

which yields:

In this case, I've added two rotated grids.

i want hatching the center an write A_5 how to do please – linda Oiladali Jul 18 '20 at 17:49 — linda Oiladali, Jul 18 '20 at 17:49
I've added it, check the modified version :) – LaTeXdraw.com Jul 18 '20 at 18:11 — LaTeXdraw.com, Jul 18 '20 at 18:11
Sebastiano did it :D Thanks! – LaTeXdraw.com Jul 29 '20 at 22:08 — LaTeXdraw.com, Jul 29 '20 at 22:08

score 6 · Answer 2 · 2020-07-18T16:49:56.197

Compile here: Ahihi do ngoc

import graph;
import patterns;
usepackage("amsmath");
// The default unit and linewidth
unitsize(1cm);
size(8cm,false);
defaultpen(linewidth(1bp));
// Definition of the graphs
real F(real x){return 1/x;}
real G(real x){return -1/x;}
path f1=graph(F,-8,-0.2,350),f2=graph(F,0.2,8,350),
        g1=graph(G,-8,-0.2,350),g2=graph(G,0.2,8,350);
// Draw patterns
picture pic1, pic2;
add("hatch1",hatch(NE));
fill(pic1,box((-8,F(-0.2)),(8,F(0.2))),pattern("hatch1"));
clip(pic1,f1--(-8,F(-0.2))--cycle^^f2--(8,F(0.2))--cycle);
add(pic1);
add("hatch2",hatch(SE));
fill(pic2,box((-8,F(-0.2)),(8,F(0.2))),pattern("hatch2"));
clip(pic2,g1--(-8,F(0.2))--cycle^^g2--(8,F(-0.2))--cycle);
add(pic2);
pic2=new picture;
fill(pic2,box((-8,F(-0.2)),(8,F(0.2))),cyan);
path AhihidoNgoc=f1--g2--reverse(f2)--reverse(g1)--cycle;
clip(pic2,AhihidoNgoc);
add(pic2);
// Draw two graphs
draw(f1^^f2,blue);
draw(g1^^g2,red);
// Draw Xaxis and Yaxis
path Xaxis=(-8,0)--(8,0),Yaxis=(0,F(0.2))--(0,F(-0.2));
draw(Xaxis,Arrow(1bp,arrowhead=TeXHead));
draw(Yaxis,BeginArrow(1bp,arrowhead=TeXHead));
// Add labels
label(Label("$(\mathcal{C}_1)$",Relative(0.6),UnFill),f1,blue);
label(Label("$(\mathcal{C}_1)$",Relative(0.4),LeftSide,UnFill),f2,blue);
label(Label("$(\mathcal{C}_2)$",Relative(0.6),LeftSide,UnFill),g1,red);
label(Label("$(\mathcal{C}_2)$",Relative(0.4),UnFill),g2,red);
label(Label("$(A_1)$",UnFill),(7,G(-0.25)),blue);
label(Label("$(A_2)$",UnFill),(-7,G(-0.25)),red);
label(Label("$(A_3)$",UnFill),(-7,G(0.25)),blue);
label(Label("$(A_4)$",UnFill),(7,G(0.25)),red);
frame f;
label(f,Label("$(A_5)$"),0,Fill(white));
add(rotate(45)*f);

That's nice, plus one. Can you give the code so that it is also compilable with a LaTeX engine? — AndréC, Jul 18 '20 at 17:45
@AndréC I usually compile Asymptote code directly, and then using \includegraphics command. However, you can see it. — , Jul 18 '20 at 18:08

How to improve this (added hatching)

2 Answers2