How not to overlap solid colors in region with inequalities using `tikzpicture` environment?

Question

Please consider this MWE:

\documentclass{article}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{pgfplots}
\usetikzlibrary{arrows,overlay-beamer-styles,babel,arrows.meta, patterns}
\pgfplotsset{compat=1.8}
% ========================
% From https://tex.stackexchange.com/a/76014/152550
\newcommand{\drawge}{-- (rel axis cs:1,0) -- (rel axis cs:1,1) -- (rel axis cs:0,1) \closedcycle}
\newcommand{\drawle}{-- (rel axis cs:1,1) -- (rel axis cs:1,0) -- (rel axis cs:0,0) \closedcycle}
% ========================
\begin{document}
\begin{tikzpicture}
    \begin{axis}[
            legend pos=outer north east,
            axis lines = center,
            xticklabel style = {font=\tiny},
            yticklabel style = {font=\tiny},
            xlabel = $x$,
            ylabel = $y$,
            legend style={cells={align=left}},
            legend cell align={left},
            xticklabel=\empty,
            yticklabel=\empty,
            ]
            \addplot[very thick,red] {0.5x+1};
            \addplot[very thick,red] {-2x+3};
            %\addplot[draw=none,pattern=vertical lines,green,opacity=0.3] {0.5x+1}\drawge;
            %\addplot[draw=none,pattern=vertical lines,blue,opacity=0.3] {0.5x+1}\drawle;
            %\addplot[draw=none,pattern=vertical lines,orange,opacity=0.3] {-2x+3}\drawge;
            %\addplot[draw=none,pattern=vertical lines,violet,opacity=0.3] {-2x+3}\drawle;
    \end{axis}
\end{tikzpicture}
\end{document}

I would like to fill the 4 regions that are divided into the plane, with no-overlapping of solid colors (including the red lines). If we uncomment the last four \addplot we get:

As you can see:

The four \addplot colors are overlapping, and
The red lines overlap with the 4 colors.

How can we prevent the overlapping between area colors and line colors?

P.S. I should be able to add a 3rd red line to the above, and paint the regions with 7 different colors in total.

https://tex.stackexchange.com/questions/75933/how-to-draw-the-region-of-inequality?noredirect=1&lq=1 — js bibra, Jul 08 '20 at 01:36
@jsbibra hello and thanks for the comment!! That's the link I put on the code. However, in the accepted answer they treat overlapping with patterns, not with solid colors. — manooooh, Jul 08 '20 at 01:37
can you elaborate what is wrong with the answer given by @ZhiyuanLck--and a handrawn sketch of the desired output--probably the question has not been understood correctly — js bibra, Jul 13 '20 at 13:20

ZhiyuanLck · Accepted Answer · 2020-07-09T05:22:29.797

UPDATE

I find a better way to color regions: find vertices of region and fill the path on axis background layer with the specification set layers=standard.

\documentclass{article}
\usepackage{pgfplots}
\usetikzlibrary{intersections}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
[
  pin distance=2mm,
  every pin edge/.style={thick,-},
]
\begin{axis}[
  set layers=standard,
  legend pos=outer north east,
  axis lines = center,
  xticklabel style = {font=\tiny},
  yticklabel style = {font=\tiny},
  xlabel = $x$,
  ylabel = $y$,
  legend style={cells={align=left}},
  legend cell align={left},
  xticklabel=\empty,
  yticklabel=\empty,
]
  \addplot[name path=l1, very thick,red] {0.5x+1}
    coordinate [pos=0] (l1-0)
    coordinate [pos=1] (l1-1)
    node [pos=0.1, pin=below:{$l_1$}] {};
  \addplot[name path=l2, very thick,teal] {-2x+3}
    coordinate [pos=0] (l2-0)
    coordinate [pos=1] (l2-1)
    node [pos=0.1, pin=below:{$l_2$}] {};
  \addplot[name path=l3, very thick,brown] {3*x-4.3}
    coordinate [pos=0] (l3-0)
    coordinate [pos=1] (l3-1)
    node [pos=0.2, pin=right:{$l_3$}] {};
% intersection point
  \path[name intersections={of=l1 and l2, name=i}];
  \path[name intersections={of=l1 and l3, name=j}];
  \path[name intersections={of=l2 and l3, name=k}];
  \node[above] at (i-1) {$i_1$};
  \node[above] at (j-1) {$j_1$};
  \node[below] at (k-1) {$k_1$};
\tikzaliascoordinatesystem{r}{rel axis}
  \pgfonlayer{axis background}
  \fill[red!10] (l2-0) -- (i-1) -- (l1-0);
  \fill[green!10] (l2-0) -- (i-1) -- (j-1) -- (l3-1) -- (r cs:1, 1);
  \fill[blue!10] (j-1) -- (l1-1) -- (l3-1);
  \fill[yellow!10] (l3-0) -- (k-1) -- (i-1) -- (l1-0);
  \fill[cyan!20] (l3-0) -- (k-1) -- (l2-1) -- (r cs:1, 0);
  \fill[teal!20] (l2-1) -- (k-1) -- (j-1) -- (l1-1);
  \fill[violet!50] (i-1) -- (j-1) -- (k-1);
  \endpgfonlayer
\end{axis}
\end{tikzpicture}
\end{document}

Old answer

Use pgfplotslibrary fillbetween. Divide the region to 6 subregions to fill.

\documentclass{article}
\usepackage{pgfplots}
\usetikzlibrary{intersections}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.17}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
  legend pos=outer north east,
  axis lines = center,
  xticklabel style = {font=\tiny},
  yticklabel style = {font=\tiny},
  xlabel = $x$,
  ylabel = $y$,
  legend style={cells={align=left}},
  legend cell align={left},
  xticklabel=\empty,
  yticklabel=\empty,
]
  \addplot[name path=l1, very thick,red] {0.5x+1};
  \addplot[name path=l2, very thick,red] {-2x+3};
% fill left and right
  \addplot[opacity=.3] fill between [
   of=l1 and l2,
   split,
   every segment no 0/.style=blue,
   every segment no 1/.style=orange,
  ];
% intersection point
  \path[name intersections={of=l1 and l2, name=i}];
% upper and lower bound lines
  \path[name path=upper] (rel axis cs:0, 1) -- (rel axis cs:1, 1);
  \path[name path=lower] (rel axis cs:0, 0) -- (rel axis cs:1, 0);
% fill upper left
  \addplot [green, opacity=.3] fill between [
   of=l2 and upper,
   % rectangle must be constructed from left to right
   soft clip={(rel axis cs:0, 1) rectangle (i-1)},
  ];
% fill upper right
  \addplot [green, opacity=.3] fill between [
   of=l1 and upper,
   soft clip={(i-1) rectangle (rel axis cs:1, 1)},
  ];
% fill lower left
  \addplot [violet, opacity=.3] fill between [
   of=l1 and lower,
   soft clip={(rel axis cs:0, 0) rectangle (i-1)},
  ];
% fill lower right
  \addplot [violet, opacity=.3] fill between [
   of=l2 and lower,
   soft clip={(i-1) rectangle (rel axis cs:1, 0)},
  ];
\end{axis}
\end{tikzpicture}
\end{document}

Thanks for the code!! It helps me. However I am unable to do it for additional line, like \addplot[name path=l3, very thick,red] {3*x-4.3};. I calculated 2 new intersection points, namely \path[name intersections={of=l1 and l3, name=j}]; and \path[name intersections={of=l2 and l3, name=k}]; but I can't draw it correctly. Is the same idea or there are new changes? — manooooh, Jul 08 '20 at 21:38

score 1 · Answer 2 · answered Jul 08 '20 at 04:33

Does this meet your rquirement--

\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
legend pos=outer north east,
axis lines = center,
xticklabel style = {font=\tiny},
yticklabel style = {font=\tiny},
xlabel = $x$,
ylabel = $y$,
legend style={cells={align=left}},
legend cell align={left},
xticklabel=\empty,
yticklabel=\empty,
]
\addplot[very thick,name path=a,draw=none] {0.5*x+1};
\addplot[very thick,draw=none,name path=b] {-2*x+3};
\path [name intersections={of=a and b,by=c}];
\node [fill=blue,inner sep=2pt,label=-90:$C$] at (c) {};

\path[name path=lower,
%thick,draw=red,
intersection segments={
    of=a and b,
    sequence=B0 -- A1,
}
]; 
\path[name path=upper,
%thick,draw=red,
intersection segments={
    of=a and b,
    sequence=B1 -- A0,
}
]; 

\addplot[red!70, opacity=.5]   fill between[of=lower and a];
    \addplot[blue!70, opacity=.5]   fill between[of=lower and b];   
            \addplot[green!70, opacity=.5]   fill between[reverse=false,of=lower 
             and a];
                    \addplot[green!70!yellow!30, opacity=.5]   fill 
                     between[of=upper and b];
\end{axis}

\end{tikzpicture}


\end{document}

Thanks for the answer!! There is nothing wrong about your answer. I selected the other because it seems more easy to implement for me, but the same output can be achieved with yours! (That's why I upvoted your question.) — manooooh, Jul 13 '20 at 17:38
i asked becos you have placed a bounty --is there some other requirement — js bibra, Jul 14 '20 at 00:32
I need the same but with 3 lines instead of 2. That's the other requirement if you want to do it. Thanks!! — manooooh, Jul 14 '20 at 01:06

How not to overlap solid colors in region with inequalities using `tikzpicture` environment?

2 Answers2

UPDATE

Old answer