LaTeX-examples/tikz/half-space/half-space.tex

\documentclass{article}
\usepackage[pdftex,active,tightpage]{preview}
\setlength\PreviewBorder{2mm}
\usepackage{tikz}
\usetikzlibrary{patterns}

\begin{document}
\begin{preview}
\begin{tikzpicture}
    \pgfdeclarepatternformonly{north east lines wide}%
    {\pgfqpoint{-1pt}{-1pt}}%
    {\pgfqpoint{10pt}{10pt}}%
    {\pgfqpoint{9pt}{9pt}}%
    {
    \pgfsetlinewidth{0.7pt}
    \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
    \pgfpathlineto{\pgfqpoint{9.1pt}{9.1pt}}
    \pgfusepath{stroke}
    }

    \pgfdeclarepatternformonly{north west lines wide}
    {\pgfqpoint{-1pt}{-1pt}}%
    {\pgfqpoint{7pt}{7pt}}%
    {\pgfqpoint{6pt}{6pt}}%
    {
    \pgfsetlinewidth{0.7pt}
    \pgfpathmoveto{\pgfqpoint{0pt}{6pt}}
    \pgfpathlineto{\pgfqpoint{6.1pt}{-0.1pt}}
    \pgfusepath{stroke}
    }

    % Draw two intersecting lines
    \draw[thick, red]   (-1,-1) coordinate (a) -- (2,-1) coordinate (b);
    \draw[thick, green] ( 1,-1) coordinate (c) -- (1, 2) coordinate (d);

    \fill[pattern=north east lines wide, pattern color=red!50]   (a) -- (b) -- (2,2) -- (-1,2) -- (a);
    \fill[pattern=north west lines wide, pattern color=green!50] (a) -- (1,-1) -- (1,2) -- (-1,2) -- (a);

    \draw[thick, green] (c) -- (d);
    \draw[thick, red]   (a) -- (b);


    % Draw axes
    \draw [<->,thick] (0,2.5) node (yaxis) [above] {$x_2$}
        |- (2.5,0) node (xaxis) [right] {$x_1$};
    \node[red]   at (1.5,2.8) {$H_2^+(-1)$};
    \node[green] at (1.5,2.3) {$H_1^-(1)$};
\end{tikzpicture}
\end{preview}
\end{document}