我怎样才能用点填充一个区域？并控制它？

Question

如何用点填充区域？如何控制点之间的距离？如何防止线和点之间的干扰？如何改变点的颜色？

\documentclass[tikz,margin=5pt]{standalone}
\usepackage{xparse}
\usetikzlibrary{calc}

\tikzset{%
    Cote node/.style={%
        midway,
        sloped,
        fill=white,
        inner sep=1.5pt,
        outer sep=2pt
    },
    Cote arrow/.style={%
        <->,
        >=latex,
        very thin
    }
}

\makeatletter
\NewDocumentCommand{\Cote}{%
    s       % cotation avec les flèches à l'extérieur
    D<>{1.5pt} % offset des traits
    O{.75cm}    % offset de cotation
    m       % premier point
    m       % second point
    m       % étiquette
    D<>{o}  % () coordonnées -> angle
            % h -> horizontal,
            % v -> vertical
            % o or what ever -> oblique
    O{}     % parametre du tikzset
    }{%

    {\tikzset{#8}

    \coordinate (@1) at #4 ;
    \coordinate (@2) at #5 ;

    \if #7v % Cotation verticale
        \coordinate (@0) at ($($#4!.5!#5$) + (#3,0)$) ; 
        \coordinate (@4) at (@0|-@1) ;
        \coordinate (@5) at (@0|-@2) ;
    \else
    \if #7h % Cotation horizontale
        \coordinate (@0) at ($($#4!.5!#5$) + (0,#3)$) ; 
        \coordinate (@4) at (@0-|@1) ;
        \coordinate (@5) at (@0-|@2) ;
    \else % cotation encoche
    \ifnum\pdfstrcmp{\unexpanded\expandafter{\@car#7\@nil}}{(}=\z@
        \coordinate (@5) at ($#7!#3!#5$) ;
        \coordinate (@4) at ($#7!#3!#4$) ;
    \else % cotation oblique    
        \coordinate (@5) at ($#5!#3!90:#4$) ;
        \coordinate (@4) at ($#4!#3!-90:#5$) ;
    \fi\fi\fi

    \draw[very thin,shorten >= #2,shorten <= -2*#2] (@4) -- #4 ;
    \draw[very thin,shorten >= #2,shorten <= -2*#2] (@5) -- #5 ;

    \IfBooleanTF #1 {% avec étoile
    \draw[Cote arrow,-] (@4) -- (@5)
        node[Cote node] {#6\strut};
    \draw[Cote arrow,<-] (@4) -- ($(@4)!-6pt!(@5)$) ;   
    \draw[Cote arrow,<-] (@5) -- ($(@5)!-6pt!(@4)$) ;   
    }{% sans étoile
    \ifnum\pdfstrcmp{\unexpanded\expandafter{\@car#7\@nil}}{(}=\z@
        \draw[Cote arrow] (@5) to[bend right]
            node[Cote node] {#6\strut} (@4) ;
    \else
    \draw[Cote arrow] (@4) -- (@5)
        node[Cote node] {#6\strut};
    \fi
    }}
    }
\makeatother
\usetikzlibrary{patterns}
\begin{document}
\begin{tikzpicture}
\coordinate (O) at (0,0);
\fill[blue!30,opacity=0.65] (0,0.5)-- (4,0.5)--(4,-0.5) -- (0,-0.5) -- cycle;
\draw[thick] (0,0.5)--(4,0.5)--(4,-0.5);
\draw[thick]  (4,-0.5)--(0,-0.5) --(0,0.5);
\Cote{(4,-.5)}{(4,.5)}{$h$}[ Cote node/.append style={right,rotate=-90}];
\Cote[1cm]{(0,0)}{(4,0)}{$a$};
\draw (0,0.25)--(4,0.25);
\draw (0,-0.25)--(4,-0.25);
\draw (0,0.25/2)--(4,0.25/2);
\draw (0,-0.25/2)--(4,-0.25/2);
\draw (0,3*0.25/2)--(4,3*0.25/2);
\draw (0,-3*0.25/2)--(4,-3*0.25/2);
\draw (0,0)--(4,0);
\fill [fill=red, pattern=crosshatch dots] 
    (0,0.5)-- (4,0.5)--(2,0) -- cycle;
\fill [fill=red, pattern=crosshatch dots] 
    (0,-0.5)-- (4,-0.5)--(2,0) -- cycle;
     \end{tikzpicture}
\end{document}  

Answer 1

\documentclass{article}

\usepackage{tikz}
\usetikzlibrary{backgrounds,patterns,calc}

\begin{document}

\def\yysep{0.25}
\def\xxsep{4}
\begin{tikzpicture}
    \foreach \y in {1,...,9} {%
        \node[inner sep=0pt] (l\y) at (0,\yysep*\y) {};
        \node[inner sep=0pt] (r\y) at (\xxsep,\yysep*\y) {};
        \draw (l\y) -- (r\y);
    };
    \begin{pgfonlayer}{background}
        \draw[fill=blue!20] (l1) rectangle (r9);
    \end{pgfonlayer}
    \coordinate (auxa) at ($(l1)!0.5!(r1)$);
    \coordinate (auxb) at ($(l1)!0.5!(l9)$);
    \coordinate (boxcenter) at (auxa |- auxb);
    \begin{scope}
        \pgfsetfillpattern{dots}{red}
        \fill (l1) -- (boxcenter) -- (r1) -- cycle;
        \fill (l9) -- (boxcenter) -- (r9) -- cycle;
    \end{scope}
\end{tikzpicture}

\end{document}