Pgfplots/Tikz：如何重现相同的图形？

Question

我试图在 Latex 中重现如下所示的相同图形：

目前我得到的最佳结果如下：

我找不到在图案线之间留出更多空间的解决方案，而且我不知道其他细节（节点、矩形的边框等）。

这是我目前使用的代码：

  \documentclass{article}
  \usepackage[dvipsnames]{xcolor}
  \usepackage{tikz}
  \usepackage{pgfplots}
  \usetikzlibrary{patterns}

  \begin{document}
    \begin{tikzpicture}
        \pgfdeclarepatternformonly{north east lines }%
           {\pgfqpoint{-1pt}{-1pt}}%
           {\pgfqpoint{10pt}{10pt}}%
           {\pgfqpoint{9pt}{9pt}}%
           {
             \pgfsetlinewidth{1.5pt}
             \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
             \pgfpathlineto{\pgfqpoint{9.1pt}{9.1pt}}
             \pgfusepath{stroke}
            }

        \pgfdeclarepatternformonly{vertical}%
           {\pgfqpoint{-1pt}{-1pt}}%
           {\pgfqpoint{10pt}{10pt}}%
           {\pgfqpoint{9pt}{9pt}}%
           {    
             \pgfsetlinewidth{1.5pt}
             \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
             \pgfpathlineto{\pgfqpoint{0pt}{10pt}}
             \pgfusepath{stroke}
            }

         \pgfdeclarepatternformonly{horizontal}%
           {\pgfqpoint{-1pt}{-1pt}}%
           {\pgfqpoint{10pt}{10pt}}%
           {\pgfqpoint{9pt}{9pt}}%
           {    
             \pgfsetlinewidth{1.5pt}
             \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
             \pgfpathlineto{\pgfqpoint{10pt}{0pt}}
             \pgfusepath{stroke}
            }

          \pgfdeclarepatternformonly{north west line}%
           {\pgfqpoint{-1pt}{-1pt}}%
           {\pgfqpoint{10pt}{10pt}}%
           {\pgfqpoint{9pt}{9pt}}%
           {    
             \pgfsetlinewidth{1.5pt}
             \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
             \pgfpathlineto{\pgfqpoint{-10pt}{10pt}}
             \pgfusepath{stroke}
            }

            \fill[pattern=north east lines wide,pattern color=blue] (0,0) rectangle(4,4);
            
            \fill[pattern= horizontal, pattern color=YellowOrange] (0,0) rectangle (4,2);

            \fill[pattern=vertical, pattern color=RubineRed] (0,0) rectangle (1,4);
           
            \fill[pattern=north west line wide,pattern color=black] (0,0) rectangle (1,2);
         
            \draw[->,>=stealth, ultra thick] (-1,0) -- (6,0)node[right] {$u$};
            \draw [->,>=stealth, ultra thick] (0,-1) -- (0,6)node[above] {$v$};

    \end{tikzpicture}
\end{document}

Answer 1

我不确定你的图案是否必须在固定点处相互交叉。我尝试重现原始绘图，使其尽可能相似。如果不是这样，我的方法可能不是最好的，而图案库才是最佳方法。

我使用\foreach和剪辑来绘制图案，如您所见：

\documentclass[border=2mm]{standalone}    
\usepackage {tikz}

\definecolor{myblue}  {HTML}{2F59D1}
\definecolor{myorange}{HTML}{FD6E06}
\definecolor{mypink}  {HTML}{DE0191}

\begin{document}
\begin{tikzpicture}[scale=4,thick,line cap=round]
  \def\aone{0.225}
  \def\atwo{0.45}
  \def\bone{0.9}
  \def\btwo{0.9}
  % blue lines
  \draw[myblue] (0,\btwo) -| (\bone,0);
  \begin{scope}
    \draw[myblue] (\bone,\btwo) circle (0.015) node [above right] {$C(b_1,b_2$)};
    \clip (0,0) rectangle (\bone,\btwo);
    \foreach\i in {-7,-5,...,7}
    {%
      \draw[myblue] (0.125*\i*\bone,0) --++ (45:2);
    }
  \end{scope}
  % pink lines
  \draw[mypink] (\aone,\btwo) circle (0.015) node [above] {$C(a_1,b_2$)};
  \draw[mypink] (0,\btwo) -- (\aone,\btwo);
  \foreach\i in {1,2,3}
  {%
    \draw[mypink] (\i*\aone/3,0) -- (\i*\aone/3,\bone);
  }
  % orange lines
  \draw[myorange] (\bone,\atwo) circle (0.015) node [right] {$C(b_1,a_2$)};
  \draw[myorange] (\bone,0) -- (\bone,\atwo);
  \foreach\i in {1,...,4}
  {%
    \draw[myorange] (0,0.25*\i*\atwo) -- (\bone,0.25*\i*\atwo);
  }
  % black lines
  \draw (0,\atwo) -| (\aone,0);
  \begin{scope}
    \draw (\aone,\atwo) circle (0.015);
    \clip (0,0) rectangle (\aone,\atwo);
    \foreach\i in {1,...,5}
    {%
      \draw (0.125*\i*\bone,0) --++ (135:2);
    }
  \end{scope}
  % axes and labels
  \node at (0,0) [below left] {$0$};
  \draw[->] (-0.1,0) -- (1.1,0) node[below] {$u_1$};
  \draw[->] (0,-0.1) -- (0,1.1) node[left]  {$u_2$};
  \foreach\i/\j in{\aone/$a_1$,\bone/$b_1$,1/1}
  {%
    \draw (\i,0.025) -- (\i,-0.025) node [below] {\j};
  }
  \foreach\i/\j in{\atwo/$a_2$,\btwo/$b_2$,1/1}
  {%
    \draw (0.025,\i) -- (-0.025,\i) node [left] {\j};
  }
 \end{tikzpicture}
\end{document}

这是我的绘图：