用于数学图形的优雅哈希区域......

Question 1

下一个代码展示了如何使用pattern用户定义\hatchthickness和\hatchdistance来定义 a 。此模式取自使用带有阴影的 tikz 形状内的图案

此图案用于fill在背景层中绘制的矩形节点：

\begin{scope}[on background layer]
\node[fit={(-5,0) (4,-1)}, inner sep=0pt, Pattern] {};
\end{scope}

该模式没有考虑holes，但你可以fill=white所有需要在其上可读的节点：

\node[violet,fill=white] at (3.8,-0.4) {\textbf{\textit{x}}};

您的代码已通过模式定义减少，但也使用了一些\foreach循环来绘制。我认为，如果您使用已加载但从未使用的代码ticks，则可以进一步减少。pgfplots

下面的这段代码只显示了左图。使用类似的工具可以轻松获得右图。

\documentclass[border=3mm,tikz]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{arrows,patterns,backgrounds,fit}

\makeatletter
\tikzset{% customization of pattern
         % based on <m.wibrow@gm...> - 2013-03-24 07:20: 
        hatch distance/.store in=\hatchdistance,
        hatch distance=5pt,
        hatch thickness/.store in=\hatchthickness,
        hatch thickness=5pt
        }
\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{north east hatch}% name
    {\pgfqpoint{-1pt}{-1pt}}% below left
    {\pgfqpoint{\hatchdistance}{\hatchdistance}}% above right
    {\pgfpoint{\hatchdistance-1pt}{\hatchdistance-1pt}}%
    {
        \pgfsetcolor{\tikz@pattern@color}
        \pgfsetlinewidth{\hatchthickness}
        \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
        \pgfpathlineto{\pgfqpoint{\hatchdistance}{\hatchdistance}}
        \pgfusepath{stroke}
    }
\makeatother

\tikzset{Pattern/.style={pattern=north east hatch, 
         pattern color=red, hatch distance=3mm, 
         hatch thickness=1pt}}

\begin{document}

%\resizebox{7.0cm}{!}{
\begin{tikzpicture}[>=triangle 45]% functia PUTERE 2^x
%\clip (-0.5,-0.5) rectangle (4.0,4.0);
% grid
%\draw[step = 0.1cm, gray, ultra thin] (-5.0, -1.0) grid (4.0, 0.0);

%
% 
\coordinate (OR) at (0.00, 0.00);
\coordinate (LX) at (-5.00, 0.00); % left x
\coordinate (RX) at (4.00, 0.00); % right x
\coordinate (BY) at (0.00, -1.00); % bottom y
\coordinate (TY) at (0.00, 8.00);
%
% axa 0x
%
\draw[->][line width=1.00pt] (LX) -- (RX);
\node[violet,fill=white] at (3.8,-0.4) {\textbf{\textit{x}}};
%
% axa 0y
%
\draw[->][line width=1.00pt] (BY) -- (TY);
\node[right,violet] at (0.2, 8.0) {{\boldmath$a^{\raisebox{+4.0pt}{$\scriptstyle{x}$}}$}};
\node[right,violet] at (0.1, 7.3) {{\boldmath$(a \,=\, 2)$}};
%
% ORIGINE
% points on the graphic
\filldraw [red] (OR) circle(2pt);
\node[violet,fill=white] at (-0.2,-0.3) {\textbf{\textit{0}}};
%
% COORDONATE -- numerotare axa Ox POZITIVA
%
\draw[violet,line width=1pt] (0.50, -0.10) -- (0.50, 0.10); % x = 0.5
\node[violet,fill=white] at (0.50, -0.40) {\textbf{\textit{x}}}; 
\draw[violet,line width=0.75pt,dotted] (0.50, 0.00) -- (0.50, 1.4142);
\filldraw [violet] (0.50, 1.4142) circle(2pt);
\node[above,violet] at (0.50, 1.4142) {\textbf{\textit{a\textsuperscript{x}}}}; 
%

\foreach \i in {-4,...,-1,1,2,3}{
 \draw[line width=1pt] (1.00*\i, -0.10) -- ++(90:0.20); % x1
 \node[fill=white] at (1.00*\i, -0.40) {$\scriptstyle{\i}$};}

%
% COORDONATE -- numerotare axa Oy POZITIVA
%
\foreach \i in {1,...,7}{
    \draw[line width=1.00pt] (-0.1, \i) -- ++(0:0.20); % y1 
    \node at (-0.40, \i) {$\scriptstyle{\i}$};
    }
%
% COORDONATE -- numerotare axa Oy NEGATIVA
%
% GRAFICUL functiei 2^x
%
\draw[violet, line width=1.75pt, domain=-5.00:3.00] plot[smooth](\x, {2^(\x)});
%
% filled circles
%
\filldraw [blue] (0.0,1.0) circle(2pt);
%
\begin{scope}[on background layer]
\node[fit={(-5,0) (4,-1)}, inner sep=0pt, Pattern] {};
\end{scope}

\end{tikzpicture}

在此处输入图片描述

更新

感谢 Gonzalo Medina，我们有pgfplots此图的版本：

\documentclass[border=3mm,tikz]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{arrows,patterns,backgrounds,fit}

\makeatletter
\tikzset{% customization of pattern
         % based on <m.wibrow@gm...> - 2013-03-24 07:20:
        hatch distance/.store in=\hatchdistance,
        hatch distance=5pt,
        hatch thickness/.store in=\hatchthickness,
        hatch thickness=5pt
        }
\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{north east hatch}% name
    {\pgfqpoint{-1pt}{-1pt}}% below left
    {\pgfqpoint{\hatchdistance}{\hatchdistance}}% above right
    {\pgfpoint{\hatchdistance-1pt}{\hatchdistance-1pt}}%
    {
        \pgfsetcolor{\tikz@pattern@color}
        \pgfsetlinewidth{\hatchthickness}
        \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
        \pgfpathlineto{\pgfqpoint{\hatchdistance}{\hatchdistance}}
        \pgfusepath{stroke}
    }
\makeatother

\tikzset{Pattern/.style={pattern=north east hatch,
         pattern color=#1, hatch distance=3mm,
         hatch thickness=1pt}}

\begin{document}

\begin{tikzpicture}[>=triangle 45]
\begin{axis}[
  axis lines=middle,
  ymax=8,
  ymin=-1,
  xmax=3.5,
  clip=false,
  xtick={-4,-3,...,3},
  ytick={1,2,...,8},
  x tick label style={fill=white}
  ]
\addplot[violet, line width=1.75pt, domain=-5.00:3.00] {2^(x)};

\node[violet,fill=white]
  at (axis cs:3.8,-0.4) {\textbf{\textit{x}}};
\node[right,violet]
  at (axis cs:0.2, 8.0)
  {{\boldmath$a^{x}$}};
\node[right,violet]
  at (axis cs:0.1, 7.3) {{\boldmath$(a \,=\, 2)$}};
\filldraw[red] (axis cs:0,0) circle(2pt);
\draw[violet,line width=0.75pt,dotted]
  (axis cs:0.50, 0.00) -- (axis cs:0.50, 1.4142);
\filldraw[violet] (axis cs:0.50, 1.4142) circle(2pt)
  node[above,violet]
    at (axis cs:0.50, 1.4142)
    {\textbf{\textit{a\textsuperscript{x}}}};
\filldraw[blue] (axis cs:0.0,1.0) circle(2pt);

\begin{scope}[on background layer]
\node[fit={(axis cs:-5,0) (axis cs:3.5,-1.3)}, inner sep=0pt, Pattern=cyan] {};
\end{scope}
\end{axis}
\end{tikzpicture}

\end{document}

生成结果：

在此处输入图片描述

Answer

下一个代码展示了如何使用pattern用户定义\hatchthickness和\hatchdistance来定义 a 。此模式取自使用带有阴影的 tikz 形状内的图案

此图案用于fill在背景层中绘制的矩形节点：

\begin{scope}[on background layer]
\node[fit={(-5,0) (4,-1)}, inner sep=0pt, Pattern] {};
\end{scope}

该模式没有考虑holes，但你可以fill=white所有需要在其上可读的节点：

\node[violet,fill=white] at (3.8,-0.4) {\textbf{\textit{x}}};

您的代码已通过模式定义减少，但也使用了一些\foreach循环来绘制。我认为，如果您使用已加载但从未使用的代码ticks，则可以进一步减少。pgfplots

下面的这段代码只显示了左图。使用类似的工具可以轻松获得右图。

\documentclass[border=3mm,tikz]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{arrows,patterns,backgrounds,fit}

\makeatletter
\tikzset{% customization of pattern
         % based on <m.wibrow@gm...> - 2013-03-24 07:20: 
        hatch distance/.store in=\hatchdistance,
        hatch distance=5pt,
        hatch thickness/.store in=\hatchthickness,
        hatch thickness=5pt
        }
\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{north east hatch}% name
    {\pgfqpoint{-1pt}{-1pt}}% below left
    {\pgfqpoint{\hatchdistance}{\hatchdistance}}% above right
    {\pgfpoint{\hatchdistance-1pt}{\hatchdistance-1pt}}%
    {
        \pgfsetcolor{\tikz@pattern@color}
        \pgfsetlinewidth{\hatchthickness}
        \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
        \pgfpathlineto{\pgfqpoint{\hatchdistance}{\hatchdistance}}
        \pgfusepath{stroke}
    }
\makeatother

\tikzset{Pattern/.style={pattern=north east hatch, 
         pattern color=red, hatch distance=3mm, 
         hatch thickness=1pt}}

\begin{document}

%\resizebox{7.0cm}{!}{
\begin{tikzpicture}[>=triangle 45]% functia PUTERE 2^x
%\clip (-0.5,-0.5) rectangle (4.0,4.0);
% grid
%\draw[step = 0.1cm, gray, ultra thin] (-5.0, -1.0) grid (4.0, 0.0);

%
% 
\coordinate (OR) at (0.00, 0.00);
\coordinate (LX) at (-5.00, 0.00); % left x
\coordinate (RX) at (4.00, 0.00); % right x
\coordinate (BY) at (0.00, -1.00); % bottom y
\coordinate (TY) at (0.00, 8.00);
%
% axa 0x
%
\draw[->][line width=1.00pt] (LX) -- (RX);
\node[violet,fill=white] at (3.8,-0.4) {\textbf{\textit{x}}};
%
% axa 0y
%
\draw[->][line width=1.00pt] (BY) -- (TY);
\node[right,violet] at (0.2, 8.0) {{\boldmath$a^{\raisebox{+4.0pt}{$\scriptstyle{x}$}}$}};
\node[right,violet] at (0.1, 7.3) {{\boldmath$(a \,=\, 2)$}};
%
% ORIGINE
% points on the graphic
\filldraw [red] (OR) circle(2pt);
\node[violet,fill=white] at (-0.2,-0.3) {\textbf{\textit{0}}};
%
% COORDONATE -- numerotare axa Ox POZITIVA
%
\draw[violet,line width=1pt] (0.50, -0.10) -- (0.50, 0.10); % x = 0.5
\node[violet,fill=white] at (0.50, -0.40) {\textbf{\textit{x}}}; 
\draw[violet,line width=0.75pt,dotted] (0.50, 0.00) -- (0.50, 1.4142);
\filldraw [violet] (0.50, 1.4142) circle(2pt);
\node[above,violet] at (0.50, 1.4142) {\textbf{\textit{a\textsuperscript{x}}}}; 
%

\foreach \i in {-4,...,-1,1,2,3}{
 \draw[line width=1pt] (1.00*\i, -0.10) -- ++(90:0.20); % x1
 \node[fill=white] at (1.00*\i, -0.40) {$\scriptstyle{\i}$};}

%
% COORDONATE -- numerotare axa Oy POZITIVA
%
\foreach \i in {1,...,7}{
    \draw[line width=1.00pt] (-0.1, \i) -- ++(0:0.20); % y1 
    \node at (-0.40, \i) {$\scriptstyle{\i}$};
    }
%
% COORDONATE -- numerotare axa Oy NEGATIVA
%
% GRAFICUL functiei 2^x
%
\draw[violet, line width=1.75pt, domain=-5.00:3.00] plot[smooth](\x, {2^(\x)});
%
% filled circles
%
\filldraw [blue] (0.0,1.0) circle(2pt);
%
\begin{scope}[on background layer]
\node[fit={(-5,0) (4,-1)}, inner sep=0pt, Pattern] {};
\end{scope}

\end{tikzpicture}

在此处输入图片描述

更新

感谢 Gonzalo Medina，我们有pgfplots此图的版本：

\documentclass[border=3mm,tikz]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{arrows,patterns,backgrounds,fit}

\makeatletter
\tikzset{% customization of pattern
         % based on <m.wibrow@gm...> - 2013-03-24 07:20:
        hatch distance/.store in=\hatchdistance,
        hatch distance=5pt,
        hatch thickness/.store in=\hatchthickness,
        hatch thickness=5pt
        }
\pgfdeclarepatternformonly[\hatchdistance,\hatchthickness]{north east hatch}% name
    {\pgfqpoint{-1pt}{-1pt}}% below left
    {\pgfqpoint{\hatchdistance}{\hatchdistance}}% above right
    {\pgfpoint{\hatchdistance-1pt}{\hatchdistance-1pt}}%
    {
        \pgfsetcolor{\tikz@pattern@color}
        \pgfsetlinewidth{\hatchthickness}
        \pgfpathmoveto{\pgfqpoint{0pt}{0pt}}
        \pgfpathlineto{\pgfqpoint{\hatchdistance}{\hatchdistance}}
        \pgfusepath{stroke}
    }
\makeatother

\tikzset{Pattern/.style={pattern=north east hatch,
         pattern color=#1, hatch distance=3mm,
         hatch thickness=1pt}}

\begin{document}

\begin{tikzpicture}[>=triangle 45]
\begin{axis}[
  axis lines=middle,
  ymax=8,
  ymin=-1,
  xmax=3.5,
  clip=false,
  xtick={-4,-3,...,3},
  ytick={1,2,...,8},
  x tick label style={fill=white}
  ]
\addplot[violet, line width=1.75pt, domain=-5.00:3.00] {2^(x)};

\node[violet,fill=white]
  at (axis cs:3.8,-0.4) {\textbf{\textit{x}}};
\node[right,violet]
  at (axis cs:0.2, 8.0)
  {{\boldmath$a^{x}$}};
\node[right,violet]
  at (axis cs:0.1, 7.3) {{\boldmath$(a \,=\, 2)$}};
\filldraw[red] (axis cs:0,0) circle(2pt);
\draw[violet,line width=0.75pt,dotted]
  (axis cs:0.50, 0.00) -- (axis cs:0.50, 1.4142);
\filldraw[violet] (axis cs:0.50, 1.4142) circle(2pt)
  node[above,violet]
    at (axis cs:0.50, 1.4142)
    {\textbf{\textit{a\textsuperscript{x}}}};
\filldraw[blue] (axis cs:0.0,1.0) circle(2pt);

\begin{scope}[on background layer]
\node[fit={(axis cs:-5,0) (axis cs:3.5,-1.3)}, inner sep=0pt, Pattern=cyan] {};
\end{scope}
\end{axis}
\end{tikzpicture}

\end{document}

生成结果：

在此处输入图片描述

Question 2

我冒昧地用该mfpic包绘制了一个例子，该包附带了一个专门为解决这类问题而构建的宏：

\thatch[<hatchsp>,<angle>][<color>]<closed path>

它用度的线填充任何封闭路径<angle>，彼此之间的距离为hatchsp。另一个宏，\hatchwd{}宏指定这些线的宽度。还有两个其他阴影宏作为\thatch具有预定义角度的变体，\rhatch（从左下角到右上角）和\lhatch（从右下角到左上角）。

在此示例中，所有孵化工作均按照以下指令完成：

\hatchwd{1pt}
\rhatch[3mm][Cyan]\rect{(\xmin, \ymin), (\xmax, 0)}

完整代码：

\documentclass{scrartcl}
\usepackage{multido, xcolor}
\usepackage[metapost, clip, overlaylabels]{mfpic}
    \setlength{\mfpicunit}{1cm}
    \opengraphsfile{\jobname}
\begin{document}
\begin{mfpic}[1]{-7}{3.9}{-1.5}{8.9}
    % Function
    \penwd{1pt}
    \fdef{f}{x}{2**x}
   \draw[magenta]\function{\xmin, \xmax, 0.05}{f(x)}    
   % Hatching
   \hatchwd{1pt}
   \rhatch[3mm][Cyan]\rect{(\xmin, \ymin), (\xmax, 0)}
   % Axes and marks
   \penwd{.5pt}
   \doaxes{xy}
   \xmarks{ceiling(\xmin) upto -1}\xmarks{1 upto floor(\xmax)}
   \ymarks{ceiling(\ymin) upto -1}\ymarks{2 upto floor(\ymax)}
   \pointcolor{red}\point[4pt]{(0, 0)}
   \pointcolor{blue}\point[4pt]{(0, 1)}
   % Labels
   \setrender{\gclear}
   \tlpointsep{3pt}
    \tlabelrect[][tr](0, 0){$O$} 
    \tlabelrect[][tc](\xmax, 0){$x$} 
    \tlabel[cr](0, \ymax){$y$}
    \tlpointsep{6pt}
    \tlpathsep{1pt}
    \multido{\i=\xmin+1}{-\xmin}{\tlabelrect[][tc](\i, 0){$\i$}}
    \multido{\i=1+1}{\xmax}{\tlabelrect[][tc](\i, 0){$\i$}}
    \multido{\i=1+1}{\ymax}{\tlabel[cr](0, \i){$\i$}}
    \tlabelrect[][cr](0, -1){$-1$}
    \drawcolor{magenta}
    \dashed\lines{(0.5, 0), (0.5, 1.414)}
    \tlabel[cr](3, 8){\textcolor{magenta}{$a^x (a=2)$}}
    \tlabel[bc](0.5, 1.414){\textcolor{magenta}{$a^x$}}
    \tlabelrect[][tc](0.5, 0){\textcolor{magenta}{$x$}}
\end{mfpic}
\closegraphsfile
\end{document}

首先使用 LaTeX 进行编译（无论使用什么引擎），然后.mp使用 MetaPost 编译生成的文件，最后.tex再次使用 LaTeX 编译该文件。

在此处输入图片描述

Answer

我冒昧地用该mfpic包绘制了一个例子，该包附带了一个专门为解决这类问题而构建的宏：

\thatch[<hatchsp>,<angle>][<color>]<closed path>

它用度的线填充任何封闭路径<angle>，彼此之间的距离为hatchsp。另一个宏，\hatchwd{}宏指定这些线的宽度。还有两个其他阴影宏作为\thatch具有预定义角度的变体，\rhatch（从左下角到右上角）和\lhatch（从右下角到左上角）。

在此示例中，所有孵化工作均按照以下指令完成：

\hatchwd{1pt}
\rhatch[3mm][Cyan]\rect{(\xmin, \ymin), (\xmax, 0)}

完整代码：

\documentclass{scrartcl}
\usepackage{multido, xcolor}
\usepackage[metapost, clip, overlaylabels]{mfpic}
    \setlength{\mfpicunit}{1cm}
    \opengraphsfile{\jobname}
\begin{document}
\begin{mfpic}[1]{-7}{3.9}{-1.5}{8.9}
    % Function
    \penwd{1pt}
    \fdef{f}{x}{2**x}
   \draw[magenta]\function{\xmin, \xmax, 0.05}{f(x)}    
   % Hatching
   \hatchwd{1pt}
   \rhatch[3mm][Cyan]\rect{(\xmin, \ymin), (\xmax, 0)}
   % Axes and marks
   \penwd{.5pt}
   \doaxes{xy}
   \xmarks{ceiling(\xmin) upto -1}\xmarks{1 upto floor(\xmax)}
   \ymarks{ceiling(\ymin) upto -1}\ymarks{2 upto floor(\ymax)}
   \pointcolor{red}\point[4pt]{(0, 0)}
   \pointcolor{blue}\point[4pt]{(0, 1)}
   % Labels
   \setrender{\gclear}
   \tlpointsep{3pt}
    \tlabelrect[][tr](0, 0){$O$} 
    \tlabelrect[][tc](\xmax, 0){$x$} 
    \tlabel[cr](0, \ymax){$y$}
    \tlpointsep{6pt}
    \tlpathsep{1pt}
    \multido{\i=\xmin+1}{-\xmin}{\tlabelrect[][tc](\i, 0){$\i$}}
    \multido{\i=1+1}{\xmax}{\tlabelrect[][tc](\i, 0){$\i$}}
    \multido{\i=1+1}{\ymax}{\tlabel[cr](0, \i){$\i$}}
    \tlabelrect[][cr](0, -1){$-1$}
    \drawcolor{magenta}
    \dashed\lines{(0.5, 0), (0.5, 1.414)}
    \tlabel[cr](3, 8){\textcolor{magenta}{$a^x (a=2)$}}
    \tlabel[bc](0.5, 1.414){\textcolor{magenta}{$a^x$}}
    \tlabelrect[][tc](0.5, 0){\textcolor{magenta}{$x$}}
\end{mfpic}
\closegraphsfile
\end{document}

首先使用 LaTeX 进行编译（无论使用什么引擎），然后.mp使用 MetaPost 编译生成的文件，最后.tex再次使用 LaTeX 编译该文件。

在此处输入图片描述

用于数学图形的优雅哈希区域......

答案1

答案2

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