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复杂平面图缩放问题

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复杂平面图缩放问题

我在 2018 年制作了所附图片。它完全满足了我的教程目的。现在我想将它添加到我的讲义中。但问题是，当我缩小它时，即使使用变换形状，它也会使用叠加，东西会扭曲。如果有人可以帮助缩小图片，以便它可以适应任何尺寸，例如缩放到 0.7 而不会扭曲它。我记得我花了很多时间来制作它，当时我还在学习 pgfplots。完整的运行代码附在此处。

\documentclass[a3paper,landscape]{article}
\usepackage{tikz}
\usetikzlibrary{shapes.misc}
\usetikzlibrary{arrows.meta}
\usepackage{steinmetz}
\usepackage{xcolor}
\usepackage{background}

\usepackage{amsmath,mleftright}
\usepackage{xparse}

\NewDocumentCommand{\evalat}{sO{\big}mm}{%



\IfBooleanTF{#1}
  {\mleft. #3 \mright|_{#4}}
  {#3#2|_{#4}}%
}

\backgroundsetup{%
  scale=1,       %% change accordingly
  angle=0,       %% change accordingly
  opacity=.5,    %% change accordingly
  color =black,  %% change accordingly
  contents={
%   \begin{tikzpicture}[remember picture,overlay]
%         \node at (-11.5,-8.5) {\includegraphics[width=0.25\textwidth]{seal.png}};    %% yshift and xshift for example only
%     \end{tikzpicture}
    }
}

\begin{document}
 \thispagestyle{empty}

\begin{tikzpicture}[remember picture, overlay]
    \node [shift={(0cm,0cm)}]  at (current page.center)
        {%
\begin{tikzpicture}

    \begin{scope}[thick,font=\scriptsize]
    % Axes:
    % Are simply drawn using line with the `->` option to make them arrows:
    % The main labels of the axes can be places using `node`s:
    \draw [->] (-10,0) -- (10,0) node [xshift=1cm]  {\large $\Re\{s\}$};
    \draw [->] (0,-10) -- (0,10) node [yshift=0.7cm] {\large $\Im\{s\}$};

    % Axes labels:
    % Are drawn using small lines and labeled with `node`s. The placement can be set using options
    \iffalse% Single
% If you only want a single label per axis side:
\draw (1,-3pt) -- (1,3pt)   node [above] {$1$};
\draw (-1,-3pt) -- (-1,3pt) node [above] {$-1$};
\draw (-3pt,1) -- (3pt,1)   node [right] {$i$};
\draw (-3pt,-1) -- (3pt,-1) node [right] {$-i$};
\else% Multiple
% If you want labels at every unit step:
\foreach \n in {-10,...,-1,1,2,...,10}{%
    \draw (\n,-3pt) -- (\n,3pt)   node [above] {$\n$};
    \draw (-3pt,\n) -- (3pt,\n)   node [right] {$\n i$};
}
\fi
\end{scope}
% The circle is drawn with `(x,y) circle (radius)`
% You can draw the outer border and fill the inner area differently.
% Here I use gray, semitransparent filling to not cover the axes below the circle
% \path [draw=none,fill=gray,semitransparent] (+1,-1) circle (3);
% Place the equation into the circle:
% \node [below right,darkgray] at (+1,-1) {$|z-1+i| \leq 3$};
\node[cross out,draw=black, line width=1mm] at (-3,3) {};
\node[cross out,draw=black, line width=1mm] at (-3,-3) {};
\draw (0,7) -- (-3,3) node[midway,above=8pt,left=1pt, rotate=45] {$5$};
\draw (0,7) -- (-3,-3) node at (-1.8,1) [above=12pt,left=2pt, rotate=65] {$10.4$};
\draw (0,7) -- (3,7);
\draw [thick,->] (1,7) arc (0:233.13:1cm) node[midway,above=1pt,left=1pt] {$233.1^{\circ}$};
\draw [thick,->] (3,7) arc (0:253.3:3cm) node[midway,above=1pt,left=1pt] {$253.3^{\circ}$};
\draw [dashed] (-3,3) -- (-2.2,3) node [xshift=10pt] {$3$};
\draw [dashed] (0,3) -- (-1.4,3);
\draw [dashed] (-3,-3) -- (-1.7,-3) node [xshift=5pt] {$3$};
\draw [dashed] (0,-3) -- (-1.4,-3);
\fill [blue]  (0,7) -- (0,5) arc (-90:-106.7:2cm) -- cycle node [rotate=45] at (-0.35,4.5) {$\mathbf{16.7^{\circ}}$};
\fill [gray] (0,7) -- (-0.57,5.08) arc (-106.7:-126.87:2cm) -- cycle node [rotate=45] at (-1.2,4.8) {$\mathbf{20.2^{\circ}}$};
\draw (0,3) -- (3,3);
\draw [<-, dashed] (1,7) -- (1,5.6) node [yshift=-15pt] {$4$}; 
\draw [->,dashed] (1,4.5) -- (1,3);
\draw [<-, dashed] (1,3) -- (1,-0.5) node [yshift=-15pt] {$6$}; 
\draw [->,dashed] (1,-1.5) -- (1,-3);
\draw (0,-3) -- (3,-3);
\node at (-9,7) {\large $\evalat{H(s)}{s=0+7i}\:=\:\dfrac{1}{5 \times 10.44}\:=\:0.019$};
\draw [thick,->] (-9.2,6.5) -- (-1.9,5.2);
\draw [thick,->] (-8,6.5) -- (-2.3,1);
\node at (-9,10) {\large $\evalat{\phase{H(s)}}{s=0+7i}\:=\:\dfrac{\phase{0^{\circ}}}{\phase{233.1^{\circ}}\:\phase{253.3^{\circ}}}\:=\:\phase{-486.4^{\circ}}$};
\node at (-10.5,8.5) {\large $\phase{-486.4^{\circ}}\:=\: \phase{-126.4^{\circ}}$};
\draw [->] (-7.3,9.6) -- (-3,9.4);
\draw [->] (-9,9.4) -- (-1.8,8);
\node at (-10,-5) {\Large $\mathbf{u(t)=sin(7t)}$};
\node at (7,-5) {\Large $\mathbf{y_{ss}(t)=0.019 \times sin(7t-126.4^{\circ})}$};
\draw [thick, orange] (0,0) -- (-3,3) node at (-1,1) [above=8pt,left=-5pt, rotate=-45] {$\sqrt{18}$};
\draw [thick, orange] (0,0) -- (-3,-3) node at (-1,-1) [below=8pt,left=-5pt, rotate=45] {$\sqrt{18}$};
\draw [thick, ->, orange] (1,0) arc (0:135:1cm) node[midway,above=8pt,left=-15pt] {$135^{\circ}$};
\draw [thick, ->, orange] (1,0) arc (0:-135:1cm) node[midway,above=8pt,left=-5pt] {$-135^{\circ}$};
 \node [orange] at (6,4) {\large $\evalat{H(s)}{s=0+0i}\:=\:\dfrac{1}{\sqrt{18} \times \sqrt{18}}\:=\:0.0\bar{5}$};
 \draw [orange, ->] (6,3.5) -- (-0.65,1.5);
 \draw [orange, ->] (7.3,3.5) -- (7.3,-1.6) -- (-0.8,-1.6);
 \node [orange] at (6,6) {\large $\color{orange}\evalat{\phase{{\color{orange}{H(s)}}}}{s=0+0i}\:=\:\color{orange}\dfrac{\color{orange}\phase{{\color{orange}{0^{\circ}}}}}{\color{orange}\phase{{\color{orange}{135^{\circ}}}}\:\phase{{\color{orange}{-135^{\circ}}}}}\:=\:\color{orange}\phase{{\color{orange}{0^{\circ}}}}$};
 \draw [orange, ->] (8.2,5.6) -- (10,5.5) -- (10,-0.65) -- (0.5,-0.65);
  \draw [orange, ->] (6,5.3) -- (9.5,4.5) -- (9.5,1.15) -- (0.8,1.15);
  \draw [line width=1mm] (6,7.5) -- (6,10.6) -- (11,10.6) -- (11,7.5) -- (6,7.5);
  \node at (8.5,10) {\large $H(s)\:=\:\dfrac{1}{s^2+6s+18}$};
  \node [orange] at (8.5,9) {\large DC Gain in orange};
  \node at (8.5,8) {\large $|H(s)|\:\&\:\phase{H(s)}$ in Black};
  \node [rotate=90, red!40!gray] at (13.5,1) {\Large 

\textbf{LTI SYSTEM STEADY STATE RESPONSE TO SINUSOIDAL INPUT}};
    \node [purple!40!gray] at (9,-9.5) {\Large \textbf{GRAPHICAL VIEW}};
\end{tikzpicture}
};
        % % Draw a page border
        % \draw (current page.north west) rectangle (current page.south east);
\end{tikzpicture}

\end{document}

图片

答案1

使用包adjustbox和

（用于笔记）\documentclass{article}

开始图片为

\begin{tikzpicture}[remember picture, overlay]
    \node [shift={(0cm,0cm)}]  at (current page.center)
    {%      
    \begin{adjustbox}{width=4.5in}% % added <<<<<<<
            \begin{tikzpicture}

和结束

    \node [purple!40!gray] at (9,-9.5) {\Large \textbf{GRAPHICAL VIEW}};
        \end{tikzpicture}   
    \end{adjustbox} % added <<<<<<<<<<
    };
    % % Draw a page border
    % \draw (current page.north west) rectangle (current page.south east);
\end{tikzpicture}

你会得到

b

宽度较小时无明显扭曲。

这是完整的代码。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{shapes.misc}
\usetikzlibrary{arrows.meta}
\usepackage{steinmetz}
\usepackage{xcolor}
\usepackage{background}

\usepackage{amsmath,mleftright}
\usepackage{xparse}

\NewDocumentCommand{\evalat}{sO{\big}mm}{%  
    \IfBooleanTF{#1}
    {\mleft. #3 \mright|_{#4}}
    {#3#2|_{#4}}%
}

\backgroundsetup{%
    scale=1,       %% change accordingly
    angle=0,       %% change accordingly
    opacity=.5,    %% change accordingly
    color =black,  %% change accordingly
    contents={
        %   \begin{tikzpicture}[remember picture,overlay]
        %         \node at (-11.5,-8.5) {\includegraphics[width=0.25\textwidth]{seal.png}};    %% yshift and xshift for example only
        %     \end{tikzpicture}
    }
}

\usepackage{showframe} % show the margin <<<<<<<<<<<<<<<<<<

\usepackage{adjustbox} % added <<<<<<<<<<<<<<<<<<<<<<<

\begin{document}
    \thispagestyle{empty}
    
    \begin{tikzpicture}[remember picture, overlay]
        \node [shift={(0cm,0cm)}]  at (current page.center)
        {%      
        \begin{adjustbox}{width=4.5in}% % added <<<<<<<
                \begin{tikzpicture}
                
                \begin{scope}[thick,font=\scriptsize]
                    % Axes:
                    % Are simply drawn using line with the `->` option to make them arrows:
                    % The main labels of the axes can be places using `node`s:
                    \draw [->] (-10,0) -- (10,0) node [xshift=1cm]  {\large $\Re\{s\}$};
                    \draw [->] (0,-10) -- (0,10) node [yshift=0.7cm] {\large $\Im\{s\}$};
                    
                    % Axes labels:
                    % Are drawn using small lines and labeled with `node`s. The placement can be set using options
                    \iffalse% Single
                    % If you only want a single label per axis side:
                    \draw (1,-3pt) -- (1,3pt)   node [above] {$1$};
                    \draw (-1,-3pt) -- (-1,3pt) node [above] {$-1$};
                    \draw (-3pt,1) -- (3pt,1)   node [right] {$i$};
                    \draw (-3pt,-1) -- (3pt,-1) node [right] {$-i$};
                    \else% Multiple
                    % If you want labels at every unit step:
                    \foreach \n in {-10,...,-1,1,2,...,10}{%
                        \draw (\n,-3pt) -- (\n,3pt)   node [above] {$\n$};
                        \draw (-3pt,\n) -- (3pt,\n)   node [right] {$\n i$};
                    }
                    \fi
                \end{scope}
                % The circle is drawn with `(x,y) circle (radius)`
                % You can draw the outer border and fill the inner area differently.
                % Here I use gray, semitransparent filling to not cover the axes below the circle
                % \path [draw=none,fill=gray,semitransparent] (+1,-1) circle (3);
                % Place the equation into the circle:
                % \node [below right,darkgray] at (+1,-1) {$|z-1+i| \leq 3$};
                \node[cross out,draw=black, line width=1mm] at (-3,3) {};
                \node[cross out,draw=black, line width=1mm] at (-3,-3) {};
                \draw (0,7) -- (-3,3) node[midway,above=8pt,left=1pt, rotate=45] {$5$};
                \draw (0,7) -- (-3,-3) node at (-1.8,1) [above=12pt,left=2pt, rotate=65] {$10.4$};
                \draw (0,7) -- (3,7);
                \draw [thick,->] (1,7) arc (0:233.13:1cm) node[midway,above=1pt,left=1pt] {$233.1^{\circ}$};
                \draw [thick,->] (3,7) arc (0:253.3:3cm) node[midway,above=1pt,left=1pt] {$253.3^{\circ}$};
                \draw [dashed] (-3,3) -- (-2.2,3) node [xshift=10pt] {$3$};
                \draw [dashed] (0,3) -- (-1.4,3);
                \draw [dashed] (-3,-3) -- (-1.7,-3) node [xshift=5pt] {$3$};
                \draw [dashed] (0,-3) -- (-1.4,-3);
                \fill [blue]  (0,7) -- (0,5) arc (-90:-106.7:2cm) -- cycle node [rotate=45] at (-0.35,4.5) {$\mathbf{16.7^{\circ}}$};
                \fill [gray] (0,7) -- (-0.57,5.08) arc (-106.7:-126.87:2cm) -- cycle node [rotate=45] at (-1.2,4.8)     {$\mathbf{20.2^{\circ}}$};
                \draw (0,3) -- (3,3);
                \draw [<-, dashed] (1,7) -- (1,5.6) node [yshift=-15pt] {$4$}; 
                \draw [->,dashed] (1,4.5) -- (1,3);
                \draw [<-, dashed] (1,3) -- (1,-0.5) node [yshift=-15pt] {$6$}; 
                \draw [->,dashed] (1,-1.5) -- (1,-3);
                \draw (0,-3) -- (3,-3);
                \node at (-9,7) {\large $\evalat{H(s)}{s=0+7i}\:=\:\dfrac{1}{5 \times 10.44}\:=\:0.019$};
                \draw [thick,->] (-9.2,6.5) -- (-1.9,5.2);
                \draw [thick,->] (-8,6.5) -- (-2.3,1);
                \node at (-9,10) {\large        $\evalat{\phase{H(s)}}{s=0+7i}\:=\:\dfrac{\phase{0^{\circ}}}{\phase{233.1^{\circ}}\:\phase{253.3^{\circ}}}\:=\:\phase{-486.4^{\circ}}$};
                \node at (-10.5,8.5) {\large $\phase{-486.4^{\circ}}\:=\: \phase{-126.4^{\circ}}$};
                \draw [->] (-7.3,9.6) -- (-3,9.4);
                \draw [->] (-9,9.4) -- (-1.8,8);
                \node at (-10,-5) {\Large $\mathbf{u(t)=sin(7t)}$};
                \node at (7,-5) {\Large $\mathbf{y_{ss}(t)=0.019 \times sin(7t-126.4^{\circ})}$};
                \draw [thick, orange] (0,0) -- (-3,3) node at (-1,1) [above=8pt,left=-5pt, rotate=-45] {$\sqrt{18}$};
                \draw [thick, orange] (0,0) -- (-3,-3) node at (-1,-1) [below=8pt,left=-5pt, rotate=45] {$\sqrt{18}$};
                \draw [thick, ->, orange] (1,0) arc (0:135:1cm) node[midway,above=8pt,left=-15pt] {$135^{\circ}$};
                \draw [thick, ->, orange] (1,0) arc (0:-135:1cm) node[midway,above=8pt,left=-5pt] {$-135^{\circ}$};
                \node [orange] at (6,4) {\large $\evalat{H(s)}{s=0+0i}\:=\:\dfrac{1}{\sqrt{18} \times \ sqrt{18}}\:=\:0.0\bar{5}$};
                \draw [orange, ->] (6,3.5) -- (-0.65,1.5);
                \draw [orange, ->] (7.3,3.5) -- (7.3,-1.6) -- (-0.8,-1.6);
                \node [orange] at (6,6) {\large     $\color{orange}\evalat{\phase{{\color{orange}{H(s)}}}}{s=0+0i}\:=\:\color{orange}\dfrac{\color{orange}\phase{{\color{orange}{0^{\circ}}}}}{\color{orange}\phase{{\color{orange}{135^{\circ}}}}\:\phase{{\color{orange}{-135^{\circ}}}}}\:=\:\color{orange}\phase{{\color{orange}{0^{\circ}}}}$};
                    \draw [orange, ->] (8.2,5.6) -- (10,5.5) -- (10,-0.65) -- (0.5,-0.65);
                \draw [orange, ->] (6,5.3) -- (9.5,4.5) -- (9.5,1.15) -- (0.8,1.15);
                \draw [line width=1mm] (6,7.5) -- (6,10.6) -- (11,10.6) -- (11,7.5) -- (6,7.5);
                \node at (8.5,10) {\large $H(s)\:=\:\dfrac{1}{s^2+6s+18}$};
                \node [orange] at (8.5,9) {\large DC Gain in orange};
                \node at (8.5,8) {\large $|H(s)|\:\&\:\phase{H(s)}$ in Black};
                \node [rotate=90, red!40!gray] at (13.5,1) {\Large                  
                \textbf{LTI SYSTEM STEADY STATE RESPONSE TO SINUSOIDAL INPUT}};
                \node [purple!40!gray] at (9,-9.5) {\Large \textbf{GRAPHICAL VIEW}};
            \end{tikzpicture}   
        \end{adjustbox} % added <<<<<<<<<<
        };
        % % Draw a page border
        % \draw (current page.north west) rectangle (current page.south east);
    \end{tikzpicture}   
    
\end{document}

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