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如何在 LaTeX 中制作这样的数学图形？

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如何在 LaTeX 中制作这样的数学图形？

该图是 Boggiatto 等人于 2010 年绘制的图片，我想在 LaTeX 中重现该图片，但无法绘制图表

  • 一个圆圈
  • 一个正方形
  • 正方形与圆形的交点
  • 将密度转化为平方

在此处输入图片描述

TeXLive：2016

答案1

我做了一些改动，比如背景颜色改为了点状，但 Tikz 中可以做出完全相同的插图。我的插图如下。

在此处输入图片描述

蒂克兹

\documentclass{article}
\usepackage{graphicx}  
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\draw [thick] (2,2) circle (3cm);
\draw (-2,-2) rectangle (6,6);
\draw (0,5.5) node{Cohen class: $\sigma * Wig$};
\draw [opacity=0.4,fill=black!15,rounded corners=2ex] (-1.9,-1.9) rectangle (5.9,2);

\draw (1,-1.6) node{Generalised spectograms: $Sp_{\phi,\psi}$};


\draw (2,2.5) node[circle,fill,inner sep=1pt,label=below:{$Q=\int_{[0,1]}Wig_{\tau} d\tau$}]{};
\draw (2,-1) node[circle,fill,inner sep=1pt,label=right:{$Sp_{\phi}$(classical spectogram)}]{};
\draw (2,5) node[circle,fill,inner sep=1pt,label=right:{$Wig_{1/2}=Wig$ (Wigner)}]{};
\draw (-0.6,3.5) node[circle,fill,inner sep=1pt,label=left:{$Wig_{\tau}$ ($\tau$-Wigner)}]{};

\draw (5,2) node[circle,fill,inner sep=1pt,label=above right:{$Wig_1=Sp_{1,\delta}=R^*$}]{};
\draw (5,1.5) node[circle,fill,inner sep=0pt,label=above right:{(conjugate-Rihaczek)}]{};

\draw (-1,2) node[circle,fill,inner sep=1pt,label=above left:{$Wig_0=Sp_{\delta,1}=R$}]{};
\draw (-1,1.5) node[circle,fill,inner sep=0pt,label=above left:{(Rihaczek)}]{};

\end{tikzpicture}

\end{document}

有关的

  1. \\我不明白为什么Tikz-draw 标签中的换行功能不起作用：如何在 TikZ 节点标签中引入换行符？应该这样，，\draw (5,2) node[circle,fill,inner sep=1pt,label=above right:{$Wig_1=Sp_{1,\delta}=R^*$\\(conjugate-Rihaczek)}]{};为什么换行不起作用？

对于自定义背景，如圆点或五角星

使用\usetikzlibrary{patterns}包来自定义背景，比如下面的星星或圆点，以及其他指令这里。

在此处输入图片描述

\documentclass{article}
\usepackage{graphicx}  
\usepackage{tikz}
\usetikzlibrary{patterns}

\begin{document}

\begin{tikzpicture}
\draw [thick] (2,2) circle (3cm);
\draw (-2,-2) rectangle (6,6);
\draw (0,5.5) node{Cohen class: $\sigma * Wig$};
\draw [opacity=0.4,fill=black!15,pattern=dots,rounded corners=2ex] (-1.9,-1.9) rectangle (5.9,2);

\draw (1,-1.6) node{Generalised spectograms: $Sp_{\phi,\psi}$};


\draw (2,2.5) node[circle,fill,inner sep=1pt,label=below:{$Q=\int_{[0,1]}Wig_{\tau} d\tau$}]{};
\draw (2,-1) node[circle,fill,inner sep=1pt,label=right:{$Sp_{\phi}$(classical spectogram)}]{};
\draw (2,5) node[circle,fill,inner sep=1pt,label=right:{$Wig_{1/2}=Wig$ (Wigner)}]{};
\draw (-0.6,3.5) node[circle,fill,inner sep=1pt,label=left:{$Wig_{\tau}$ ($\tau$-Wigner)}]{};

\draw (5,2) node[circle,fill,inner sep=1pt,label=above right:{$Wig_1=Sp_{1,\delta}=R^*$}]{};
\draw (5,1.5) node[circle,fill,inner sep=0pt,label=above right:{(conjugate-Rihaczek)}]{};

\draw (-1,2) node[circle,fill,inner sep=1pt,label=above left:{$Wig_0=Sp_{\delta,1}=R$}]{};
\draw (-1,1.5) node[circle,fill,inner sep=0pt,label=above left:{(Rihaczek)}]{};

\end{tikzpicture}

\end{document}

在此处输入图片描述

这里更像原版

\usepackage{tikz}
\usetikzlibrary{patterns}

\begin{document}

\begin{tikzpicture}
\draw [thick] (2,2) circle (3cm);
\draw (-2,-2) rectangle (6,6);
\draw (0,5.5) node{Cohen class: $\sigma * Wig$};
\draw [opacity=0.4,fill=black!15,pattern=dots] (-1.9,-1.9) rectangle (5.9,2);

\draw (1,-1.6) node{Generalised spectograms: $Sp_{\phi,\psi}$};


\draw (2,2.5) node[circle,fill,inner sep=1pt,label=below:{$Q=\int_{[0,1]}Wig_{\tau} d\tau$}]{};
\draw (2,-1) node[circle,fill,inner sep=1pt,label=right:{$Sp_{\phi}$(classical spectogram)}]{};
\draw (2,5) node[circle,fill,inner sep=1pt,label=right:{$Wig_{1/2}=Wig$ (Wigner)}]{};
\draw (-0.6,3.5) node[circle,fill,inner sep=1pt,label=left:{$Wig_{\tau}$ ($\tau$-Wigner)}]{};

\draw (5,2) node[circle,fill,inner sep=1pt,label=above right:{$Wig_1=Sp_{1,\delta}=R^*$}]{};
\draw (5,1.5) node[circle,fill,inner sep=0pt,label=above right:{(conjugate-Rihaczek)}]{};

\draw (-1,2) node[circle,fill,inner sep=1pt,label=above left:{$Wig_0=Sp_{\delta,1}=R$}]{};
\draw (-1,1.5) node[circle,fill,inner sep=0pt,label=above left:{(Rihaczek)}]{};

\end{tikzpicture}

\end{document}

在此处输入图片描述

答案2

这是一个pstricks解决方案，需要以下代码，取自pstricks 页面在 TUG 网站上，它定义了新的填充样式：

% D.G. addition begin - Sep. 1, 2002
% To define dashed and dotted hatched styles
\ProvidesPackage{pst-hatch}%% Added B.  A.  Nov.  23, 2016
\RequirePackage{pstricks}%% added
\def\pshs@solid{0 setlinecap }
\def\pshs@dashed{[ \psk@dash ] 0 setdash }
\def\pshs@dotted{[ 0 \psk@dotsep CLW add ] 0 setdash 1 setlinecap }
\def\psset@hatchstyle#1{%
\@ifundefined{pshs@#1}%
{\@pstrickserr{Hatch style `#1' not defined}\@eha}%
{\edef\pshatchstyle{#1}}}

\psset@hatchstyle{solid}

\def\pst@linefill{%
% D.G. modification begin - Sep. 1, 2002
\@nameuse{pshs@\pshatchstyle}
% D.G. modification end
\psk@hatchangle rotate
\psk@hatchwidth SLW
\pst@usecolor\pshatchcolor
\psk@hatchsep
\tx@LineFill}

\pst@def{LineFill}<{%
gsave
  abs CLW add
  /a ED
  a 0 dtransform
  round exch round exch 2 copy idtransform
  exch Atan rotate idtransform
  pop
  /a ED
  .25 .25 itransform
  pathbbox
  /y2 ED
  a Div ceiling cvi
  /x2 ED
  /y1 ED
  a Div cvi
  /x1 ED
  /y2 y2 y1 sub def
  clip
  newpath
% D.G. modification begin - Sep. 1, 2002
% 2 setlinecap
% D.G. modification end
  systemdict
  /setstrokeadjust
    known { true setstrokeadjust } if
    x2 x1 sub 1 add
    { x1 a mul y1 moveto
      0 y2 rlineto
      stroke
      /x1 x1 1 add def } repeat
  grestore
pop pop}>

该图的 pstricks 代码：

\documentclass[border=12pt]{standalone}
\usepackage{amsmath} %
\DeclareMathOperator\Wig{\mathit{Wig}}
\DeclareMathOperator\Sp{\textit{Sp}}

\usepackage{pstricks-add, pst-hatch, auto-pst-pdf}%

\begin{document}

\small
\psset{linejoin=1, unit =3cm }
\begin{pspicture}[PointSymbol=none](-2,-2)(2,2)
    \psframe(-1.65,-1.6)(1.65,1.6)
    \psframe[fillstyle=vlines, hatchstyle=dotted](-1.55,-1.55)(1.55,0)
    \pscircle(0,0){1}
    \dotnodes(1; 0){A}(1; 90){B}(1; 135){C}(1; 180){D}(1; 270){E}(0.25; 90){F}
    \uput[d](A){\begin{tabular}{c}$\Wig₁ = \Sp_{1,δ} = R^*$ \\(conjugate-Rihaczeck)\end{tabular}}
    \uput[-75](D){\begin{tabular}{c}$\Wig₀ = \Sp_{δ,1} = R$ \\(Rihaczeck)\end{tabular}}
    \uput[50](B){$ \Wig_{1/2} = \Wig$\quad(Wigner)}
    \uput[-70](C){$ Wig_τ\quad\tau$-Wigner}
    \uput[65](E){$\Sp_\phi$ (classical spectrogram)}
    \uput[-65](F){$Q = ∫_{[0,1]}\Wig_τ\,dτ$}
    \rput [l](-1.5,-1.4){\textbf{generalised spectrogram: } $\Sp_{\phi, ψ}$}
    \rput[l](-1.5,1.4){\textbf{Cohen class: } $σ*\Wig$}
\end{pspicture}

\end{document}

在此处输入图片描述

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