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绘制持久同源条形码

tag-icon • tag-icon tikz-pgf pstricks asymptote draw
绘制持久同源条形码

我正在尝试绘制持久同源性条形码，但我不知道该怎么做。它必须是这样的：

（示例取自 Polterovich 等人著《几何与分析中的拓扑持久性》第 56 页）

任何帮助将非常感激。

答案1

使用 TikZ：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{arrows.meta}
\tikzset{    
    mypoint/.style={
        circle,
        draw,
        inner sep=.3mm
        },  
    whitepoint/.style={
        fill=white, 
        mypoint
        },  
    blackpoint/.style={
        fill=black, 
        mypoint
        },  
    textnode/.style={
        text height=2.5ex, 
        text depth=1ex
        },  
    }
\begin{document}
\begin{tikzpicture}[scale=2]
\draw[-latex] (-.5,0) -- (3,0); \draw[dashed, lightgray] (0,0) -- (0,.8);
\draw[dashed, lightgray] (1,0) -- (1,.8);
\draw[dashed, lightgray] (1.732,0) -- (1.732,.9);
\draw[dashed, lightgray] (2,0) -- (2,.9);
\foreach \x in  {0,1,1.732,2}
\node[blackpoint] at (\x,0){};
\foreach \x in  {0,1,2}
\node[textnode] at (\x,-.2) {\x};
\node[textnode] at (1.732,-.2) {$\sqrt{3}$};
\node[textnode] at (2.9,-.2) {$t$};
\node[whitepoint] (h01) at (0,.2){};
\draw (0,.2) node[whitepoint] {} -- (3,.2);
\foreach \x in  {.3,.4,...,.7}
\draw (0,\x) node[whitepoint] {} -- (1,\x) node[blackpoint] {};
\draw (1,.8) node[whitepoint] {} --  node[above]{$H_1$} (1.732,.8) node[blackpoint] {};
\draw (1.732,.9) node[whitepoint] {} -- node[above]{$H_2$} (2,.9) node[blackpoint] {};
\draw (0,.1) -- ++(-.1,0) -- node[left]{$H_0$}  ++(0,.7) -- ++(.1,0);
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

这是一个简单的 PSTricks 解决方案，仅用于娱乐或比较目的。

在此处输入图片描述

\documentclass[pstricks,border=12pt,12pt]{standalone}
\begin{document}
\psset{xunit=3cm,yunit=1.2cm}
\begin{pspicture}(-.25,-.5)(2.25,2.25)
    \psline[arrowinset=0]{->}(-.25,0)(2.25,0)
    \psset{linecolor=gray,linestyle=dashed,dash=2pt 1pt}
    \psline(0,0)(0,1.7)
    \psline(1,0)(1,1.7)
    \psline(!3 sqrt 0)(!3 sqrt 1.9)
    \psline(2,0)(2,1.9)
    \psset{linecolor=black,linestyle=solid}
    \foreach \i/\j in {0/0,1/1,{3/\sqrt{3}},4/2}{%
        \pscircle*(!\i\space sqrt 0){2pt}
        \rput(!\i\space sqrt -.35){$\j$}}
    \rput(2.2,-.35){$t$}
    \psline{o-}(0,.5)(2.25,.5)
    \foreach \i in {1,2,...,5}{\psline{o-*}(!0 .5 0.2 \i\space mul add)(!1 .5 0.2 \i\space mul add)}
    \psline{o-*}(1,1.7)(!3 sqrt 1.7)
    \psline{o-*}(!3 sqrt 1.9)(2,1.9)
    \rput(1.35,1.9){$H_1$}
    \rput(!3 sqrt .15 add 2.1){$H_2$}
    \rput(-.17,1){$H_0$}
    \psline(0,1.6)(-.05,1.6)(-.05,.4)(0,.4)
\end{pspicture}
\end{document}

答案3

arrows对于使用（和calc的）稍微不同的 TikZ 解决方案sqrt(3)：

\documentclass[tikz]{standalone}

\usetikzlibrary{arrows,calc}

\begin{document}
\begin{tikzpicture}[scale=3]
    % Vertical dashed lines
    \draw[dashed, lightgray] (0,0) -- (0,.8);
    \draw[dashed, lightgray] (1,0) -- (1,.8);
    \draw[dashed, lightgray] ({sqrt(3)},0) -- ({sqrt(3)},.9);
    \draw[dashed, lightgray] (2,0) -- (2,.9);
    % Axis
    \draw [-latex,shorten >=-3pt] (-.2,0) -- (3,0) node [below] {$\phantom{\sqrt{3}}t\phantom{\sqrt{3}}$};
    \foreach \x in  {0,1,2}
        \node at (\x,0) {$\bullet$}
         node at (\x,0) [below] {$\phantom{\sqrt{3}}\x\phantom{\sqrt{3}}$};
    \node at ({sqrt(3)},0) {$\bullet$}
     node at ({sqrt(3)},0) [below] {$\sqrt{3}$};
    % Horizontal lines
    \draw [{*[fill=white]}-,shorten <=-2.4pt] (0,.2) -- (3,.2);
    \foreach \x in  {.3,.4,...,.7}
        \draw [{*[fill=white]}-*,shorten >=-2.4pt,shorten <=-2.4pt] (0,\x) -- (1,\x) ;
    \draw [{*[fill=white]}-*,shorten >=-2.4pt,shorten <=-2.4pt] (1,.8) --  node [above] {$H_1$} ({sqrt(3)},.8) ;
    \draw [{*[fill=white]}-*,shorten >=-2.4pt,shorten <=-2.4pt] ({sqrt(3)},.9) -- node [above] {$H_2$} (2,.9) ;
    \draw (0,.1) -- (-.1,.1) -- node[left]{$H_0$} (-.1,.8) -- (0,.8);
\end{tikzpicture}
\end{document}

而输出结果则稍微不太理想（项目符号不居中，且大小与箭头不同）： 带箭头的 tikz

此外，缩短只是猜测，可能不是像素完美的。

编辑：另一种解决方案arrows.meta解决了上述代码的大部分问题，但在某些部分不太优雅：

\documentclass[tikz]{standalone}

\usetikzlibrary{arrows.meta,calc}

\begin{document}
% Arrows are shifted by half their width
\tikzset{open/.style={{Circle[fill=white]}-,shorten <=-1.196825pt-1.595769\pgflinewidth}}
\tikzset{close/.style={-{Circle},shorten >=-1.196825pt-1.595769\pgflinewidth]}}
\tikzset{openclose/.style={{Circle[fill=white]}-{Circle},shorten <=-1.196825pt-1.595769\pgflinewidth,shorten >=-1.196825pt-1.595769\pgflinewidth]}}
\begin{tikzpicture}[scale=2]
    % Vertical dashed lines
    \draw[dashed, lightgray] (0,0) -- (0,.8);
    \draw[dashed, lightgray] (1,0) -- (1,.8);
    \draw[dashed, lightgray] ({sqrt(3)},0) -- ({sqrt(3)},.9);
    \draw[dashed, lightgray] (2,0) -- (2,.9);
    % Axis
    \draw [close] (-.2,0) -- (0,0) node [below] {$\phantom{\sqrt{3}}0\phantom{\sqrt{3}}$};
    \draw [close] (0,0) -- (1,0) node [below] {$\phantom{\sqrt{3}}1\phantom{\sqrt{3}}$};
    \draw [close] (1,0) -- ({sqrt(3)},0) node [below] {$\sqrt{3}$};
    \draw [close] ({sqrt(3)},0) -- (2,0) node [below] {$\phantom{\sqrt{3}}2\phantom{\sqrt{3}}$};
    \draw [-latex,shorten >=-3pt] (2,0) -- (3,0) node [below] {$\phantom{\sqrt{3}}t\phantom{\sqrt{3}}$};
    % Horizontal lines
    \draw [open] (0,.2) -- (3,.2);
    \foreach \x in  {.3,.4,...,.7}
    \draw [openclose] (0,\x) -- (1,\x) ;
    \draw [openclose] (1,.8) --  node [above] {$H_1$} ({sqrt(3)},.8) ;
    \draw [openclose] ({sqrt(3)},.9) -- node [above] {$H_2$} (2,.9) ;
    \draw (0,.1) -- (-.1,.1) -- node[left]{$H_0$} (-.1,.8) -- (0,.8);
\end{tikzpicture}
\end{document}

它的输出（我认为更好）： tikz 带有 arrows.meta

答案4

使用 Asymptote 进行一点小改动。编译http://asymptote.ualberta.ca/

size(300,100,false);

defaultpen(linewidth(0.6bp));
dotfactor=7;

real s=0.1;
// Last drawing
draw((0,0)--(0,0.2+6s)^^(1,0)--(1,0.2+6s)^^
     (sqrt(3),0)--(sqrt(3),0.2+7s)^^(2,0)--(2,0.2+7s),linetype(new real[]{7,7})+gray);

draw(Label("$t$",Relative(.96)),(-0.2,0)--(2.8,0),Arrow);
dot("$0$",(0,0),2S,Fill());
dot("$1$",(1,0),2S,Fill());
dot("$\sqrt{3}$",(sqrt(3),0),S,Fill());
dot("$2$",(2,0),2S,Fill());
draw((0,0.2)--(2.8,0.2));
dot((0,0.2),Fill(white));

for (int i=1; i<=5 ; i=i+1)
{
  draw((0,0.2+i*s)--(1,0.2+i*s));
  dot((0,0.2+i*s),Fill(white));
  dot((1,0.2+i*s),Fill());
}

draw(Label("$H_1$",Relative(.4),LeftSide),(1,0.2+6s)--(sqrt(3),0.2+6s));
dot((1,0.2+6s),Fill(white));
dot((sqrt(3),0.2+6s),Fill());

draw(Label("$H_2$",LeftSide),(sqrt(3),0.2+7s)--(2,0.2+7s));
dot((sqrt(3),0.2+7s),Fill(white));
dot((2,0.2+7s),Fill());

draw(Label("$H_0$"),(0,0.2+5.5s)--(-s/2,0.2+5.5s)--(-s/2,0.2+-0.5s)--(0,0.2+-0.5s));

在此处输入图片描述

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