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如何用一些附加线条绘制正六边形

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如何用一些附加线条绘制正六边形

我写这封信是因为我需要画一个正六边形，并加多几条线，如附图所示。

我知道如何画六边形，这是我的代码

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

\begin{document}
\begin{tikzpicture}
    \newdimen\R
    \R=4cm
    \draw[thick] (330:\R) \foreach \x in {30,90,...,330} {  -- (\x:\R) };
    %\fill [black] (30:\R) circle (3pt);
    \foreach \x in {30,150,270} 
    { 
    \draw[line width=0.5pt,black,fill=white] (\x:\R) circle (3pt);
    }
    \foreach \x in {90,210,330} 
    { 
    \draw[line width=0.5pt,black,fill=black] (\x:\R) circle (3pt);
    }
    %\draw (90:\R) [out=0, in=180] (10,1);
    \end{tikzpicture}
\end{document}

它可以工作，但我不知道如何添加线条，因为我需要点坐标，而且我遇到了麻烦，因为我没有明确的顶点参考。我想画的图片是这样的

在此处输入图片描述

质量不佳，最长的曲线是红色，另外两条曲线是绿色。

谁能帮我？

答案1

您可以使用选项中的极坐标shift。结合使用示波器，可以相对轻松地在此六边形设置中获得正确的坐标：

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

\begin{document}
\begin{tikzpicture}
    \newdimen\R
    \R=4cm
    \draw[thick] (330:\R) foreach \x in {30,90,...,330} { -- (\x:\R) };
    %\fill [black] (30:\R) circle (3pt);
    \foreach \x in {30,150,270} { 
        \draw[dashed] (\x:\R) -- (\x:{\R+3cm});
        \draw[line width=0.5pt,black,fill=white] (\x:\R) circle (3pt);
    }
    \foreach \x in {90,210,330} { 
        \draw[line width=0.5pt,black,fill=black] (\x:\R) circle (3pt);
    }
    %\draw (90:\R) [out=0, in=180] (10,1);
    
    \begin{scope}[shift=(150:\R)]
        \draw[thick, green, rounded corners=5pt] 
            (30:1cm) -- (90:1cm) -- (150:1cm) -- (210:1cm) -- (270:1cm);
    \end{scope}

    \begin{scope}[shift=(330:\R)]
        \draw[thick, green, rounded corners=5pt] 
            (210:3cm) -- ([shift=(330:1cm)]210:3cm) -- (330:1cm) -- ([shift=(330:1cm)]90:3cm) -- (90:3cm);
    \end{scope}
    
    \begin{scope}[shift=(30:\R)]
        \draw[thick, red, rounded corners=5pt] 
            ([shift=(210:2cm)]150:4cm) -- ([shift=(150:2cm)]150:4cm) -- ([shift=(90:2cm)]150:4cm) -- (30:2cm) -- ([shift=(330:2cm)]270:4cm) -- ([shift=(270:2cm)]270:4cm) -- ([shift=(210:2cm)]270:4cm);
    \end{scope}
    
    \end{tikzpicture}
\end{document}

在此处输入图片描述

彩色线与六边形直角相交的替代方案：

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

\begin{document}
\begin{tikzpicture}
    \newdimen\R
    \R=4cm
    \draw[thick] (330:\R) foreach \x in {30,90,...,330} { -- (\x:\R) };
    %\fill [black] (30:\R) circle (3pt);
    \foreach \x in {30,150,270} { 
        \draw[dashed] (\x:\R) -- (\x:{\R+3cm});
        \draw[line width=0.5pt,black,fill=white] (\x:\R) circle (3pt);
    }
    \foreach \x in {90,210,330} { 
        \draw[line width=0.5pt,black,fill=black] (\x:\R) circle (3pt);
    }
    %\draw (90:\R) [out=0, in=180] (10,1);
    
    \begin{scope}[shift=(150:\R)]
        \draw[thick, green, rounded corners=5pt] 
            (30:.5cm) -- (90:1cm) -- (150:1cm) -- (210:1cm) -- (270:.5cm);
    \end{scope}
    
    \begin{scope}[shift=(330:\R)]
        \draw[thick, green, rounded corners=5pt] 
            (210:2.5cm) -- ([shift=(330:1cm)]210:3cm) -- (330:1cm) -- ([shift=(330:1cm)]90:3cm) -- (90:2.5cm);
    \end{scope}
    
    \begin{scope}[shift=(30:\R)]
        \draw[thick, red, rounded corners=5pt] 
            ([shift=(210:1cm)]150:4cm) -- ([shift=(150:2cm)]150:4cm) -- ([shift=(90:2cm)]150:4cm) -- (30:2cm) -- ([shift=(330:2cm)]270:4cm) -- ([shift=(270:2cm)]270:4cm) -- ([shift=(210:1cm)]270:4cm);
    \end{scope}
    
    \end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

这里有一个元帖子替代方案，纯粹用于比较。

在此处输入图片描述

这被包裹在内，luamplib因此用 进行编译lualatex。

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}

vardef rounded_corners expr p = 
    point 0 of p for t=1 upto length p:
        .. (subpath (t-1, t) of p 
            cutbefore fullcircle scaled 5 shifted point t-1 of p
            cutafter  fullcircle scaled 5 shifted point t of p)
    endfor .. point infinity of p
enddef;

beginfig(1);
    % define the base hexagon
    numeric r; r = 50;
    path h; h = for t=0 upto 5: up scaled r rotated 60t -- endfor cycle;

    % mark the three sectors 
    for m = (0.8, 1.2, 10), (3.25, 4.75, 10), (3.7, 6.3, 20):
        numeric a, b, c; path g; 
        a = redpart m; b = greenpart m; c = bluepart m;
        % build the sector path
        g = subpath (a, b) of h scaled (1 + c/r);
        g := (up -- origin) scaled r rotated angle direction 0 of g 
            shifted point 0 of g cutbefore h & g;
        g := g & ((origin -- up) scaled r rotated angle direction infinity of g 
            shifted point infinity of g cutafter h);
        % draw it with rounded corners
        draw rounded_corners g 
            if c=10: withcolor 2/3 green elseif c=20: withcolor 2/3 red fi;
    endfor

    % draw the hexagon and mark the vertices
    draw h;
    for i=0 upto 5:
        if odd i:
            draw point i of h -- 2 point i of h dashed evenly;
        fi
        draw point i of h withpen pencircle scaled 3;
        if odd i:
            draw point i of h withpen pencircle scaled 2 withcolor white;
        fi
    endfor
endfig;
\end{mplibcode}
\end{document}

答案3

这是一个calc有动力的解决方案。

最终，这可以让你做到

\draw [red] [around hex={1-2 / 1, 6, 5 / 5-4}];

从角 1 和角 2 之间的边缘（即从角 1 到角 2 的缩进长度）画出该线，绕过角 1、角 6 和角 5 并回到角 2 和角 1 之间的边缘。

六边形周围的路径分为三个部分：

  1. 从六边形的边缘向外 ( up from)，
  2. 到角落上方的点（above corner）和
  3. 回到边缘（down to）。

关键是从远离六边形up from = <c1>-<c2>的点向上（正交）画一条线到六边形“上方”的点。Indent<c1><c2>cos(30°) * Distance

键down to绘制相同的路径，但是方向相反。

并且键在角落“上方”above corner = <c>的角落处绘制一条线。Distance<c>

该钥匙around hex = <up from> / <corner list> / <down to>将这三个部分合并为一个钥匙。

我添加了第四行，虽然没有使用around hex，但允许改变距离。

代码

\documentclass[border=2mmm, tikz]{standalone}
\usetikzlibrary{shapes.geometric,calc}
\begin{document}
\begin{tikzpicture}[
    thick, rounded corners,
    %
    main/.style={% this is the polygon, it's a shape
      draw=black, name=hex, 
      shape=regular polygon, regular polygon sides=6, minimum size=8cm, rotate=30},
    corner/.style={% these are the circles at the corners, they're sahpes, too.
      draw=black, shape=circle, minimum size=6pt,
      at=(hex.corner #1), node contents=},% , label=#1
    %
    % default values for …
    Indent/.initial=10mm,  % … the distance from the corner to the line
    Distance/.initial=10mm,% … from the polygon to the lines around it
    %
    % draws a line from the point that is Indent away from corner #1 to corner #2
    % to the point that lies Distance away from that point orthogonally
    % to the line between corner #1 and corner #2°
    up from/.style args={#1-#2}{
      insert path={
      ($(hex.corner #1)!\pgfkeysvalueof{/tikz/Indent}!(hex.corner #2)$) --
      ($(hex.corner #1)!\pgfkeysvalueof{/tikz/Indent}!(hex.corner #2)!
        .86602540 * sign(#1 - #2) * (abs(#1 - #2) == 5 ? -1 : 1)
          * \pgfkeysvalueof{/tikz/Distance}!90:(hex.corner #2)$)}},
    %
    % the same as "up from" just reversed
    down to/.style args={#1-#2}{
      insert path={ --
      ($(hex.corner #1)!\pgfkeysvalueof{/tikz/Indent}!(hex.corner #2)!
        .86602540 * sign(#1 - #2) * (abs(#1 - #2) == 5 ? -1 : 1)
          * \pgfkeysvalueof{/tikz/Distance}!90:(hex.corner #2)$) --
      ($(hex.corner #1)!\pgfkeysvalueof{/tikz/Indent}!(hex.corner #2)$)}},
    %
    % draws a line to the point Distance away from corner #1 "above" the hexagon
    % i.e. away from the center
    above corner/.value required,
    above corner/.style={insert path={% Distance away from corner #1
        -- ($(hex.corner #1)!\pgfkeysvalueof{/tikz/Distance}!180:(hex.center)$)}},
    %
    % all together
    around hex/.style args={#1/#2/#3}{
      up from=#1, above corner/.list={#2}, down to=#3}]
    
    \node[main] {};
    \foreach \cor[evaluate={\col=mod(\cor,2)?"black":"white";}] in {1,...,6}
      \node[corner=\cor, fill=\col];
    
    \draw [red] [around hex={1-2 / 1, 6, 5 / 5-4}];
    \draw [green, Distance=7.5mm] [around hex={6-5 / 5 / 4-5}]
                                  [around hex={2-1 / 2 / 2-3}];
    \draw [dashed, Indent=15mm, Distance=15mm]
      [up from=1-6, above corner=6, Indent=5mm, down to=6-5];
\end{tikzpicture}
\end{document}

输出

在此处输入图片描述

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