使用 PSTricks (或 TikZ) 绘制多边形数字

Question 1

这是使用 TikZ 的解决方案。

有几个可以改变图形参数的键：

sides：多边形的边数/角数；
level：多边形的重复次数；
side length：多边形一边的长度；
对于“酒吧”：
- x padding和
- y padding也
- bars可用于关闭/打开条形图绘制的开关。

多边形是用绘制的，center node位于您使用键的当前路径所在的位置polynum。可以通过旋转路径来旋转“多边形”。如果您将路径旋转，多边形将位于其中心角360/<corners>/2。

绘制条形图时会考虑主动旋转（这就是的原因\pgfpointshapeborder），这样就可以按原样包含节点，而无需旋转它们或使用transform shape。但是，如果节点大小不相同，条形图绘制算法将产生不良结果。

宏

\polynumcorner，
\polynumlevel，
\polynumsublevel和
\polynumcorners（即角球总数）

可用于影响样式，这在every corner edge样式（实际上是一个.code键）中使用，可以明确关闭某些角节点之间的边的绘制。

节点名为：pn@<corner>@<level>@<sublevel>。红色中心节点名为pn@0@1@0，它是唯一的第 0 个角节点。

代码

\documentclass[tikz,png={size=315,density=600},convert=false]{standalone}
\pgfkeys{% http://tex.stackexchange.com/a/125700/16595
  /handlers/.tikz/.code=\pgfkeys{\pgfkeyscurrentpath/.code=\tikzset{#1}},%
  /handlers/.append tikz/.code=\pgfkeys{\pgfkeyscurrentpath/.append code=\tikzset{#1}},%
  /handlers/.prefix tikz/.code=\pgfkeys{\pgfkeyscurrentpath/.prefix code=\tikzset{#1}}}
\def\polynumset{\pgfqkeys{/polynum}}
\newif\ifpolynumbars
\polynumset{
  sides/.initial=4,
  levels/.initial=5,
  side length/.initial=+.5cm,
  x padding/.initial=+2pt,
  y padding/.initial=+2pt,
  bars/.is if=polynumbars,
  every bar/.tikz={draw=blue, thick, rounded corners=+1pt},
  %
  every node/.tikz={shape=circle,draw,inner sep=+0pt,minimum size=+4pt},
  center node/.tikz={fill=red},
  level nodes/.tikz={fill=blue},
  sublevel nodes/.tikz={fill=yellow},
  %
  every edge/.tikz={},
  %
  every corner edge/.code={
    \ifnum\polynumcorner>1\relax
      \ifnum\polynumcorner<\polynumcorners\relax
        \tikzset{draw=none}
      \fi
    \fi
  },
}
\makeatletter
\def\polynumutil@firstofone#1{\tikz@scan@next@command#1\pgf@stop}
\def\polynumutil@firstoftwo#1#2{\tikz@scan@next@command#1\pgf@stop}
\def\polynumutil@secondoftwo#1#2{\tikz@scan@next@command#2\pgf@stop}
\polynumset{
  bar path/.style={
    to path={
      [/utils/exec=%
         \pgfmathanglebetweenpoints{\pgfpointanchor{\tikztostart} {center}}
                                   {\pgfpointanchor{\tikztotarget}{center}}%
         \let\polynum@a\pgfmathresult
         \pgftransformrotate{\polynum@a}%
         \pgfpointdiff{\pgfpointanchor{\tikztostart}{center}}
                      {\pgfpointshapeborder{\tikztostart}{\pgfpointadd{\pgfpointanchor{\tikztostart}{center}}{\pgfpointpolar{90}{1pt}}}}%
         \pgfmathveclen{\pgf@x}{\pgf@y}%
         \edef\polynum@ydistance{\pgfmathresult pt}%
         \pgfcoordinate{pn@aux1}
                       {\pgfpointshapeborder
                         {\tikztostart}
                         {\pgfpointadd{\pgfpointanchor{\tikztostart}{center}}
                                      {\pgfpointpolar{180}{1pt}}}}%
         \pgfcoordinate{pn@aux2}
                       {\pgfpointshapeborder
                         {\tikztotarget}
                         {\pgfpointadd{\pgfpointanchor{\tikztotarget}{center}}
                                      {\pgfpointpolar{0}{1pt}}}}%
       ]
             ([shift=(left:\pgfkeysvalueof{/polynum/x padding})]pn@aux1) coordinate (pn@aux)
       -- ++ (up:\polynum@ydistance+\pgfkeysvalueof{/polynum/y padding})
       -|    ([shift=(right:\pgfkeysvalueof{/polynum/x padding})] pn@aux2)
       |-    ([shift=(down:\polynum@ydistance+\pgfkeysvalueof{/polynum/y padding})] pn@aux)
       -- cycle
    }
  }}
\tikzset{
  polynum/.default=,
  polynum/.style={
    insert path={
      node[/polynum/every node/.try, /polynum/inner nodes/.try, /polynum/center node/.try] (pn@0@1@0) {}
      { [/polynum/.cd,#1]
        [/utils/exec=%
          \pgfmathtruncatemacro\polynumcorners{\pgfkeysvalueof{/polynum/sides}-1}%
          \pgfmathtruncatemacro\polynum@levels{\pgfkeysvalueof{/polynum/levels}}%
          \pgfmathsetlengthmacro\polynum@sidelength{\pgfkeysvalueof{/polynum/side length}}%
          \pgfmathsetmacro\polynum@angle{360/(\the\numexpr\polynumcorners+1\relax)}%
        ]
        \foreach \polynumcorner[evaluate={\polynum@@angle={(\polynumcorner-1)*\polynum@angle}}] in {1,...,\polynumcorners} {
          % get to the next corner,
          % level 1
          ++ (\polynum@@angle:\polynum@sidelength)
            node[/polynum/every node/.try, /polynum/level nodes/.try, /polynum/level 1 nodes/.try] (pn@\polynumcorner @1@0) {}
          % last level
          [/utils/exec={%
            \ifnum\polynumcorner=1\relax
              \expandafter\polynumutil@firstoftwo
            \else
              \expandafter\polynumutil@secondoftwo
            \fi
              {+(\polynum@@angle:\the\numexpr\polynum@levels-1\relax*\polynum@sidelength)}
              {   (pn@\the\numexpr\polynumcorner-1\relax @\polynum@levels @0.center)
               ++ (\polynum@@angle:\polynum@levels*\polynum@sidelength)}}]
          % it's only a coordinate because it is used to place everything else
          % including the node at the exact same position
          node[shape=coordinate, alias=pn@\polynumcorner @last] (pn@\polynumcorner @\polynum@levels @0) {}
          % all other levels
          \foreach \polynumlevel[count=\polynum@level from 1, evaluate={\polynum@pos=\polynum@level/\the\numexpr\polynum@levels-1\relax}] in {2,...,\polynum@levels} {
            (pn@\polynumcorner @[email protected])
              edge[draw=none] node[pos=\polynum@pos, /polynum/every node/.try, /polynum/level nodes/.try, style/.expanded={/polynum/level \polynumlevel\space nodes/.try}] (pn@\polynumcorner @\polynumlevel @0) {}
            (pn@\polynumcorner @last.center)
            % the edges between the corner nodes (blue -- blue)
            (pn@\polynumcorner @\the\numexpr\polynumlevel-1\relax @0) edge[/polynum/every edge/.try, /polynum/every corner edge/.try] (pn@\polynumcorner @\polynumlevel @0)
            % now the sublevels (except for the first corner because it has no previous corner)
            [/utils/exec={%
              \ifnum\polynumcorner>1\relax
                \expandafter\polynumutil@firstofone
              \else
                \expandafter\pgfutil@gobble
              \fi
              {\foreach \polynumsublevel[evaluate={\polynum@pos=\polynumsublevel/\polynumlevel}] in {1,...,\the\numexpr\polynumlevel-1\relax}{
                 (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @0.center)
                   edge[draw=none] node[pos=\polynum@pos, /polynum/every node/.try, /polynum/sublevel nodes/.try, style/.expanded={/polynum/sublevel \polynumsublevel\space nodes/.try}] (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @\polynumsublevel) {}
                 (pn@\polynumcorner @\polynumlevel @0.center)
                 % the edges between sublevel nodes (blue -- yellow and yellow -- yellow)
                 (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @\the\numexpr\polynumsublevel-1\relax)
                   edge[/polynum/every edge/.try]
                 (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @\polynumsublevel)
               }
               % the edge between the last sublevel node and the next corner node (yellow -- blue)
               (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @\the\numexpr\polynumlevel-1\relax)
                 edge[/polynum/every edge/.try]
               (pn@\polynumcorner @\polynumlevel @0)
              }}]
          }
          % the edges between corner nodes (level 1, the smallest polygon: red -- blue and blue -- blue)
           (pn@\the\numexpr\polynumcorner-1\relax @1@0) edge[/polynum/every edge/.try] (pn@\polynumcorner @1@0)
           (pn@\polynumcorner @[email protected])
        }
        % the last edge (blue -- red)
        (pn@\polynumcorners @1@0) edge[/polynum/every edge/.try] (pn@0@1@0)
        % the bars are drawn in an extra loop to make sure they are on top
        [/utils/exec=%
          \ifpolynumbars\expandafter\polynumutil@firstofone\else\expandafter\pgfutil@gobble\fi
            {\foreach \polynumcorner in {1,...,\polynumcorners} {
            (pn@\polynumcorner @1@0) edge[/polynum/bar path/.try, /polynum/every bar/.try] (pn@\polynumcorner @\polynum@levels @0)}}
        ]
      }
    }
  }
}
\makeatother
\polynumset{bars}
\begin{document}
\foreach \sides in {3,...,6}{
\begin{tikzpicture}[/polynum/levels=3]
\path [polynum={/tikz/rotate=360/\sides/2,sides=\sides}];
\end{tikzpicture}}
\foreach \level in {2,...,5,5,4,3,2}{
\begin{tikzpicture}
\path [polynum={levels=\level}];
\useasboundingbox (-8pt,-8pt) rectangle (2.5cm+8pt,2.5cm+8pt);
\end{tikzpicture}}
\end{document}

输出

在此处输入图片描述 <code>sides=7</code> 的图片

Answer

这是使用 TikZ 的解决方案。

有几个可以改变图形参数的键：

sides：多边形的边数/角数；
level：多边形的重复次数；
side length：多边形一边的长度；
对于“酒吧”：
- x padding和
- y padding也
- bars可用于关闭/打开条形图绘制的开关。

多边形是用绘制的，center node位于您使用键的当前路径所在的位置polynum。可以通过旋转路径来旋转“多边形”。如果您将路径旋转，多边形将位于其中心角360/<corners>/2。

绘制条形图时会考虑主动旋转（这就是的原因\pgfpointshapeborder），这样就可以按原样包含节点，而无需旋转它们或使用transform shape。但是，如果节点大小不相同，条形图绘制算法将产生不良结果。

宏

\polynumcorner，
\polynumlevel，
\polynumsublevel和
\polynumcorners（即角球总数）

可用于影响样式，这在every corner edge样式（实际上是一个.code键）中使用，可以明确关闭某些角节点之间的边的绘制。

节点名为：pn@<corner>@<level>@<sublevel>。红色中心节点名为pn@0@1@0，它是唯一的第 0 个角节点。

代码

\documentclass[tikz,png={size=315,density=600},convert=false]{standalone}
\pgfkeys{% http://tex.stackexchange.com/a/125700/16595
  /handlers/.tikz/.code=\pgfkeys{\pgfkeyscurrentpath/.code=\tikzset{#1}},%
  /handlers/.append tikz/.code=\pgfkeys{\pgfkeyscurrentpath/.append code=\tikzset{#1}},%
  /handlers/.prefix tikz/.code=\pgfkeys{\pgfkeyscurrentpath/.prefix code=\tikzset{#1}}}
\def\polynumset{\pgfqkeys{/polynum}}
\newif\ifpolynumbars
\polynumset{
  sides/.initial=4,
  levels/.initial=5,
  side length/.initial=+.5cm,
  x padding/.initial=+2pt,
  y padding/.initial=+2pt,
  bars/.is if=polynumbars,
  every bar/.tikz={draw=blue, thick, rounded corners=+1pt},
  %
  every node/.tikz={shape=circle,draw,inner sep=+0pt,minimum size=+4pt},
  center node/.tikz={fill=red},
  level nodes/.tikz={fill=blue},
  sublevel nodes/.tikz={fill=yellow},
  %
  every edge/.tikz={},
  %
  every corner edge/.code={
    \ifnum\polynumcorner>1\relax
      \ifnum\polynumcorner<\polynumcorners\relax
        \tikzset{draw=none}
      \fi
    \fi
  },
}
\makeatletter
\def\polynumutil@firstofone#1{\tikz@scan@next@command#1\pgf@stop}
\def\polynumutil@firstoftwo#1#2{\tikz@scan@next@command#1\pgf@stop}
\def\polynumutil@secondoftwo#1#2{\tikz@scan@next@command#2\pgf@stop}
\polynumset{
  bar path/.style={
    to path={
      [/utils/exec=%
         \pgfmathanglebetweenpoints{\pgfpointanchor{\tikztostart} {center}}
                                   {\pgfpointanchor{\tikztotarget}{center}}%
         \let\polynum@a\pgfmathresult
         \pgftransformrotate{\polynum@a}%
         \pgfpointdiff{\pgfpointanchor{\tikztostart}{center}}
                      {\pgfpointshapeborder{\tikztostart}{\pgfpointadd{\pgfpointanchor{\tikztostart}{center}}{\pgfpointpolar{90}{1pt}}}}%
         \pgfmathveclen{\pgf@x}{\pgf@y}%
         \edef\polynum@ydistance{\pgfmathresult pt}%
         \pgfcoordinate{pn@aux1}
                       {\pgfpointshapeborder
                         {\tikztostart}
                         {\pgfpointadd{\pgfpointanchor{\tikztostart}{center}}
                                      {\pgfpointpolar{180}{1pt}}}}%
         \pgfcoordinate{pn@aux2}
                       {\pgfpointshapeborder
                         {\tikztotarget}
                         {\pgfpointadd{\pgfpointanchor{\tikztotarget}{center}}
                                      {\pgfpointpolar{0}{1pt}}}}%
       ]
             ([shift=(left:\pgfkeysvalueof{/polynum/x padding})]pn@aux1) coordinate (pn@aux)
       -- ++ (up:\polynum@ydistance+\pgfkeysvalueof{/polynum/y padding})
       -|    ([shift=(right:\pgfkeysvalueof{/polynum/x padding})] pn@aux2)
       |-    ([shift=(down:\polynum@ydistance+\pgfkeysvalueof{/polynum/y padding})] pn@aux)
       -- cycle
    }
  }}
\tikzset{
  polynum/.default=,
  polynum/.style={
    insert path={
      node[/polynum/every node/.try, /polynum/inner nodes/.try, /polynum/center node/.try] (pn@0@1@0) {}
      { [/polynum/.cd,#1]
        [/utils/exec=%
          \pgfmathtruncatemacro\polynumcorners{\pgfkeysvalueof{/polynum/sides}-1}%
          \pgfmathtruncatemacro\polynum@levels{\pgfkeysvalueof{/polynum/levels}}%
          \pgfmathsetlengthmacro\polynum@sidelength{\pgfkeysvalueof{/polynum/side length}}%
          \pgfmathsetmacro\polynum@angle{360/(\the\numexpr\polynumcorners+1\relax)}%
        ]
        \foreach \polynumcorner[evaluate={\polynum@@angle={(\polynumcorner-1)*\polynum@angle}}] in {1,...,\polynumcorners} {
          % get to the next corner,
          % level 1
          ++ (\polynum@@angle:\polynum@sidelength)
            node[/polynum/every node/.try, /polynum/level nodes/.try, /polynum/level 1 nodes/.try] (pn@\polynumcorner @1@0) {}
          % last level
          [/utils/exec={%
            \ifnum\polynumcorner=1\relax
              \expandafter\polynumutil@firstoftwo
            \else
              \expandafter\polynumutil@secondoftwo
            \fi
              {+(\polynum@@angle:\the\numexpr\polynum@levels-1\relax*\polynum@sidelength)}
              {   (pn@\the\numexpr\polynumcorner-1\relax @\polynum@levels @0.center)
               ++ (\polynum@@angle:\polynum@levels*\polynum@sidelength)}}]
          % it's only a coordinate because it is used to place everything else
          % including the node at the exact same position
          node[shape=coordinate, alias=pn@\polynumcorner @last] (pn@\polynumcorner @\polynum@levels @0) {}
          % all other levels
          \foreach \polynumlevel[count=\polynum@level from 1, evaluate={\polynum@pos=\polynum@level/\the\numexpr\polynum@levels-1\relax}] in {2,...,\polynum@levels} {
            (pn@\polynumcorner @[email protected])
              edge[draw=none] node[pos=\polynum@pos, /polynum/every node/.try, /polynum/level nodes/.try, style/.expanded={/polynum/level \polynumlevel\space nodes/.try}] (pn@\polynumcorner @\polynumlevel @0) {}
            (pn@\polynumcorner @last.center)
            % the edges between the corner nodes (blue -- blue)
            (pn@\polynumcorner @\the\numexpr\polynumlevel-1\relax @0) edge[/polynum/every edge/.try, /polynum/every corner edge/.try] (pn@\polynumcorner @\polynumlevel @0)
            % now the sublevels (except for the first corner because it has no previous corner)
            [/utils/exec={%
              \ifnum\polynumcorner>1\relax
                \expandafter\polynumutil@firstofone
              \else
                \expandafter\pgfutil@gobble
              \fi
              {\foreach \polynumsublevel[evaluate={\polynum@pos=\polynumsublevel/\polynumlevel}] in {1,...,\the\numexpr\polynumlevel-1\relax}{
                 (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @0.center)
                   edge[draw=none] node[pos=\polynum@pos, /polynum/every node/.try, /polynum/sublevel nodes/.try, style/.expanded={/polynum/sublevel \polynumsublevel\space nodes/.try}] (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @\polynumsublevel) {}
                 (pn@\polynumcorner @\polynumlevel @0.center)
                 % the edges between sublevel nodes (blue -- yellow and yellow -- yellow)
                 (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @\the\numexpr\polynumsublevel-1\relax)
                   edge[/polynum/every edge/.try]
                 (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @\polynumsublevel)
               }
               % the edge between the last sublevel node and the next corner node (yellow -- blue)
               (pn@\the\numexpr\polynumcorner-1\relax @\polynumlevel @\the\numexpr\polynumlevel-1\relax)
                 edge[/polynum/every edge/.try]
               (pn@\polynumcorner @\polynumlevel @0)
              }}]
          }
          % the edges between corner nodes (level 1, the smallest polygon: red -- blue and blue -- blue)
           (pn@\the\numexpr\polynumcorner-1\relax @1@0) edge[/polynum/every edge/.try] (pn@\polynumcorner @1@0)
           (pn@\polynumcorner @[email protected])
        }
        % the last edge (blue -- red)
        (pn@\polynumcorners @1@0) edge[/polynum/every edge/.try] (pn@0@1@0)
        % the bars are drawn in an extra loop to make sure they are on top
        [/utils/exec=%
          \ifpolynumbars\expandafter\polynumutil@firstofone\else\expandafter\pgfutil@gobble\fi
            {\foreach \polynumcorner in {1,...,\polynumcorners} {
            (pn@\polynumcorner @1@0) edge[/polynum/bar path/.try, /polynum/every bar/.try] (pn@\polynumcorner @\polynum@levels @0)}}
        ]
      }
    }
  }
}
\makeatother
\polynumset{bars}
\begin{document}
\foreach \sides in {3,...,6}{
\begin{tikzpicture}[/polynum/levels=3]
\path [polynum={/tikz/rotate=360/\sides/2,sides=\sides}];
\end{tikzpicture}}
\foreach \level in {2,...,5,5,4,3,2}{
\begin{tikzpicture}
\path [polynum={levels=\level}];
\useasboundingbox (-8pt,-8pt) rectangle (2.5cm+8pt,2.5cm+8pt);
\end{tikzpicture}}
\end{document}

输出

在此处输入图片描述 <code>sides=7</code> 的图片

Question 2

在此处输入图片描述

此解决方案基于的面向对象特性Asymptote。基本结构struct PolygonalNumber在环境中定义asydef，稍后可在asy图片中用于创建和绘制此类对象。例如，一个名为的三角形对象，P3其层数为， PolygonalNumber P3=PolygonalNumber(3,5);命令draw(P3);将绘制它。 PolygonalNumber对象可以像往常一样进行变换，例如 draw(shift(6,0)*P4);绘制P4向右移动的对象。或者它们可以直接在命令中使用draw：生成上述图像的代码只是

size(400);
for(int i=3;i<=7;++i){
  draw(shift((i-3)*(5+i-3),0)*PolygonalNumber(i,5));
};

完整的 MWE polynum.tex：

\documentclass{article}
\usepackage[inline]{asymptote}
\begin{asydef}
struct PolygonalNumber{
  int n,m;
  real unitStep;
  real boxW;
  transform t;
  pair O=(0,0);
  pair[][] dots;

  pen originPen=red;
  pen sideLinePen=darkblue;
  pen cornerDotPen=blue;
  pen sideDotPen=orange;
  pen boxPen=blue;

  void drawSides(){
    guide g; 
    pair center,p;
    pair[] skin;    
    for(int i=1;i<=m;++i){
      p=(i*unitStep,0);
      g=O;
      center=i*unitStep/2*(1,1/Tan(180/n));
      for(int j=0;j<n-1;++j){
        g=g--(rotate(j*360.0/n,center)*p);
      }
      g=g--cycle;
      draw(t*g,sideLinePen);
      skin=new pair[];      
      for(int j=0;j<size(g);++j){
        skin.push(point(g,j));  
      }
      dots.push(skin);
    }
  }

  void drawCornerDots(){
    for(int i=0;i<dots.length;++i){
      for(int j=1;j<dots[i].length;++j){
        dot(t*dots[i][j],cornerDotPen);
      }
    }
  }

  void drawSideDots(){
    pair p,q;
    real s;
    for(int i=1;i<dots.length;++i){
      for(int j=1;j<dots[i].length-1;++j){
        p=dots[i][j];
        q=dots[i][j+1];
        for(int k=1;k<i+1;++k){
          s=k/(i+1);
          dot(t*(p*(1-s)+q*s),sideDotPen);
        }  
      }
    }
  }

  void drawOriginDots(){
    for(int i=0;i<dots.length;++i){
      dot(t*O,originPen);      
    }    
  }

  guide buildBox(pair a, pair b){
    pair d,p,q,ds;
    d=dir(b-a);
    ds=boxW*d;
    p=a-ds; q=b+ds; 
    guide[] g=strokepath(p--q,red+boxW);
    return g[0];
  }

  void drawBoxes(){
    pair a,b;
    for(int j=1;j<n;++j){
      a=dots[0][j];
      b=dots[m-1][j];
      draw(t*buildBox(a,b),boxPen);      
    }
  }

  void draw(){
    drawSides();
    drawCornerDots();
    drawSideDots();
    drawOriginDots();
    drawBoxes();
  }

  void operator init(int n=3,int m=6,real unitStep=1,transform t=identity(),real boxW=0.4){
    assert(n>2 && m>0);
    this.n=n; this.m=m; 
    this.unitStep=unitStep;
    this.boxW=boxW;
    this.t=t;
  }
}
PolygonalNumber operator*(transform t=identity(),PolygonalNumber p){p.t=t; return p;}; 
void draw(PolygonalNumber p){p.draw();};
\end{asydef}

\begin{document}
\begin{figure}
\begin{asy}
size(400);
for(int i=3;i<=7;++i){
  draw(shift((i-3)*(5+i-3),0)*PolygonalNumber(i,5));
};
\end{asy}
\end{figure}
\end{document}

为了处理它latexmk，请创建文件latexmkrc：

sub asy {return system("asy '$_[0]'");}
add_cus_dep("asy","eps",0,"asy");
add_cus_dep("asy","pdf",0,"asy");
add_cus_dep("asy","tex",0,"asy");

然后运行latexmk -pdf polynum.tex。

Answer

在此处输入图片描述

此解决方案基于的面向对象特性Asymptote。基本结构struct PolygonalNumber在环境中定义asydef，稍后可在asy图片中用于创建和绘制此类对象。例如，一个名为的三角形对象，P3其层数为， PolygonalNumber P3=PolygonalNumber(3,5);命令draw(P3);将绘制它。 PolygonalNumber对象可以像往常一样进行变换，例如 draw(shift(6,0)*P4);绘制P4向右移动的对象。或者它们可以直接在命令中使用draw：生成上述图像的代码只是

size(400);
for(int i=3;i<=7;++i){
  draw(shift((i-3)*(5+i-3),0)*PolygonalNumber(i,5));
};

完整的 MWE polynum.tex：

\documentclass{article}
\usepackage[inline]{asymptote}
\begin{asydef}
struct PolygonalNumber{
  int n,m;
  real unitStep;
  real boxW;
  transform t;
  pair O=(0,0);
  pair[][] dots;

  pen originPen=red;
  pen sideLinePen=darkblue;
  pen cornerDotPen=blue;
  pen sideDotPen=orange;
  pen boxPen=blue;

  void drawSides(){
    guide g; 
    pair center,p;
    pair[] skin;    
    for(int i=1;i<=m;++i){
      p=(i*unitStep,0);
      g=O;
      center=i*unitStep/2*(1,1/Tan(180/n));
      for(int j=0;j<n-1;++j){
        g=g--(rotate(j*360.0/n,center)*p);
      }
      g=g--cycle;
      draw(t*g,sideLinePen);
      skin=new pair[];      
      for(int j=0;j<size(g);++j){
        skin.push(point(g,j));  
      }
      dots.push(skin);
    }
  }

  void drawCornerDots(){
    for(int i=0;i<dots.length;++i){
      for(int j=1;j<dots[i].length;++j){
        dot(t*dots[i][j],cornerDotPen);
      }
    }
  }

  void drawSideDots(){
    pair p,q;
    real s;
    for(int i=1;i<dots.length;++i){
      for(int j=1;j<dots[i].length-1;++j){
        p=dots[i][j];
        q=dots[i][j+1];
        for(int k=1;k<i+1;++k){
          s=k/(i+1);
          dot(t*(p*(1-s)+q*s),sideDotPen);
        }  
      }
    }
  }

  void drawOriginDots(){
    for(int i=0;i<dots.length;++i){
      dot(t*O,originPen);      
    }    
  }

  guide buildBox(pair a, pair b){
    pair d,p,q,ds;
    d=dir(b-a);
    ds=boxW*d;
    p=a-ds; q=b+ds; 
    guide[] g=strokepath(p--q,red+boxW);
    return g[0];
  }

  void drawBoxes(){
    pair a,b;
    for(int j=1;j<n;++j){
      a=dots[0][j];
      b=dots[m-1][j];
      draw(t*buildBox(a,b),boxPen);      
    }
  }

  void draw(){
    drawSides();
    drawCornerDots();
    drawSideDots();
    drawOriginDots();
    drawBoxes();
  }

  void operator init(int n=3,int m=6,real unitStep=1,transform t=identity(),real boxW=0.4){
    assert(n>2 && m>0);
    this.n=n; this.m=m; 
    this.unitStep=unitStep;
    this.boxW=boxW;
    this.t=t;
  }
}
PolygonalNumber operator*(transform t=identity(),PolygonalNumber p){p.t=t; return p;}; 
void draw(PolygonalNumber p){p.draw();};
\end{asydef}

\begin{document}
\begin{figure}
\begin{asy}
size(400);
for(int i=3;i<=7;++i){
  draw(shift((i-3)*(5+i-3),0)*PolygonalNumber(i,5));
};
\end{asy}
\end{figure}
\end{document}

为了处理它latexmk，请创建文件latexmkrc：

sub asy {return system("asy '$_[0]'");}
add_cus_dep("asy","eps",0,"asy");
add_cus_dep("asy","pdf",0,"asy");
add_cus_dep("asy","tex",0,"asy");

然后运行latexmk -pdf polynum.tex。

Question 3

我开始用这个，但后来就觉得无聊了 :) 总是很高兴能从 Jakencbar那里偷来TikZ 是否有与 PSTricks \ncbar 命令等效的命令？

\numofsides并\numofiters定义多边形的形状以及重复的次数。我没有 Qrrbrbirlbel 的耐心。所以这只是为了好玩。

\documentclass[tikz,border=4mm]{standalone}
\usetikzlibrary{calc,shapes.geometric,backgrounds}
\begin{document}
\tikzset{
    ncbar angle/.initial=90,
    ncbar/.style={to path=(\tikztostart)--($(\tikztostart)!#1!\pgfkeysvalueof{/tikz/ncbar angle}:(\tikztotarget)$)
        -- ($(\tikztotarget)!($(\tikztostart)!#1!\pgfkeysvalueof{/tikz/ncbar angle}:(\tikztotarget)$)!\pgfkeysvalueof{/tikz/ncbar angle}:(\tikztostart)$)
        -- (\tikztotarget)},
    ncbar/.default=0.5cm,
}
\begin{tikzpicture}[
bluedot/.style={circle,fill=blue,draw,inner sep=0,minimum size=3pt,anchor=center},
yellowdot/.style={bluedot,fill=yellow},
]
\def\numofsides{10} %Change these
\def\numofiters{10} %Change these
\foreach \x in {1,...,\numofiters}{
\begin{scope}[on background layer]\node[rotate={floor(\numofsides/2)*360/\numofsides}, 
      inner sep=0,anchor=corner 1,
      draw,minimum size=\x*8mm,
      blue,regular polygon,regular polygon sides=\numofsides] (n\x) {};\end{scope}
    \foreach \y[count=\yi,count=\yj from 0,remember=\y as \lasty] in {corner 2,corner 3,corner ...,corner \numofsides} {
    \node[bluedot,rotate={((1-(1-(2/\numofsides)))*90)*\yj-90}] (n\x c\yi) at (n\x.\y) {};
    \ifnum\x>1\ifnum\yi>1\foreach\z in{1,...,\numexpr\x-1\relax}{
        \node[yellowdot] at ($(n\x.\lasty)!\z/\x!(n\x.\y)$){};}\fi\fi
    }
}
\foreach \x[count=\xi from 0] in {1,...,\numexpr\numofsides-1}{
\pgfmathsetmacro\myangle{((1-(1-(2/\numofsides)))*90)*\xi+180}
\draw[rounded corners=1pt,blue] ([shift={(\myangle:1pt)}]n1c\x.south) to[ncbar=2pt] 
                           ([shift={(\myangle:-1pt)}]n\numofiters c\x.north) to[ncbar=2pt]
                           ([shift={(\myangle:1pt)}]n1c\x.south);
}

\end{tikzpicture}

\end{document}

真是可笑的画面

在此处输入图片描述

使用\def\numofsides{24}和\def\numofiters{24}：

惊人的！:)

Answer

我开始用这个，但后来就觉得无聊了 :) 总是很高兴能从 Jakencbar那里偷来TikZ 是否有与 PSTricks \ncbar 命令等效的命令？

\numofsides并\numofiters定义多边形的形状以及重复的次数。我没有 Qrrbrbirlbel 的耐心。所以这只是为了好玩。

\documentclass[tikz,border=4mm]{standalone}
\usetikzlibrary{calc,shapes.geometric,backgrounds}
\begin{document}
\tikzset{
    ncbar angle/.initial=90,
    ncbar/.style={to path=(\tikztostart)--($(\tikztostart)!#1!\pgfkeysvalueof{/tikz/ncbar angle}:(\tikztotarget)$)
        -- ($(\tikztotarget)!($(\tikztostart)!#1!\pgfkeysvalueof{/tikz/ncbar angle}:(\tikztotarget)$)!\pgfkeysvalueof{/tikz/ncbar angle}:(\tikztostart)$)
        -- (\tikztotarget)},
    ncbar/.default=0.5cm,
}
\begin{tikzpicture}[
bluedot/.style={circle,fill=blue,draw,inner sep=0,minimum size=3pt,anchor=center},
yellowdot/.style={bluedot,fill=yellow},
]
\def\numofsides{10} %Change these
\def\numofiters{10} %Change these
\foreach \x in {1,...,\numofiters}{
\begin{scope}[on background layer]\node[rotate={floor(\numofsides/2)*360/\numofsides}, 
      inner sep=0,anchor=corner 1,
      draw,minimum size=\x*8mm,
      blue,regular polygon,regular polygon sides=\numofsides] (n\x) {};\end{scope}
    \foreach \y[count=\yi,count=\yj from 0,remember=\y as \lasty] in {corner 2,corner 3,corner ...,corner \numofsides} {
    \node[bluedot,rotate={((1-(1-(2/\numofsides)))*90)*\yj-90}] (n\x c\yi) at (n\x.\y) {};
    \ifnum\x>1\ifnum\yi>1\foreach\z in{1,...,\numexpr\x-1\relax}{
        \node[yellowdot] at ($(n\x.\lasty)!\z/\x!(n\x.\y)$){};}\fi\fi
    }
}
\foreach \x[count=\xi from 0] in {1,...,\numexpr\numofsides-1}{
\pgfmathsetmacro\myangle{((1-(1-(2/\numofsides)))*90)*\xi+180}
\draw[rounded corners=1pt,blue] ([shift={(\myangle:1pt)}]n1c\x.south) to[ncbar=2pt] 
                           ([shift={(\myangle:-1pt)}]n\numofiters c\x.north) to[ncbar=2pt]
                           ([shift={(\myangle:1pt)}]n1c\x.south);
}

\end{tikzpicture}

\end{document}

真是可笑的画面

在此处输入图片描述

使用\def\numofsides{24}和\def\numofiters{24}：

惊人的！:)

使用 PSTricks (或 TikZ) 绘制多边形数字

答案1

代码

输出

答案2

答案3

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