连接点-光明节

Question

节日来临，我们当然都会拿出自己最喜欢的 TikZ光明节烛台庆祝一下。然而，我们的孩子仍然不满足，他们要求在漫长的黑暗夜晚做点活动。尽管我们试图为他们提供下载的连点拼图，但他们很快就意识到没有在 TikZ 中制作。

我们能否通过提供色彩缤纷的连点光明节烛台（甚至是陀螺）来消磨时间，从而挽救这种情况？

这是光明节（Hanukiah）的无色示例（嗯...实际上是犹太烛台，因为其蜡烛数量与光明节不符，应为八加一）。

这是无色的陀螺样品。

Answer 1

好的，加上一点点颜色，这是一个join the dots装饰：

\documentclass[border=0.125cm]{standalone}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\makeatletter
\newcount\tikzjointhedotsnumber


\pgfdeclaredecoration{join the dots}{initial}{%
  \state{initial}[width=0pt, next state=do dots, persistent precomputation={\global\tikzjointhedotsnumber=1}]{}
  %
  \state{do dots}[width=\pgfdecoratedinputsegmentlength, persistent postcomputation={\global\advance\tikzjointhedotsnumber by1}]{%
    \pgfcoordinate{@dot-\the\tikzjointhedotsnumber}{\pgfpointorigin}%
  }
  %
  \state{final}{%
    % Is the last point the same as the first?
      \pgfpointdiff{\pgfpointdecoratedpathlast}{\pgfpointdecoratedpathfirst}%
      \pgfmathveclen{\the\pgf@x}{\the\pgf@y}%
      \ifdim\pgfmathresult pt=0pt\relax%
        \global\advance\tikzjointhedotsnumber by-1\relax
      \else
        \pgftransformshift{\pgfpointdecoratedpathlast}%
        \pgfcoordinate{@dot-\the\tikzjointhedotsnumber}{\pgfpointorigin}%
      \fi
      % Ok, now we do everything. Draw the dots and place the numbers.
      %
      \c@pgf@counta=\tikzjointhedotsnumber%
      \c@pgf@countb=2\relax%
      \edef\lastdot{\the\tikzjointhedotsnumber}%
      \def\nextdot{2}%
      \pgftransformreset%
      \pgfmathloop%
      \ifnum\pgfmathcounter>\tikzjointhedotsnumber
      \else%
        % Draw the dot.
        \edef\tmp{\the\tikzjointhedotsnumber}%
                \tikzjointhedotsnumber=\pgfmathcounter\relax%
        \path [shift={(@dot-\pgfmathcounter)}, every dot/.try, dot \pgfmathcounter/.try]; 
         \tikzjointhedotsnumber=\tmp% 
        %
        % Calculate the dot number node anchor
        \pgfmathanglebetweenpoints{\pgfpointanchor{@dot-\pgfmathcounter}{center}}{\pgfpointanchor{@dot-\the\c@pgf@counta}{center}}%
        \pgf@xc=\pgfmathresult pt\relax%
        \ifdim0pt>\pgf@xc%
          \advance\pgf@xc by360pt\relax%
        \fi%
        \pgfmathanglebetweenpoints{\pgfpointanchor{@dot-\pgfmathcounter}{center}}{\pgfpointanchor{@dot-\the\c@pgf@countb}{center}}%
        \pgf@yc=\pgfmathresult pt\relax%
        \ifdim0pt>\pgf@yc%
          \advance\pgf@yc by360pt\relax%
        \fi%
        \ifdim\pgf@xc>\pgf@yc%
          \pgf@x=360pt\relax%
        \else%
          \pgf@x=0pt\relax%
        \fi%
        \advance\pgf@x by-\pgf@xc%
        \advance\pgf@x by\pgf@yc%
        \divide\pgf@x by2\relax%
        \advance\pgf@x by\pgf@xc%
        \advance\pgf@x by180pt\relax%
        \edef\dotnumberanchor{\the\pgf@x}%
        \node [anchor=\dotnumberanchor, every dot number/.try, dot number \pgfmathcounter/.try] 
          at (@dot-\pgfmathcounter)
          {\tikzjointhedotsnumber=\pgfmathcounter\relax\tikzjointhedotstypesetnumber{\tikzjointhedotsnumber}};
        \c@pgf@counta=\pgfmathcounter\relax%
            \advance\c@pgf@countb by1\relax%
            \ifnum\c@pgf@countb>\tikzjointhedotsnumber%
              \c@pgf@countb=1\relax%
            \fi%
        \repeatpgfmathloop%
  }
}

% Command for typesetting dot number
% #1 - a count register holding the current dot number
%
\def\tikzjointhedotstypesetnumber#1{\the#1}
\makeatletter
% Keys for setting dot number styles
\tikzset{%
  syle dot number range/.code args={#1 to #2 with #3}{%
    \c@pgf@counta=#1
    \pgfmathloop
    \ifnum\c@pgf@counta>#2\relax%
    \else%
      \tikzset{dot number \the\c@pgf@counta/.style={#3}}%
      \advance\c@pgf@counta by1
    \repeatpgfmathloop%
  },
    style dot number list/.code args={#1 with #2}{%
      \pgfutil@for\tmp:=#1\do{%
        \tikzset{dot number \tmp/.style={#2}}%
      }%
    }
}
\makeatother

\tikzset{%
  % Executed for every dot
  every dot/.style={fill=black,
    insert path={  circle [radius=.75mm] coordinate [alias=dot-last] (dot-\the\tikzjointhedotsnumber)  }
  },
  % Executed for every dot number
  every dot number/.style={
   shape=circle,
   font=\footnotesize\sf,
  },
  join the dots/.style={
    decoration=join the dots, decorate
  },
  lines/.style={
    ultra thick,
    line join=round,
    line cap=round
  },
  crayon/.style={
    draw=#1,
    line join=round,
    line cap=round,
    line width=1mm
  },
  sketch/.style={
    bend right, out=rand*10, in=180-rand*10
  }
}

\begin{document}
\begin{tikzpicture}
% Draw and number the dots
\path [postaction={join the dots}]
    (-1/2,11) 
    \foreach \a [count=\c from 1, evaluate={\d=\a+1;\s=90/\d;}] in {1,2,3,4}{
        -- ++(0,{\a==1?-2:-1})
        \foreach \i in {1,...,\d}{
            arc (270-\i*\s+\s:270-\i*\s:\a*2-1 and \a*3/2-1/2) 
        }
        -- ++(-1,0) coordinate [midway] (candle-\c)
        \foreach \i in {1,...,\d}{
            arc (180+\i*\s-\s:180+\i*\s:\a*2 and \a*3/2) 
        }
    }
    -- ++(0,-1) 
    -| ++(-1,-1/2) -| ++(-1,-1/2) -| ++(-1,-1/2)
    -- ++(7,0)
    |- ++(-1,1/2) |- ++(-1,1/2) |- ++(-1,1/2)
    \foreach \a [count=\c from 5, evaluate={\d=\a+1;\s=90/\d;}] in {4,3,2,1}{
        -- ++(0,1)
        \foreach \i in {1,...,\d}{
            arc (270+\i*\s-\s:270+\i*\s:\a*2 and \a*3/2) 
        }
        -- ++(-1,0) coordinate [midway] (candle-\c)
        \foreach \i in {1,...,\d}{
            arc (360-\i*\s+\s:360-\i*\s:\a*2-1 and \a*3/2-1/2) 
        }
    }
    -- ++(0,2);
% Draw the lines that are visible.
\draw [lines] 
  (dot-1)  -- (dot-last) coordinate [midway] (candle-9);

% Draw candles
\foreach \cn in {1,...,9}{% 
 \tikzset{shift=(candle-\cn), yshift=1pt}%
 % Candle
 \fill [lines, fill=purple!80, rounded corners=0.125cm]
  (-1/3,0) to [sketch] (-1/3,3) -- (1/3,3)  to [sketch] (1/3,0);
 % Wick
 \draw [lines] (0,3) -- ++(0,1/4);
 \tikzset{shift={(0,3+1/8)}, xscale=round(rnd)*2-1,yscale=1+rand/8}
 \foreach \s/\c in {1/yellow,.5/red}
 \path [lines, fill=\c!50!orange, opacity=3/4, scale=\s] 
   (0,0) 
   arc (270:180:3/8) 
   .. controls ++(0,1/4) and ++(0,-1/4) .. (0,3/2)
   arc (90:0:3/8 and 1) arc (360:270:3/8 and 1/2);
} 
\end{tikzpicture}%

\end{document}

这需要长的编译时间。

\documentclass[border=0.125cm]{standalone}
\standaloneenv{minipage}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\makeatletter
\newcount\tikzjointhedotsnumber


\pgfdeclaredecoration{join the dots}{initial}{%
  \state{initial}[width=0pt, next state=do dots, persistent precomputation={\global\tikzjointhedotsnumber=1}]{}
  %
  \state{do dots}[width=\pgfdecoratedinputsegmentlength, persistent postcomputation={\global\advance\tikzjointhedotsnumber by1}]{%
    \pgfcoordinate{@dot-\the\tikzjointhedotsnumber}{\pgfpointorigin}%
  }
  %
  \state{final}{%
    % Is the last point the same as the first?
      \pgfpointdiff{\pgfpointdecoratedpathlast}{\pgfpointdecoratedpathfirst}%
      \pgfmathveclen{\the\pgf@x}{\the\pgf@y}%
      \ifdim\pgfmathresult pt=0pt\relax%
        \global\advance\tikzjointhedotsnumber by-1\relax
      \else
        \pgftransformshift{\pgfpointdecoratedpathlast}%
        \pgfcoordinate{@dot-\the\tikzjointhedotsnumber}{\pgfpointorigin}%
      \fi
      % Ok, now we do everything. Draw the dots and place the numbers.
      %
      \c@pgf@counta=\tikzjointhedotsnumber%
      \c@pgf@countb=2\relax%
      \edef\lastdot{\the\tikzjointhedotsnumber}%
      \def\nextdot{2}%
      \pgftransformreset%
      \pgfmathloop%
      \ifnum\pgfmathcounter>\tikzjointhedotsnumber
      \else%
        % Draw the dot.
        \edef\tmp{\the\tikzjointhedotsnumber}%
                \tikzjointhedotsnumber=\pgfmathcounter\relax%
        \path [shift={(@dot-\pgfmathcounter)}, every dot/.try, dot \pgfmathcounter/.try]; 
         \tikzjointhedotsnumber=\tmp% 
        %
        % Calculate the dot number node anchor
        \pgfmathanglebetweenpoints{\pgfpointanchor{@dot-\pgfmathcounter}{center}}{\pgfpointanchor{@dot-\the\c@pgf@counta}{center}}%
        \pgf@xc=\pgfmathresult pt\relax%
        \ifdim0pt>\pgf@xc%
          \advance\pgf@xc by360pt\relax%
        \fi%
        \pgfmathanglebetweenpoints{\pgfpointanchor{@dot-\pgfmathcounter}{center}}{\pgfpointanchor{@dot-\the\c@pgf@countb}{center}}%
        \pgf@yc=\pgfmathresult pt\relax%
        \ifdim0pt>\pgf@yc%
          \advance\pgf@yc by360pt\relax%
        \fi%
        \ifdim\pgf@xc>\pgf@yc%
          \pgf@x=360pt\relax%
        \else%
          \pgf@x=0pt\relax%
        \fi%
        \advance\pgf@x by-\pgf@xc%
        \advance\pgf@x by\pgf@yc%
        \divide\pgf@x by2\relax%
        \advance\pgf@x by\pgf@xc%
        \advance\pgf@x by180pt\relax%
        \edef\dotnumberanchor{\the\pgf@x}%
        \node [anchor=\dotnumberanchor, every dot number/.try, dot number \pgfmathcounter/.try] 
          at (@dot-\pgfmathcounter)
          {\tikzjointhedotsnumber=\pgfmathcounter\relax\tikzjointhedotstypesetnumber{\tikzjointhedotsnumber}};
        \c@pgf@counta=\pgfmathcounter\relax%
            \advance\c@pgf@countb by1\relax%
            \ifnum\c@pgf@countb>\tikzjointhedotsnumber%
              \c@pgf@countb=1\relax%
            \fi%
        \repeatpgfmathloop%
  }
}

% Command for typesetting dot number
% #1 - a count register holding the current dot number
%
\def\tikzjointhedotstypesetnumber#1{\the#1}
\makeatletter
% Keys for setting dot number styles
\tikzset{%
  syle dot number range/.code args={#1 to #2 with #3}{%
    \c@pgf@counta=#1
    \pgfmathloop
    \ifnum\c@pgf@counta>#2\relax%
    \else%
      \tikzset{dot number \the\c@pgf@counta/.style={#3}}%
      \advance\c@pgf@counta by1
    \repeatpgfmathloop%
  },
  style dot number list/.code args={#1 with #2}{%
    \pgfutil@for\tmp:=#1\do{%
      \tikzset{dot number \tmp/.style={#2}}%
    }%
  }
}
\makeatother

\tikzset{%
  % Executed for every dot
  every dot/.style={fill=black,
    insert path={  circle [radius=.75mm] coordinate [alias=dot-last] (dot-\the\tikzjointhedotsnumber)  }
  },
  % Executed for every dot number
  every dot number/.style={
   shape=circle,
   font=\footnotesize\sf,
  },
  join the dots/.style={
    decoration=join the dots, decorate
  },
  lines/.style={
    ultra thick,
    line join=round,
    line cap=round
  },
  crayon/.style={
    draw=#1,
    line join=round,
    line cap=round,
    line width=1mm
  },
  sketch/.style={
    bend right, out=rand*10, in=180-rand*10
  }
}

\begin{document}
% Put (most of) the picture in a box, so it doesn't
% have to be redrawn every iteration.
\newbox\hanukkahbox
\setbox\hanukkahbox=\hbox{%
\begin{tikzpicture}[baseline={(0,0)}]
% Draw and number the dots
\path [postaction={join the dots}]
    (-1/2,11) 
    \foreach \a [count=\c from 1, evaluate={\d=\a+1;\s=90/\d;}] in {1,2,3,4}{
        -- ++(0,{\a==1?-2:-1})
        \foreach \i in {1,...,\d}{
            arc (270-\i*\s+\s:270-\i*\s:\a*2-1 and \a*3/2-1/2) 
        }
        -- ++(-1,0) coordinate [midway] (candle-\c)
        \foreach \i in {1,...,\d}{
            arc (180+\i*\s-\s:180+\i*\s:\a*2 and \a*3/2) 
        }
    }
    -- ++(0,-1) 
    -| ++(-1,-1/2) -| ++(-1,-1/2) -| ++(-1,-1/2)
    -- ++(7,0)
    |- ++(-1,1/2) |- ++(-1,1/2) |- ++(-1,1/2)
    \foreach \a [count=\c from 5, evaluate={\d=\a+1;\s=90/\d;}] in {4,3,2,1}{
        -- ++(0,1)
        \foreach \i in {1,...,\d}{
            arc (270+\i*\s-\s:270+\i*\s:\a*2 and \a*3/2) 
        }
        -- ++(-1,0) coordinate [midway] (candle-\c)
        \foreach \i in {1,...,\d}{
            arc (360-\i*\s+\s:360-\i*\s:\a*2-1 and \a*3/2-1/2) 
        }
    }
    -- ++(0,2);
% Draw the lines that are visible.
\draw [lines] 
  (dot-1)  -- (dot-last) coordinate [midway] (candle-9);
\end{tikzpicture}}%
%
\foreach \k in {1,...,88}{%
\begin{minipage}{\wd\hanukkahbox}%
\begin{tikzpicture}
% Place the picture box.
\pgftext[bottom]{\copy\hanukkahbox}%
% Draw candles
\foreach \cn in {1,...,9}{% 
 \tikzset{shift=(candle-\cn), yshift=1pt}
 % Set the random seed as fixed with the candle number as
 % a parameter so that candles are different from each
 % other, but drawn the same on each outer iteration.
 \pgfmathsetseed{99+\cn*50}%
 % Candle
 \fill [lines, fill=purple!80, rounded corners=0.125cm]
  (-1/3,0) to [sketch] (-1/3,3) -- (1/3,3)  to [sketch] (1/3,0);
 % Wick
 \draw [lines] (0,3) -- ++(0,1/4);
 % Ensure highest point for bounding box
 \path (candle-9) -- ++(0,5);
 \pgfmathsetseed{99+\k*50+\cn*25}%
 \tikzset{shift={(0,3+1/8)}, xscale=round(rnd)*2-1,yscale=1+rand/8}
 \foreach \s/\c in {1/yellow,.5/red}
 \path [lines, fill=\c!50!orange, opacity=3/4, scale=\s] 
   (0,0) 
   arc (270:180:3/8) 
   .. controls ++(0,1/4) and ++(0,-1/4) .. (0,3/2)
   arc (90:0:3/8 and 1) arc (360:270:3/8 and 1/2);
} 
\pgfmathsetseed{99}%
\draw [crayon=black!80] (dot-1) \foreach \l in {1,...,\k}{ to [sketch] (dot-\l) };
\end{tikzpicture}%
\end{minipage}}

\end{document}

通过使用动画功能瘸子可以pdf转换为gif：

最后，这是一个陀螺：

\documentclass[tikz,border=0.125cm]{standalone}
\newcount\TeXXeTstate% <- Why?
\usepackage{cjhebrew}
\usepackage{tikz}
\usetikzlibrary{decorations.pathreplacing}
\makeatletter
\newcount\tikzjointhedotsnumber


\pgfdeclaredecoration{join the dots}{initial}{%
  \state{initial}[width=0pt, next state=do dots, persistent precomputation={\global\tikzjointhedotsnumber=1}]{}
  %
  \state{do dots}[width=\pgfdecoratedinputsegmentlength, persistent postcomputation={\global\advance\tikzjointhedotsnumber by1}]{%
    \pgfcoordinate{@dot-\the\tikzjointhedotsnumber}{\pgfpointorigin}%
  }
  %
  \state{final}{%
    % Is the last point the same as the first?
      \pgfpointdiff{\pgfpointdecoratedpathlast}{\pgfpointdecoratedpathfirst}%
      \pgfmathveclen{\the\pgf@x}{\the\pgf@y}%
      \ifdim\pgfmathresult pt=0pt\relax%
        \global\advance\tikzjointhedotsnumber by-1\relax
      \else
        \pgftransformshift{\pgfpointdecoratedpathlast}%
        \pgfcoordinate{@dot-\the\tikzjointhedotsnumber}{\pgfpointorigin}%
      \fi
      % Ok, now we do everything. Draw the dots and place the numbers.
      %
      \c@pgf@counta=\tikzjointhedotsnumber%
      \c@pgf@countb=2\relax%
      \edef\lastdot{\the\tikzjointhedotsnumber}%
      \def\nextdot{2}%
      \pgftransformreset%
      \pgfmathloop%
      \ifnum\pgfmathcounter>\tikzjointhedotsnumber
      \else%
        % Draw the dot.
        \edef\tmp{\the\tikzjointhedotsnumber}%
                \tikzjointhedotsnumber=\pgfmathcounter\relax%
        \path [shift={(@dot-\pgfmathcounter)}, every dot/.try, dot \pgfmathcounter/.try]; 
         \tikzjointhedotsnumber=\tmp% 
        %
        % Calculate the dot number node anchor
        \pgfmathanglebetweenpoints{\pgfpointanchor{@dot-\pgfmathcounter}{center}}{\pgfpointanchor{@dot-\the\c@pgf@counta}{center}}%
        \pgf@xc=\pgfmathresult pt\relax%
        \ifdim0pt>\pgf@xc%
          \advance\pgf@xc by360pt\relax%
        \fi%
        \pgfmathanglebetweenpoints{\pgfpointanchor{@dot-\pgfmathcounter}{center}}{\pgfpointanchor{@dot-\the\c@pgf@countb}{center}}%
        \pgf@yc=\pgfmathresult pt\relax%
        \ifdim0pt>\pgf@yc%
          \advance\pgf@yc by360pt\relax%
        \fi%
        \ifdim\pgf@xc>\pgf@yc%
          \pgf@x=360pt\relax%
        \else%
          \pgf@x=0pt\relax%
        \fi%
        \advance\pgf@x by-\pgf@xc%
        \advance\pgf@x by\pgf@yc%
        \divide\pgf@x by2\relax%
        \advance\pgf@x by\pgf@xc%
        \advance\pgf@x by180pt\relax%
        \edef\dotnumberanchor{\the\pgf@x}%
        \node [anchor=\dotnumberanchor, every dot number/.try, dot number \pgfmathcounter/.try] 
          at (@dot-\pgfmathcounter)
          {\tikzjointhedotsnumber=\pgfmathcounter\relax\tikzjointhedotstypesetnumber{\tikzjointhedotsnumber}};
        \c@pgf@counta=\pgfmathcounter\relax%
            \advance\c@pgf@countb by1\relax%
            \ifnum\c@pgf@countb>\tikzjointhedotsnumber%
              \c@pgf@countb=1\relax%
            \fi%
        \repeatpgfmathloop%
  }
}

% Command for typesetting dot number
% #1 - a count register holding the current dot number
%
\def\tikzjointhedotstypesetnumber#1{\the#1}
\makeatletter
% Keys for setting dot number styles
\tikzset{%
  syle dot number range/.code args={#1 to #2 with #3}{%
    \c@pgf@counta=#1
    \pgfmathloop
    \ifnum\c@pgf@counta>#2\relax%
    \else%
      \tikzset{dot number \the\c@pgf@counta/.style={#3}}%
      \advance\c@pgf@counta by1
    \repeatpgfmathloop%
  },
    style dot number list/.code args={#1 with #2}{%
      \pgfutil@for\tmp:=#1\do{%
        \tikzset{dot number \tmp/.style={#2}}%
      }%
    }
}
\makeatother

\tikzset{%
  % Executed for every dot
  every dot/.style={fill=black,
    insert path={  circle [radius=.75mm] coordinate [alias=dot-last] (dot-\the\tikzjointhedotsnumber)  }
  },
  % Executed for every dot number
  every dot number/.style={
   font=\footnotesize\sf,
   anchor=\pgfdecoratedangle-90
  },
  join the dots/.style={
    decoration=join the dots, decorate
  },
  lines/.style={
    ultra thick,
    line join=round,
    line cap=round
  },
  style dot number list={15,16,17 with anchor=0},
}

\def\tikzjointhedotstypesetnumber#1{%
  \textcjheb{\ifcase#1\or'\or b\or g\or d\or h\or w\or z\or.h\or.t\or y\or k|%
    \or l\or m|\or n|\or s\or `\or p|\or.s|\or q\or r\or/s\or t\else?\fi}}
\begin{document}

\begin{tikzpicture}[x=(-40:0.5cm), y=(195:0.5cm), z=(75:0.5cm)]
\draw [lines] (1*cos 45,-1*sin 45,7) -- (1*cos 45,-1*sin 45,3) arc (-45:135:1) -- (-1*cos 45,1*sin 45,5.25);
\path[postaction=join the dots] 
  (1*cos 45,-1*sin 45,5.25) -- (3,-3, 3) -- (3,0,3) -- (3,3,3)
  -- (3,3,1) -- (3,3,-1) -- (3,3,-3) -- (3,0,-3) -- (3,-3,-3)
  -- (2,-2,-5) -- (1,-1,-7) -- (0,0,-9)
  -- (-1,1,-7) -- (-2,2,-5) -- (-3,3,-3)
  -- (-3,3,0) -- (-3,3,3)  -- (-1*cos 45,1*sin 45,5.25) -- (-1*cos 45,1*sin 45,7)
  -- (-1*cos 45,1*sin 45,9) -- (1*cos 45,-1*sin 45,9) -- (1*cos 45,-1*sin 45,7);

\node [yslant=-cos 40, scale=8, text=blue!50!purple] at (0,3,0) {\textcjheb{h}};
\node [yslant=cos 75, scale=8, text=red!50!orange] at (3,0,0) {\textcjheb{n|}};

\draw [lines]
  (dot-4) -- (dot-17)
  (dot-2) -- (dot-9)
  (dot-7) -- (dot-15);

\end{tikzpicture}
\end{document}