数字螺旋

Question

我相信有更有效的方法来处理你的星爆（例如，使用LaTeX3)，但下面的代码处理它们的方式是，首先定义一个逗号分隔的特殊数字列表，然后循环遍历所有数字以查看是否有匹配项。5使用可以轻松处理数字 mod \pgfmathparseresult。

最终结果是：

以下是代码：

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{stix}
\usepackage{tikz}
\usetikzlibrary{shapes,shapes.geometric,calc}
\usepackage{pifont}
\usepackage{wasysym}
\usepackage{graphicx}
\newif\ifnotfound% to mark the stars as we print them
\newcommand\starbursts{3,6,11,13,17,23,29,37,43,52,56,61,63,68,69,71,72,80,91,99}
\begin{document}

  \begin{tikzpicture}
    \coordinate (a) at (0,0);
    \coordinate (b) at (0:1);
    \foreach \x in {1,...,100}{%
        \coordinate (c) at ($(b)!0.9cm!270:(a)$);
        \pgfmathparse{int(mod(\x,5))}
        \ifnum\pgfmathresult=0
        \node[fill=white,draw,regular polygon, regular polygon sides=5,inner sep=1pt] at (c) {$\x$};
        \else
          \notfoundtrue% this will mark any starbursts
          \foreach \y in \starbursts {% check for stars
            \ifnum\x=\y% a star is born!
                \node[fill=white,draw,starburst,inner sep=1pt] at (c) {$\x$};
                \global\notfoundfalse% need \global as inside a loop
            \fi
          }
          \ifnotfound% we have not printed a node yet
        \node[fill=white,draw,circle,inner sep=1pt] at (c) {$\x$};
          \fi
        \fi
        \coordinate (b) at (c);
    };
  \end{tikzpicture}

\end{document}

编辑

这是一个LaTeX3版本。代码更加简洁但从某种意义上说，它也比较慢，因为我的笔记本电脑返回以下时间：

tikz：实际 2.436 用户 2.136 系统 0.281 pcpu 99.18

tikz：实际 2.479 用户 2.169 系统 0.294 pcpu 99.34

解释：实际 2.557 用户 2.250 系统 0.293 PCPU 99.45

解释：实际 2.552 用户 2.238 系统 0.301 PCPU 99.49

输出与上面相同。以下是修改后的代码：

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{stix}
\usepackage{tikz}
\usetikzlibrary{shapes,shapes.geometric,calc}
\usepackage{pifont}
\usepackage{wasysym}
\usepackage{graphicx}

\tikzset{
  mynode/.style = {fill=white,draw,inner sep=1pt}
}
\usepackage{expl3}
\ExplSyntaxOn
\clist_new:N \l_starbursts
\clist_set:Nn \l_starbursts {3,6,11,13,17,23,29,37,43,52,56,61,63,68,69,71,72,80,91,99}
\newcommand\SetNode[1]{
  \int_compare:nTF { \int_mod:nn { #1 } { 5 } = 0 }
    {\tikzset{mynode/.append~style={regular~polygon, regular~polygon~sides=5}}}
    {
      \clist_if_in:NoTF \l_starbursts {#1}
        {\tikzset{mynode/.append~style={starburst}}}
        {\tikzset{mynode/.append~style={circle}}}
    }
}
\cs_generate_variant:Nn \clist_if_in:NnTF {noTF}
\ExplSyntaxOff

\newif\ifnotfound% to mark the stars as we print them
\begin{document}

  \begin{tikzpicture}
    \coordinate (a) at (0,0);
    \coordinate (b) at (0:1);
    \foreach \x in {1,...,100}{%
        \coordinate (c) at ($(b)!0.9cm!270:(a)$);
        \SetNode{\x}
        \node[mynode] at (c) {$\x$};
        \coordinate (b) at (c);
    };
  \end{tikzpicture}

\end{document}

编辑二

这是遵循 jfbu 建议的第三种“纯 TeX”方法，其中星号优先于六边形（与上面不同，正如 sgmoye 在评论中指出的那样）。我改用纯 TeX，因为令人惊讶的是，以类似的方式使用 LaTeX3 序列会导致代码速度变慢。也许 clists 会更好？也可能是第一个解决方案直接绘制节点，而解决方案 II 和 III 使用了一些\tikzset{...}技巧。无论如何，这是代码：

\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{stix}
\usepackage{tikz}
\usetikzlibrary{shapes,shapes.geometric,calc}
\usepackage{pifont}
\usepackage{wasysym}
\usepackage{graphicx}

\tikzset{
  mynode/.style = {fill=white,draw,inner sep=1pt}
}
\newcommand\starbursts{3,6,11,13,17,23,29,37,43,52,56,61,63,68,69,71,72,80,91,99}
\def\setnextstar#1,#2!{%
  \if\relax\detokenize{#1}\relax\gdef\nextstar{200}\else\gdef\nextstar{#1}\gdef\starbursts{#2}\fi%
}
\expandafter\setnextstar\starbursts,,!

\newcommand\SetNode[1]{
  \ifnum#1=\nextstar
      \tikzset{mynode/.append style={starburst}}
      \expandafter\setnextstar\starbursts!
  \else
      \pgfmathparse{int(mod(\x,5))}
      \ifnum\pgfmathresult=0
         \tikzset{mynode/.append style={regular polygon, regular polygon sides=5}}
      \else
         \tikzset{mynode/.append style={circle}}
      \fi
  \fi
}
\begin{document}

  \begin{tikzpicture}
    \coordinate (a) at (0,0);
    \coordinate (b) at (0:1);
    \foreach \x in {1,...,100}{%
        \coordinate (c) at ($(b)!0.9cm!270:(a)$);
        \SetNode{\x}
        \node[mynode] at (c) {$\x$};
        \coordinate (b) at (c);
    };
  \end{tikzpicture}

\end{document}

输出略有不同，因为80现在有一个星号。

Answer 1