Rooty 螺旋的构建、代码解释

Question

有人能解释一下这段代码的某些部分吗？我是 LaTeX 新手，有些部分看不懂。

这\foreach \y in {86,38,15}意味着什么？

你能详细解释一下这个循环在做什么吗 \foreach \x in {1,...,\y}{ ... %here the dots represent all the code included in the main code below }

？

如果您愿意提供任何帮助，我将不胜感激。谢谢。

% Rooty helix
% Author: Felix Lindemann


\documentclass{minimal}

\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}

\pagestyle{empty}
\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\xdefinecolor{darkgreen}{RGB}{175, 193, 36}
\newcounter{cntShader}
\newcounter{cntRoot}
\setcounter{cntShader}{20}
\def\couleur{darkgreen}

\begin{tikzpicture}
    \foreach \y in {86,38,15}{
        \setcounter{cntShader}{1}
        \coordinate (a) at (0,0);
        \coordinate (b) at (0:1);
        \foreach \x in {1,...,\y}{%
            \coordinate (c) at ($ (b)!1cm!270:(a) $);
            \begin{pgfonlayer}{background}
                \draw[fill=\couleur!\thecntShader] (a)--(b)--(c)--cycle;
            \end{pgfonlayer}
            \setcounter{cntRoot}{\x}
            \addtocounter{cntRoot}{1}
            \node[fill=white,draw,circle,inner sep=1pt] at (c)
                {$\sqrt{\thecntRoot}$};
            \coordinate (b) at (c);
            \pgfmathsetcounter{cntShader}{\thecntShader+4}
            \setcounter{cntShader}{\thecntShader}
       }
    }
    \node[fill=white,draw,circle,inner sep=1pt] at (0:1) {$\sqrt{1}$};
\end{tikzpicture}

\end{document} 

Answer 1

这里有一个建议，以更易于理解的方式重写代码。它是否真的更易于理解可能取决于谁在看它。无论如何，此代码只有一个循环而不是两个循环。它使用decorations.marking（当然内部也使用循环）来放置节点。从我对代码的理解来看，计算算法用于使圆之间的距离大致相等，但这decorations.markings是免费的。阴影是在背景层上完成的，如上面的代码所示，但在单个循环中。特别是，如果您想要不同的最大值或不同的螺旋，我认为下面的方法将更容易调整。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.markings}
\begin{document}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\xdefinecolor{darkgreen}{RGB}{175, 193, 36}

\begin{tikzpicture}
    \draw[decorate,decoration={markings,
    mark=between positions 0 and 1 step 1/86 with {%
    \node[fill=white,circle,draw,inner sep=1pt] 
    (n-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}){%
    $\sqrt{\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}}$};}}] 
    plot[variable=\x,domain=45:945,samples=86]
    (\x:{0.5+pow(\x/66,4/5)});     
    \begin{pgfonlayer}{background}
    \foreach \X [remember=\X as \LastX,evaluate=\X as \Y using
    {int(3*\X+255-3*87)}] in {87,86,...,1}
    {\ifnum\X=87
    \else
     \draw[fill=darkgreen!\Y] (n-\LastX.center) -- (n-\X.center) -- (0,0) -- cycle;
    \fi}
    \end{pgfonlayer}
\end{tikzpicture}
\end{document}

也可以一次完成所有操作，即通过一个循环有效地完成。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.markings}
\begin{document}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\xdefinecolor{darkgreen}{RGB}{175, 193, 36}

\begin{tikzpicture}
\pgfmathtruncatemacro{\xmax}{87}
\pgfmathtruncatemacro{\xnmax}{\xmax-1}
\coordinate (O) at (0,0);
    \draw[decorate,decoration={markings,
    mark=between positions 0 and 1 step 1/\xnmax with {%
    \pgfmathtruncatemacro{\myx}{1+\xmax-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}}
    \pgfmathtruncatemacro{\myy}{\myx+1}
    \pgfmathtruncatemacro{\myz}{3*\myx+255-3*\xmax}
    \node[fill=white,circle,draw,inner sep=1pt] 
    (n-\myx){%
    $\sqrt{\myx}$};
    \ifnum\myx=\xmax
    \else
    \begin{pgfonlayer}{background}
     \draw[fill=darkgreen!\myz] (n-\myx.center) -- (n-\myy.center) -- (O) -- cycle;
    \end{pgfonlayer}
    \fi
    }}] 
    plot[variable=\x,domain=930:0,samples=\xmax]
    (\x:{0.5+pow(\x/66,4/5)+ifthenelse(\x<0.1,0.3,0)});     
\end{tikzpicture}
\end{document}

如果要绘制更多或更少的根，则需要更改\xmax并调整域，即domain=930:0用其他内容替换。由于半径增大，域的上限（930在本例中）和之间的关系\xmax不是线性的。相反，存在一个经验定律（我通过积分弧长并拟合一个函数“推导”出该定律，该定律表明域的上限类似于pow(\xmax/87,0.65)*930，其中\xmax是最大数字，即上述示例中的 87。

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.markings}
\begin{document}

\pgfdeclarelayer{background}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}

\xdefinecolor{darkgreen}{RGB}{175, 193, 36}
\foreach \X in {10,15,...,100}
{\begin{tikzpicture}[declare
function={Rad(\x)=1+pow(\x/66,4/5)+ifthenelse(\x<1,0.3,0);}]
\path[use as bounding box] (-12,-10.5) rectangle (12,9.5);
\pgfmathtruncatemacro{\xmax}{\X}
\pgfmathtruncatemacro{\xnmax}{\xmax-1}
\pgfmathsetmacro{\Xmax}{pow(\xmax/87,0.65)*930}
\coordinate (O) at (0,0);
    \draw[decorate,decoration={markings,
    mark=between positions 0 and 1 step 1/\xnmax with {%
    \pgfmathtruncatemacro{\myx}{1+\xmax-\pgfkeysvalueof{/pgf/decoration/mark info/sequence number}}
    \pgfmathtruncatemacro{\myy}{\myx+1}
    \pgfmathtruncatemacro{\myz}{3*\myx+255-3*\xmax}
    \node[fill=white,circle,draw,inner sep=1pt] 
    (n-\myx){%
    $\sqrt{\myx}$};
    \ifnum\myx=\xmax
    \else
    \begin{pgfonlayer}{background}
     \draw[fill=darkgreen!\myz] (n-\myx.center) -- (n-\myy.center) -- (O) -- cycle;
    \end{pgfonlayer}
    \fi
    }}] 
    plot[variable=\x,domain=\Xmax:0,samples=\xmax]
    (\x:{Rad(\x)});     
\end{tikzpicture}}
\end{document}