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直角三角形中重复的垂直线

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直角三角形中重复的垂直线

我正在尝试从直角三角形 (OAB) 中的 O 向斜边画垂线。从它的垂线脚（例如 X0）向矩形轴画两条垂线，垂线脚分别为 A0 和 B0。同样，从 O 向 A0B0 线画垂线，垂线脚在轴上为 A1 和 B1。我想重复这个过程 2-3 次。到目前为止，我已经到达了以下点。

\documentclass[varwidth]{standalone}
\usepackage{tkz-euclide}
\usepackage{tikz}
\usepackage{xcolor}
\usetikzlibrary{calc,spy}
\makeatletter
\usetikzlibrary{angles, intersections, positioning, quotes}
\usepackage{siunitx}
\begin{document}
\centering
\begin{tikzpicture}[x=2cm,y=2cm,
        spy using outlines={circle, size=3cm, connect spies}]
    \path  (0,0) coordinate[label=left:\Large $O$] (O) (0,3) coordinate[label=left:\Large $B$] (B) (4,0) coordinate[label=right:\Large $A$] (A);
    \draw [thick, black] (O) -- (B) -- (A) -- cycle;
    \draw [black!90, thick] (O) --  ($(B)!(O)!(A)$);
    \fill [red!70] ($(B)!(O)!(A)$) node[right]{\Large $X_0$};
\end{tikzpicture}
\end{document}

我卡在了 X0。如何在 latex 代码中获取垂直线的脚？

在此处输入图片描述

答案1

如果我误解了这个问题，请原谅我，但它读起来就像你想递归地绘制高度。所以这里有一个替代方案元帖子裹着luamplib……

在此处输入图片描述

使用以下命令进行编译lualatex：

\documentclass[border=5mm]{standalone}
\usepackage{luamplib}
\begin{document}
\mplibtextextlabel{enable}
\begin{mplibcode}
input colorbrewer-rgb
vardef recursive_pedal(expr level, o, a, b) = 
    save p; pair p; p = whatever[a,b]; p - o = whatever * (a-b) rotated 90;
    if level > 1:
        recursive_pedal(level - 1, p, o, a);
        recursive_pedal(level - 1, p, o, b);
    fi
    draw o -- p withcolor Blues[6][level];
enddef;
beginfig(1);
    pair O, A, B;
    O = origin;
    A = 377 right;
    B = 233 up;
    recursive_pedal(6, O, A, B);
    draw O -- A -- B -- cycle;
    label.llft("$O$", O);
    label.lrt("$A$", A);
    label.top("$B$", B);
endfig;
\end{mplibcode}
\end{document}

答案2

像这样？

在此处输入图片描述

（我不确定我是否正确理解了你的问题）

\documentclass[varwidth]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}

\begin{document}
\centering
\begin{tikzpicture}[x=2cm,y=2cm,
       % spy using outlines={circle, size=3cm, connect spies}
every label/.append style = {font=\large}
                    ]
\draw[thick] (0,0) coordinate[label= left:$O$] (O) -- (0,3) 
                   coordinate[label= left:$B$] (B) -- (4,0) 
                   coordinate[label=right:$A$] (A) -- cycle;
\draw [thick]   (O) --  ($(B)!(O)!(A)$) coordinate[red, label=above right:$X_0$] (x0);
\draw[dashed]   (x0 -| O) coordinate[label= left:$B_0$] (b0) -|
                (x0 |- O) coordinate[label=below:$A_0$] (a0);
\end{tikzpicture}
\end{document}

答案3

我相信Zarko 已经给你答案了你正在寻找Thruston 制作了一张美丽的照片。

让我在他的 Metapost 答案中添加一个 TikZ 解决方案。

通过\unexpanded（我们只需要，因为我们想要的结果#4-1）在\tikzPerpNameScheme所有级别上存活下来，然后可以让\tikzPerpPrintScheme坐标名称正确显示。

（在这种情况下，我们可以直接使用，[#2,#3]_{#1}^{#4}但这使得自定义标签变得更容易。）

我无法找出遵循您的命名方案的正确规则。

代码 1（仅代码行）

\documentclass[tikz]{standalone}
\usetikzlibrary{calc, ext.misc}
\tikzset{
  draw perpendicular from/.style args={#1 onto #2--#3 at level #4}{
    /utils/exec=\pgfmathtruncatemacro\tikzPerpLevel{int(#4)},% sanitize input
    draw perpendicular from'/.expanded={#1}{#2}{#3}{\tikzPerpLevel}},
  draw perpendicular from'/.style n args={4}{
    insert path={coordinate (#1>#2-#3<#4) at ($(#2)!(#1)!(#3)$)},
    /utils/TeX/ifnum={#4>0}{% not yet at level 0? → recursion
      draw perpendicular from'/.expanded=%
        {#1>#2-#3<#4}{#1}{#3}{\pgfinteval{#4-1}},
      draw perpendicular from'/.expanded=%
        {#1>#2-#3<#4}{#1}{#2}{\pgfinteval{#4-1}}}{},
    insert path={
      (#1) edge[perpendicular line/.try=
        {#4}{\tikzPerpLevel}] (#1>#2-#3<#4)}}}
\begin{document}
\begin{tikzpicture}[x=2cm, y=2cm]
\path[font=\Large] (0,0) coordinate[label=below left:$O$] (O)
                   (0,3) coordinate[label=left:$B$]       (B)
                   (4,0) coordinate[label=right:$A$]      (A);
\draw[
  perpendicular line/.style 2 args={
    color/.pgfmath wrap={blue!##1}{100*(#1+1)/(#2+1)}},
  draw perpendicular from=O onto A--B at level 4];
\draw[thick] (O) -- (B) -- (A) -- cycle;
\end{tikzpicture}
\end{document}

代码 2（带标签）

\documentclass[tikz, convert]{standalone}
\usetikzlibrary{calc, ext.misc}
\newcommand*\tikzPerpNameScheme[4]{#1>#2-#3<#4} % no fancy math for TikZ names
\newcommand*\tikzPerpPrintScheme[4]{% (#1) onto [(#2)--(#3)] at level #4
  [#2,#3]_{#1}^{#4}}
\tikzset{
  draw perpendicular from/.style args={#1 onto #2--#3 at level #4}{
    /utils/exec=\pgfmathtruncatemacro\tikzPerpLevel{int(#4)},% sanitize input
    draw perpendicular from'/.expanded={#1}{#2}{#3}{\tikzPerpLevel}},
  draw perpendicular from'/.style n args={4}{
    insert path={
      coordinate (\tikzPerpNameScheme{#1}{#2}{#3}{#4}) at ($(#2)!(#1)!(#3)$)},
    /utils/TeX/ifnum={#4>0}{% not yet at level 0? → recursion
      draw perpendicular from'/.expanded={%
        \unexpanded{\tikzPerpNameScheme{#1}{#2}{#3}{#4}}}
        {\unexpanded{#1}}{\unexpanded{#3}}{\pgfinteval{#4-1}},
      draw perpendicular from'/.expanded={%
        \unexpanded{\tikzPerpNameScheme{#1}{#2}{#3}{#4}}}
        {\unexpanded{#1}}{\unexpanded{#2}}{\pgfinteval{#4-1}}}{},
    insert path={
      (#1) edge[perpendicular line/.try=
        {#4}{\tikzPerpLevel}{\tikzPerpNameScheme{#1}{#2}{#3}{#4}}]
                            (\tikzPerpNameScheme{#1}{#2}{#3}{#4})}}}
\begin{document}
\begin{tikzpicture}[x=2cm, y=2cm]
\pgfmathsetseed{114666}
\path[font=\Large] (0+rnd,0+rnd) coordinate[label=below left:$O$] (O)
                   (0+rnd,3+rnd) coordinate[label=left:$B$]       (B)
                   (4+rnd,0+rnd) coordinate[label=right:$A$]      (A);
\draw[
  perpendicular line/.style n args={3}{
    color/.pgfmath wrap={blue!##1}{100*(#1+1)/(#2+1)}},
  draw perpendicular from=O onto A--B at level 5]; % 9 crashes
\draw[thick] (O) -- (B) -- (A) -- cycle;
\end{tikzpicture}

\begin{tikzpicture}[x=2cm, y=2cm]
\path[font=\Large] (0,0) coordinate[label=below left:$O$] (O)
                   (0,3) coordinate[label=left:$B$]       (B)
                   (4,0) coordinate[label=right:$A$]      (A);
\draw[
  perpendicular line/.style n args={3}{
    dash pattern=on 1pt off #2pt-#1pt,
    edge node={node[at end,
      /utils/exec=\let\tikzPerpNameScheme\tikzPerpPrintScheme]{$#3$}}},
  draw perpendicular from=O onto A--B at level 2];
\draw[thick] (O) -- (B) -- (A) -- cycle;
\node[below left] at (A|-B)
  {$\tikzPerpPrintScheme{\mathit{point}}{p_1}{p_2}{\mathit{level}}$};
\end{tikzpicture}
\end{document}

输出 2

在此处输入图片描述 在此处输入图片描述

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