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使用 TikZ 制作正交圆

tag-icon • tag-icon tikz-pgf tkz-euclide
使用 TikZ 制作正交圆

我正在制作一个图表，以便向我的学生解释正交圆。我使用的代码如下：

   \documentclass{article}
   \usepackage{tikz,tkz-euclide}
   \usetkzobj{all}
   \begin{document}
        \begin{tikzpicture}[scale=0.4 ]
        \draw[thick, color=gray,->] (-15,0) -- (12,0) node[right] {\textcolor{black}{$x$}};
        \draw[thick, color=gray, ->] (0,-6) -- (0,12) node[above] {\textcolor{black}{$y$}};
        \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=left:{$C_1$}] (C1) at (-6,4) {};
        \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=right:{$C_2$}] (C2) at (2,1) {};  
        \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=above:{$~~A$}] (A) at (15/73,478/73) {};
        \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=below:{$B~$}] (B) at (-3,-2) {};       
        \node at (-14, 4) {$K_1$};
        \node at (9, -1) {$K_2$};
        \draw[gray] (C1) -- (C2);
        \draw[blue] (C1) --(B);
        \draw[red] (C2) --(B);
        \draw[blue] (C1) --(A);
        \draw[red] (C2) --(A);
        \draw (C1) circle (6.7082);
        \draw (C2) circle (5.83095);
        \tkzMarkSegment[color=blue,pos=.5,mark=||](C1,B);
        \tkzMarkSegment[color=red,pos=.5,mark=|](B,C2);
        \tkzMarkSegment[color=blue,pos=.5,mark=||](C1,A);
        \tkzMarkSegment[color=red,pos=.5,mark=|](A,C2);
        \tkzMarkRightAngle[size=0.7](C1,A,C2);
        \tkzMarkRightAngle[size=0.7](C1,B,C2);
        \end{tikzpicture}
\end{document}

请注意，位于\tkzMarkRightAngle代码的最末端，这通常意味着它们位于图的最顶部。但是，我得到的输出是这样的：

输出

注意直角符号内的两条神秘的黑色曲线。它们肯定不是圆圈的延伸。我不知道它们是什么。我也试过用，\tkzMarkRightAngle[fill=white]但即使这样也无法消除它。

答案1

问题是 A 和 B 是nodes这样的，连接将被绘制到它们边界上距离起始点最近的点。因此连接点并不像您想象的那样位于中心。

这是一个最小化的案例：

  \begin{tikzpicture}
    [
      scale=0.4,
    ]
    \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=left:{$C_1$}] (C1) at (-6,4) {};
    \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=right:{$C_2$}] (C2) at (2,1) {};
    \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=above:{$~~A$}] (A) at (15/73,478/73) {};
    \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=below:{$B~$}] (B) at (-3,-2) {};
    \tkzMarkRightAngle[size=0.7](C1,A,C2)
    \tkzMarkRightAngle[size=0.7](C1,B,C2)
  \end{tikzpicture}

这表明了问题：

倾斜标记

我假设cycle是用来返回原始点的，这会扭曲最终的线条。但这只是一个猜测。

为了解决这个问题，您可以放置​​一个坐标和一个节点，只命名坐标。

例如：

\documentclass[tikz,border=10pt]{standalone}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
  \begin{tikzpicture}
    [
      scale=0.4,
      my circle/.style={circle, fill=black, inner sep=0pt, minimum size=3pt}
    ]
    \draw[thick, color=gray,->] (-15,0) -- (12,0) node[right] {$x$};
    \draw[thick, color=gray, ->] (0,-6) -- (0,12) node[above] {$y$};
    \path [my circle]  (-6,4) coordinate (C1) node [label=left:{$C_1$}] {}
     (2,1) coordinate  (C2) node [label=right:{$C_2$}] {}
     (15/73,478/73) coordinate  (A) node [label=above:{$~~A$}] {}
     (-3,-2) coordinate (B) node [label=below:{$B~$}] {};
    \node at (-14, 4) {$K_1$};
    \node at (9, -1) {$K_2$};
    \draw[gray] (C1) -- (C2);
    \draw[blue] (C1) --(B);
    \draw[red] (C2) --(B);
    \draw[blue] (C1) --(A);
    \draw[red] (C2) --(A);
    \draw (C1) circle (6.7082);
    \draw (C2) circle (5.83095);
    \tkzMarkSegment[color=blue,pos=.5,mark=||](C1,B)
    \tkzMarkSegment[color=red,pos=.5,mark=|](B,C2)
    \tkzMarkSegment[color=blue,pos=.5,mark=||](C1,A)
    \tkzMarkSegment[color=red,pos=.5,mark=|](A,C2)
    \tkzMarkRightAngle[size=0.7](C1,A,C2)
    \tkzMarkRightAngle[size=0.7](C1,B,C2)
  \end{tikzpicture}
\end{document}

去偏斜标记

答案2

没有tkz-euclide，只有tikz

   \documentclass{article}
   \usepackage[T1]{fontenc}  %% Makes | to work properly
   \usepackage{tikz}
   \usetikzlibrary{calc}
   \begin{document}
        \begin{tikzpicture}[scale=0.4 ]
        \draw[thick, color=gray,->] (-15,0) -- (12,0) node[right] {\textcolor{black}{$x$}};
        \draw[thick, color=gray, ->] (0,-6) -- (0,12) node[above] {\textcolor{black}{$y$}};
        \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=left:{$C_1$}] (C1) at (-6,4) {};
        \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=right:{$C_2$}] (C2) at (2,1) {};
        \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=above:{$~~A$}] (A) at (15/73,478/73) {};
        \node[circle,fill=black,inner sep=0pt,minimum size=3pt,label=below:{$B~$}] (B) at (-3,-2) {};
        \node at (-14, 4) {$K_1$};
        \node at (9, -1) {$K_2$};
        \draw[gray] (C1) -- (C2);
        \draw[blue] (C1) -- node[sloped]{||}(B);
        \draw[red] (C2) --node[sloped]{|}(B);
        \draw[blue] (C1) --node[sloped]{||}(A);
        \draw[red] (C2) -- node[sloped]{|}(A);
        \draw (C1) circle (6.7082);
        \draw (C2) circle (5.83095);

        %% right angle mark
        \coordinate (a) at ($(A)!8mm!45:(C1)$);
        \draw (a) -- ($(A)!(a)!(C1)$);
        \draw (a) -- ($(A)!(a)!(C2)$);
        %% second right angle mark
        \coordinate (b) at ($(B)!8mm!-45:(C1)$);
        \draw (b) -- ($(B)!(b)!(C1)$);
        \draw (b) -- ($(B)!(b)!(C2)$);
        \end{tikzpicture}
\end{document}

在此处输入图片描述

答案3

一个“更好”的解决方案是使用宏来tkz-euclide定义“点”。这node是一个坏主意，就像 cfr 在他的回答中解释的那样。您不需要在命令后使用 ; tkz。 tkz-euclide您tikz 还可以避免调用它。我写得更好，我认为您的代码是这样的，tkz-euclide但最后我意识到它只是用来绘制一个直角标记。代码的有趣之处在于tkz可以将定义、绘图和标签分开。我认为代码更“可读”。

A) 与tkz

\documentclass{article}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
    \begin{tikzpicture}[scale=0.4]
    %def
    \tkzInit[xmin=-15,xmax=12,ymin=-6,ymax=12]
    \tkzDrawXY[noticks]
    \tkzDefPoints{-6/4/C1, 2/1/C2,0.205/6.548/A,-3/-2/B}
    %drawing
    \tkzDrawPoints(A,B)
    \tkzDrawSegments[gray](C1,C2)
    \tkzDrawSegments[red](C2,A C2,B)
    \tkzDrawSegments[blue](C1,A C1,B)
    \tkzDrawCircle(C1,A)
    \tkzDrawCircle(C2,A)
  % notation
    \tkzLabelPoints(C2)
    \tkzLabelPoints[left](C1)
    \tkzLabelPoints[above](A)
    \tkzLabelPoints[below](B)       
    \tkzMarkSegment[color=blue,pos=.5,mark=||](C1,B)
    \tkzMarkSegment[color=red,pos=.5,mark=|](B,C2)
    \tkzMarkSegment[color=blue,pos=.5,mark=||](C1,A)
    \tkzMarkSegment[color=red,pos=.5,mark=|](A,C2)
    \tkzMarkRightAngle[size=0.7](C1,A,C2)
    \tkzMarkRightAngle[size=0.7](C1,B,C2)
    \tkzLabelCircle[above left](C1,A)(180){$K_1$}
    \tkzLabelCircle[right](C2,A)(-60){$K_2$}
    \end{tikzpicture}
 \end{document}

B) 与tkz和tikz

您的问题来自点 A、B、C1 等的定义。tkz定义基于coordinate并注意node。对于大数字，我认为最好组织您的代码：1) 定义点 2) 通过计算或转换获取一些点 3) 绘制一些线、线段、圆等。4) 添加一些标记和标签。

\documentclass{article}
\usepackage{tkz-euclide}
\usetkzobj{all}
\begin{document}
    \begin{tikzpicture}[scale=0.4 ]
    \draw[thick, color=gray,->] (-15,0) -- (12,0)node[right] {\textcolor{black}{$x$}};
    \draw[thick, color=gray, ->] (0,-6) -- (0,12) node[above] {\textcolor{black}{$y$}};
    \coordinate[label=left:{$C_1$}] (C1) at (-6,4) {};
    \coordinate[label=right:{$C_2$}] (C2) at (2,1) {};  
    \coordinate[label=above:{$~~A$}] (A) at (15/73,478/73) {};
    \coordinate[label=below:{$B~$}] (B) at (-3,-2) {};       

    \draw[gray] (C1) -- (C2);
    \draw[blue] (B) -- (C1) -- (A);
    \draw[red]  (B) -- (C2) -- (A);

    % tkz commands
    \tkzDrawCircle(C1,A)
    \tkzDrawCircle(C2,A)

    \tkzMarkSegment[color=blue,pos=.5,mark=||](C1,B)
    \tkzMarkSegment[color=red,pos=.5,mark=|](B,C2)
    \tkzMarkSegment[color=blue,pos=.5,mark=||](C1,A)
    \tkzMarkSegment[color=red,pos=.5,mark=|](A,C2)
    \tkzMarkRightAngle[size=0.7](C1,A,C2)
    \tkzMarkRightAngle[size=0.7](C1,B,C2)
    % tkz commands

    \node at (-14, 4) {$K_1$};
    \node at (9, -1) {$K_2$};

    \fill   (A) circle (4pt)
            (B) circle (4pt)
            (C1) circle (4pt)
            (C2) circle (4pt);
    \end{tikzpicture}
\end{document}

C)仅tikz

对于直角标记，您可以使用 Harish 的代码

      %% right angle mark
      \coordinate (a) at ($(A)!8mm!45:(C1)$);
      \draw (a) -- ($(A)!(a)!(C1)$);
      \draw (a) -- ($(A)!(a)!(C2)$);

对于圆圈，你需要像这样的代码

      \draw (C1) let \p1 = ($ (A) - (C1) $)
               in
               circle ({veclen(\x1,\y1)});
      \draw (C2) let \p1 = ($ (A) - (C2) $)
               in
               circle ({veclen(\x1,\y1)});

在此处输入图片描述]1

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