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如何填入TikZ中n個相交點之間的區域

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如何填入TikZ中n個相交點之間的區域

給定兩個相交的形狀，我們如何在 TikZ 中填滿它們共同的區域（即它們相交點之間的區域）。

在這裡，even odd rule可能不起作用，因為它不是交替填充而是相交點。

請注意確定交點，我正在使用該intersections庫。

在下面的 MWE 中，如何填滿C和之間的區域C'：

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections,through}
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (1.25,0.25);


  \node (E) [name path=E,draw,circle through=(B)] at (A) {};
  \node (F) [name path=F,draw,circle through=(A)] at (B) {};

  \path [name intersections={of=E and F, by={[label=above:$C$]C,[label=below:$C'$]C'}}];


\end{tikzpicture}
\end{document}

在此輸入影像描述

答案1

公共區域是透過剪切其中一個圓圈並填充另一個圓圈來獲得的。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections,through}
\makeatletter % from https://tex.stackexchange.com/a/127045/121799
\tikzset{use path/.code=\tikz@addmode{\pgfsyssoftpath@setcurrentpath#1}}
\makeatother
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (1.25,0.25);


  \node (E) [name path=E,draw,circle through=(B),save path=\pathA] at (A) {};
  \node (F) [name path=F,draw,circle through=(A),save path=\pathB] at (B) {};
  \begin{scope}
  \clip[use path=\pathA];
  \fill[blue,use path=\pathB];
  \end{scope}

  \path [name intersections={of=E and F, by={[label=above:$C$]C,[label=below:$C'$]C'}}];


\end{tikzpicture}
\end{document}

在此輸入影像描述

如果您擔心圓形輪廓被部分覆蓋，請使用backgrounds。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections,through,backgrounds}
\makeatletter % from https://tex.stackexchange.com/a/127045/121799
\tikzset{use path/.code=\tikz@addmode{\pgfsyssoftpath@setcurrentpath#1}}
\makeatother
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (1.25,0.25);


  \node (E) [name path=E,draw,circle through=(B),save path=\pathA] at (A) {};
  \node (F) [name path=F,draw,circle through=(A),save path=\pathB] at (B) {};
  \begin{scope}[on background layer]
  \clip[use path=\pathA];
  \fill[blue,use path=\pathB];
  \end{scope}

  \path [name intersections={of=E and F, by={[label=above:$C$]C,[label=below:$C'$]C'}}];


\end{tikzpicture}
\end{document}

您始終可以填滿交叉線段。 （您可以將其與上面的背景內容結合。）

\documentclass{article}
\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\pgfplotsset{compat=1.16}
\usetikzlibrary{through}
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (1.25,0.25);


  \node (E) [name path=E,draw,circle through=(B)] at (A) {};
  \node (F) [name path=F,draw,circle through=(A)] at (B) {};

  \path [name intersections={of=E and F, by={[label=above:$C$]C,[label=below:$C'$]C'}}];

  \path[%draw,red,thick,
  fill=blue,
  intersection segments={of=E and F,sequence={L1--R2--L3}}];
\end{tikzpicture}
\end{document}

（與上面相同的輸出。）

弧的分析確定是另一種可能性。

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{intersections,through,calc}
\begin{document}
\begin{tikzpicture}
  \coordinate (A) at (0,0);
  \coordinate (B) at (1.25,0.25);


  \node (E) [name path=E,draw,circle through=(B)] at (A) {};
  \node (F) [name path=F,draw,circle through=(A)] at (B) {};

  \path [name intersections={of=E and F, by={[label=above:$C$]C,[label=below:$C'$]C'}}];
  \path[fill=blue] let \p1=($(A.center)-(B.center)$),\p2=($(C.center)-(A.center)$),
  \p3=($(C'.center)-(A.center)$),\p4=($(C.center)-(B.center)$),
  \p5=($(C'.center)-(B.center)$),
  \n1={veclen(\x2,\y2)}, % radius A
  \n2={veclen(\x4,\y4)}, % radius B
  \n3={atan2(\y2,\x2)}, % angle A 1
  \n4={atan2(\y3,\x3)}, % angle A 2
  \n5={atan2(\y4,\x4)}, % angle B 1
  \n6={atan2(\y5,\x5)} % angle B 2
  in (C) arc(\n3:\n4:\n1)  arc(\n6:\n5-360:\n2);

\end{tikzpicture}
\end{document}

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