20 如何将两段圆弧的围成的区域染成绿色

发布于 2024-07-12 19:55:55

2f7d4da798babf17f2494469cd764b8.jpg
如何优化代码,实现如图的效果,将阴影区域染成淡蓝色。以下是部分原始代码。
documentclass{standalone}
usepackage{tikz,pgfplots}
usetikzlibrary{arrows.meta}

begin{document}


\begin{tikzpicture}
    
    % Define the coordinates
    \coordinate (O1) at (0, {-5*sqrt(2)});
    \coordinate (O2) at (0, 0);
    
    % Define the square vertices
    \coordinate (A) at (0, {5*sqrt(2)});
    \coordinate (B) at ({5*sqrt(2)}, 0);
    \coordinate (C) at (0, {-5*sqrt(2)});
    \coordinate (D) at ({-5*sqrt(2)}, 0);
    
    % Define point P
    \coordinate (P) at ({(5/4)*sqrt(14)}, {(5/4)*sqrt(2)});
    
    % Draw the axes
    \draw[->] (-9, 0) -- (9, 0) node[right] {$x$};
    \draw[->] (0, -9) -- (0, 9) node[above] {$y$};
    
    % Clip to the region above the x-axis for the first circle
    \begin{scope}
        \clip (-12, 0) rectangle (12, 15);
        
        % Draw the circle C: x^2 + (y + 5*sqrt(2))^2 = 100, only above x-axis
        \draw (O1) circle[radius=10];
    \end{scope}
    
    % Draw the circle x^2 + y^2 = 25
    \draw (O2) circle[radius=5];
    
    % Draw the square
    \draw (A) -- (B) -- (C) -- (D) -- cycle;
    
    % Draw and label point P
    \fill (P) circle (2pt);
    \node[above right] at (P) {$P\left(\frac{5}{4}\sqrt{14}, \frac{5}{4}\sqrt{2}\right)$};
    
    % Label the circles
    \node at (0, {5*sqrt(2) - 5}) {$x^2 + (y + 5\sqrt{2})^2 = 100$};
    \node at (0,-5.5) {$x^2 + y^2 = 25$};
    
\end{tikzpicture}


end{document}

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M 2024-07-13
这家伙很懒,什么也没写!
\documentclass{standalone}
\usepackage{tikz,pgfplots}
\usetikzlibrary{arrows.meta}

\begin{document}

\begin{tikzpicture}
    
  % Define the coordinates
  \coordinate (O1) at (0, {-5*sqrt(2)});
  \coordinate (O2) at (0, 0);
  
  % Define the square vertices
  \coordinate (A) at (0, {5*sqrt(2)});
  \coordinate (B) at ({5*sqrt(2)}, 0);
  \coordinate (C) at (0, {-5*sqrt(2)});
  \coordinate (D) at ({-5*sqrt(2)}, 0);
  
  % Define point P
  \coordinate (P) at ({(5/4)*sqrt(14)}, {(5/4)*sqrt(2)});
  
  % ++++++++++++++++++++++++++++++++++++++++++++++
  \begin{scope}[even odd rule]
    \clip (P) rectangle +(-10, 5);
    \clip (O1) circle[radius=10] (O2) circle[radius=5];
    \fill[green!70] (O1) circle[radius=10] (O2) circle[radius=5];
  \end{scope}
  % ++++++++++++++++++++++++++++++++++++++++++++++

  % Draw the axes
  \draw[->] (-9, 0) -- (9, 0) node[right] {$x$};
  \draw[->] (0, -9) -- (0, 9) node[above] {$y$};
  
  % Clip to the region above the x-axis for the first circle
  \begin{scope}
      \clip (-12, 0) rectangle (12, 15);
      
      % Draw the circle C: x^2 + (y + 5*sqrt(2))^2 = 100, only above x-axis
      \draw (O1) circle[radius=10];
  \end{scope}

  % Draw the circle x^2 + y^2 = 25
  \draw (O2) circle[radius=5];
  
  % Draw the square
  \draw (A) -- (B) -- (C) -- (D) -- cycle;
  
  % Draw and label point P
  \fill (P) circle (2pt);
  \node[above right] at (P) {$P\left(\frac{5}{4}\sqrt{14}, \frac{5}{4}\sqrt{2}\right)$};
  
  % Label the circles
  \node at (0, {5*sqrt(2) - 5}) {$x^2 + (y + 5\sqrt{2})^2 = 100$};
  \node at (0,-5.5) {$x^2 + y^2 = 25$};
  
\end{tikzpicture}

\end{document}

bef92a577c7f5b1b1145dd18fb593e0d.png

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