填充球体圆弧之间的区域

Question

我已经测试了几种不同的方法来做到这一点，但似乎无法正确完成——我需要遮蔽标有 的球体上半球两个圆弧之间的小区域\Delta \Theta。

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \draw[line width = 0.1mm](0,0) circle (2cm);
  \draw[line width = 0.1mm](-2,0) arc (180:360:2 and 0.6);
  \draw[line width = 0.05mm, dashed] (2,0) arc (0:180:2 and 0.6);
  \draw[line width=0.1mm, fill=black] (0,0) -- (1.6,1.2);
  \draw[line width=0.1mm, fill=black] (0,0) -- (1.42,1.4);
  \draw[line width = 0.1mm] (-1.60,1.2) arc (180:360:1.60 and 0.15);
  \draw[line width = 0.05mm, dashed] (1.60,1.2) arc (0:180:1.60 and 0.15);
  \draw[line width = 0.1mm] (-1.42,1.4) arc (180:360:1.42 and 0.15);
  \draw[line width = 0.05mm, dashed] (1.42,1.4) arc (0:180:1.42 and 0.15);
  \fill[line width = 0.1mm, fill=black] (0,0) circle (0.7pt);
  \draw[line width = 0.1mm] (0,0) -- (2,0);
  \node[scale = 0.4] at (0.33,0.13) {$\theta$};
  \node[scale = 0.4] at (0.83,0.3) {$\theta + \Delta \theta$};
  \draw[->, line width = 0.05mm] (0.5,0) arc (0:18:2 and 1);
  \draw[->, line width = 0.05mm] (0.6,0) arc (0:26:1.6 and 1);
  \draw[->, line width = 0.05mm] (1.7,1.23) arc (20:30:3 and 1.6);
  \node[scale = 0.4] at (1.74, 1.42) {$\Delta \theta$};
  \node[scale =0.4] at (0.55, 0.8) {$r=1$};
  \fill[line width = 0.05mm, fill=black] (0,1.4) circle (0.7pt);
  \draw[line width = 0.1mm] (0,1.4) -- (1.42,1.4);
  \node[scale =0.4, fill = white] at (0.2,1.7) {$R = \cos (\theta + \Delta \theta)$};
\end{tikzpicture}
\end{document}

Answer 1

我希望我使用了正确的弧。

注意：实际上没有必要将一个圆弧的端点连接到下一个圆弧的第一个点，但它确实有助于减少错误的积累。

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
  \draw[line width = 0.1mm](0,0) circle (2cm);
  \draw[line width = 0.1mm](-2,0) arc (180:360:2 and 0.6);
  \draw[line width = 0.05mm, dashed] (2,0) arc (0:180:2 and 0.6);
  \draw[line width=0.1mm, fill=black] (0,0) -- (1.6,1.2);
  \draw[line width=0.1mm, fill=black] (0,0) -- (1.42,1.4);
  \draw[line width = 0.1mm] (-1.60,1.2) arc (180:360:1.60 and 0.15);
  \draw[line width = 0.05mm, dashed] (1.60,1.2) arc (0:180:1.60 and 0.15);
  \draw[line width = 0.1mm] (-1.42,1.4) arc (180:360:1.42 and 0.15);
  \draw[line width = 0.05mm, dashed] (1.42,1.4) arc (0:180:1.42 and 0.15);
  \fill[line width = 0.1mm, fill=black] (0,0) circle (0.7pt);
  \draw[line width = 0.1mm] (0,0) -- (2,0);
  \node[scale = 0.4] at (0.33,0.13) {$\theta$};
  \node[scale = 0.4] at (0.83,0.3) {$\theta + \Delta \theta$};
  \draw[->, line width = 0.05mm] (0.5,0) arc (0:18:2 and 1);
  \draw[->, line width = 0.05mm] (0.6,0) arc (0:26:1.6 and 1);
  \draw[->, line width = 0.05mm] (1.7,1.23) arc (20:30:3 and 1.6);
  \node[scale = 0.4] at (1.74, 1.42) {$\Delta \theta$};
  \node[scale =0.4] at (0.55, 0.8) {$r=1$};
  \fill[line width = 0.05mm, fill=black] (0,1.4) circle (0.7pt);
  \draw[line width = 0.1mm] (0,1.4) -- (1.42,1.4);
  \node[scale =0.4, fill = white] at (0.2,1.7) {$R = \cos (\theta + \Delta \theta)$};

  \fill[blue,opacity=0.5] (-1.60,1.2) arc (180:360:1.60 and 0.15) --
    (1.60,1.2) arc (36.87:44.59:2) --
    (1.42,1.4) arc (360:180:1.42 and 0.15) --
    (-1.42,1.4) arc (135.41:143.13:2) -- cycle;
\end{tikzpicture}
\end{document}