3D 球面上的随机闭合线

Question

我想在 3d 球体表面画一条随机闭合线（像一个有点变形的圆）。它看起来应该像是从球体上切下一小块。它应该位于北半球。球体应该用除了“圆”之外的线条阴影突出显示，然后反转。

到目前为止我成功地画出了一个球体：

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\draw[thick,->] (0,0,0) -- (3,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,3,0) node[anchor=north west]{$z$};
\draw[thick,->] (0,0,0) -- (0,0,3) node[anchor=south]{$y$};


  \draw (0,0) circle (2cm);
  \draw (-2,0) arc (180:360:2 and 0.6);
  \draw[dashed] (2,0) arc (0:180:2 and 0.6);
  \fill[fill=black] (0,0) circle (1pt);


\end{tikzpicture}
\end{document}

Answer 1

这是一个手动但简单的解决方案，不需要太多代码。

• 该hobby库提供了创建封闭的块状形状的解决方案。
• 该patterns库用于用图案填充形状。
• 可even odd rule用于填充圆圈，但不能填充其中的斑点。

\documentclass[border=5mm]{standalone}
\usepackage{tikz}
\usetikzlibrary{patterns,hobby}
\begin{document}
\begin{tikzpicture}

\draw  (0,0) circle (2cm);
\draw[use Hobby shortcut,closed=true,pattern=north east lines]
(-0.2,0.3) .. (0.2,0.2) .. (1.1,0.6) .. (1.1,1) .. (0.3,1.4) .. (-0.4,1.2) .. (-0.3,0.8);
\draw (-2,0) arc (180:360:2 and 0.6);
\draw[dashed] (2,0) arc (0:180:2 and 0.6);
\fill[fill=black] (0,0) circle (1pt);

\begin{scope}[xshift=5cm]
\draw[use Hobby shortcut,closed=true,pattern=north east lines,even odd rule]  (0,0) circle (2cm)
(-0.2,0.3) .. (0.2,0.2) .. (1.1,0.6) .. (1.1,1) .. (0.3,1.4) .. (-0.4,1.2) .. (-0.3,0.8);
\draw (-2,0) arc (180:360:2 and 0.6);
\draw[dashed] (2,0) arc (0:180:2 and 0.6);
\fill[fill=black] (0,0) circle (1pt);
\end{scope}

\end{tikzpicture}
\end{document}