这是我想在背面绘制的图形：
请问关于如何绘制这个，您有什么建议吗？
答案1
这是一个基于剪辑和范围（很多剪辑和范围）的 2d 解决方案。它还使用 tikz 库intersetctions来获取一些点。我做了几个宏，第一个被调用\spherepoints并在球体周围放置一些剪辑所需的坐标。这些坐标是根据曲线之间的交点定义的。它们在这里：
然后我制作了其他宏来绘制椭圆：完整、可见部分（剪辑）或隐藏部分（再次剪辑）。考虑到所有这些，这是（不是很短的）代码：
\documentclass[border=2mm]{standalone}
\usepackage {tikz}
\usetikzlibrary{intersections}
\def\sr{2} % sphere radius
% some points in the sphere
\newcommand{\spherepoints}
{%
\foreach[count=\xi]\i in {-1,1}
{%
\cellipse{0.25*\i*\sr}{draw=none,name path global=A-\xi}
}
\begin{scope}[rotate=120]
\cellipse{0}{draw=none,name path global=A-3}
\end{scope}
\path [name intersections={of=A-1 and A-3,name=B}];
\path [name intersections={of=A-2 and A-3,name=C}];
\coordinate (P1) at (-\sr-0.1, \sr+0.1);
\coordinate (P2) at (-\sr-0.1, 0.375*\sr);
\coordinate (P3) at (-\sr-0.1, 0);
\coordinate (P4) at (-\sr-0.1,-0.375*\sr);
\coordinate (P5) at (-\sr-0.1,-\sr-0.1);
\coordinate (Q1) at ( \sr+0.1, \sr+0.1);
\coordinate (Q2) at ( \sr+0.1, 0.375*\sr);
\coordinate (Q3) at ( \sr+0.1, 0);
\coordinate (Q4) at ( \sr+0.1,-0.375*\sr);
\coordinate (Q5) at ( \sr+0.1,-\sr-0.1);
\coordinate (S1) at (intersection of C-2--C-4 and Q1--Q5);
\coordinate (R1) at (intersection of C-2--C-4 and P1--P5);
\coordinate (S2) at (intersection of B-2--B-4 and Q1--Q5);
\coordinate (R2) at (intersection of B-2--B-4 and P1--P5);
}
% complete ellipse
\newcommand{\cellipse}[2]% height, style
{
\pgfmathsetmacro\a{sqrt(\sr*\sr-1.5*#1*#1)}
\pgfmathsetmacro\b{\a/sqrt(3)}
\draw[#2] (0,#1) ellipse (\a cm and \b cm);
}
% ellipse, hidden part
\newcommand{\hellipse}[2]% height, style
{
\pgfmathsetmacro\a{sqrt(\sr*\sr-1.5*#1*#1)}
\pgfmathsetmacro\b{\a/sqrt(3)}
\begin{scope}
\clip (-\sr-0.1,1.5*#1) rectangle (\sr+0.1,\sr+0.1);
\draw[#2] (0,#1) ellipse (\a cm and \b cm);
\end{scope}
}
% ellipse, visible part
\newcommand{\vellipse}[2]% height, style
{
\pgfmathsetmacro\a{sqrt(\sr*\sr-1.5*#1*#1)}
\pgfmathsetmacro\b{\a/sqrt(3)}
\begin{scope}
\clip (-\sr-0.1,1.5*#1) rectangle (\sr+0.1,-\sr-0.1);
\draw[#2] (0,#1) ellipse (\a cm and \b cm);
\end{scope}
}
\begin{document}
\begin{tikzpicture}[line cap=round,line join=round]
% top left sphere
\begin{scope}
\vellipse{0}{blue}
\hellipse{0}{blue!25}
\draw[thick] (0,0) circle (\sr);
\end{scope}
% arrow
\draw[magenta,thick,-latex] (1.3*\sr,0) -- (1.7*\sr,0);
% top right sphere, bottom half
\begin{scope}[shift={(3.5*\sr,-0.5*\sr)}]
\cellipse{0}{thick}
\draw[thick] (\sr,0) arc (0:-180:\sr);
\end{scope}
% top right sphere, top half
\begin{scope}[shift={(3.5*\sr,0.5*\sr)}]
\cellipse{0}{draw=none,fill=white,fill opacity=0.75}
\vellipse{0}{thick}
\hellipse{0}{blue!25}
\draw[thick] (\sr,0) arc (0:180:\sr);
\end{scope}
% bottom left sphere
\begin{scope}[shift={(0,-4*\sr)}]
\spherepoints
\foreach[count=\xi]\i in {-1,1}
{%
\vellipse{0.25*\i*\sr}{blue,name path global=A-\xi}
\hellipse{0.25*\i*\sr}{blue!25}
}
\begin{scope}[rotate=120]
\clip (R1) -- (S1) -- (S2) -- (R2) -- cycle;
\vellipse{0}{blue}
\hellipse{0}{blue!25}
\end{scope}
\draw[thick] (0,0) circle (\sr);
\end{scope}
% arrow
\draw[magenta,thick,-latex] (1.3*\sr,-4*\sr) -- (1.7*\sr,-4*\sr);
% bottom right sphere, bottom part
\begin{scope}[shift={(3.5*\sr,-5*\sr)}]
\cellipse{-0.25*\sr}{thick}
\clip (-\sr-0.1,-0.375*\sr) rectangle (\sr+0.1,-\sr-0.1);
\draw[thick] (0,0) circle (\sr);
\end{scope}
% bottom right sphere, middle left part
\begin{scope}[shift={(3*\sr,-4*\sr)}]
\spherepoints
\cellipse{-0.25*\sr}{draw=none,fill=white,fill opacity=0.75}
\begin{scope}
\clip (R1) -- (S1) |- (P5) -- cycle;
\cellipse{0.25*\sr}{thick}
\end{scope}
\begin{scope}
\clip (R2) |- (0,0) |- (P4) |- (Q5) -- (S2) -- cycle;
\cellipse{-0.25*\sr}{thick}
\end{scope}
\begin{scope}
\clip (P4) rectangle (0,0);
\hellipse{-0.25*\sr}{blue!25}
\end{scope}
\begin{scope}[rotate=120]
\clip (R1) -- (S1) -- (S2) -- (R2) -- cycle;
\cellipse{0}{thick}
\end{scope}
\clip (P2) -| (0,0) |- (P4) -- cycle;
\draw[thick] (0,0) circle (\sr);
\end{scope}
% bottom right sphere, middle right part
\begin{scope}[shift={(4*\sr,-4*\sr)}]
\spherepoints
\begin{scope}
\clip (R1) -- (S1) |- (P1) -- cycle;
\cellipse{0.25*\sr}{thick}
\end{scope}
\begin{scope}
\clip (S2) -- (R2) |- (Q1) |- (0,0) |- (Q4) -- cycle;
\cellipse{-0.25*\sr}{thick}
\end{scope}
\begin{scope}
\clip (Q4) rectangle (0,0);
\hellipse{-0.25*\sr}{blue!25}
\end{scope}
\begin{scope}[rotate=120]
\clip (R1) -- (S1) -- (S2) -- (R2) -- cycle;
\cellipse{0}{thick}
\end{scope}
\clip (Q2) -| (0,0) |- (Q4) -- cycle;
\draw[thick] (0,0) circle (\sr);
\end{scope}
% bottom right sphere, top part
\begin{scope}[shift={(3.5*\sr,-3*\sr)}]
\spherepoints
\vellipse{0.25*\sr}{thick,fill=white,fill opacity=0.75}
\hellipse{0.25*\sr}{blue!25}
\clip (P2) rectangle (Q1);
\draw[thick] (0,0) circle (\sr);
\end{scope}
\end{tikzpicture}
\end{document}
结果如下：
