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ZXZ 角度 TikZ 图片 3d：

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ZXZ 角度 TikZ 图片 3d：

我愿意创建一个类似的图表： 在此处输入图片描述

我尝试了第一个图形旋转，结果非常酷：

在此处输入图片描述

它的代码如下：

\documentclass[tikz,border=10mm]{standalone}
\usepackage{tikz}
\usepackage{pgfplots}
\usepackage{tikz-3dplot}
\pgfplotsset{compat=1.18}
\usetikzlibrary{arrows.meta, shapes.geometric, positioning, perspective, patterns.meta, decorations.pathreplacing, decorations.pathmorphing, patterns, snakes, arrows, shapes, decorations.text, angles, quotes,calc, 3d, decorations.markings, math, circuits.ee.IEC}
\usepackage{circuitikz}
\begin{document}
\definecolor{jack}{HTML}{380036}
\definecolor{back}{HTML}{0CBABA}
\tdplotsetmaincoords{75}{130}
\begin{tikzpicture}[>=stealth, tdplot_main_coords, scale=2]

\draw[->, thick, back] (0,0,0)--(2,0,0) node[above] {$\vec{x}$};
\draw[->, thick, back] (0,0,0)--(0,2,0) node[above] {$\vec{y}$};
\draw[->, thick, back] (0,0,0)--(0,0,2) node[above] {$\vec{z}$};
\tdplotsetrotatedcoords{40}{0}{0}
\tdplotdrawarc[tdplot_rotated_coords,circle, dashed, fill=back!30, opacity=0.3]{(0,0,0)}{2}{0}{360}{}{}
\draw[tdplot_rotated_coords, thick, jack, ->] (0,0,0)--(2,0,0) node[anchor=north east]{$\vec{u}$};
\draw[tdplot_rotated_coords, thick, jack, ->] (0,0,0)--(0,2,0) node[anchor=west]{$\vec{v}$};
    \tdplotdrawarc[tdplot_rotated_coords,jack]{(0,0,0)}{0.7}{-40}{0}{anchor=north east}{$\psi$} 
\tdplotdrawarc[tdplot_rotated_coords,jack]{(0,0,0)}{0.7}{90-40}{90}{anchor=west}{$\psi$}    
\tdplotdrawarc[->,color=jack!75,thick]{(0,0,1.75)}{0.2}{0}{310}{anchor=south west,color=jack!75}{Précession $\psi$}
\end{tikzpicture}
\end{document}

问题是当我尝试绕新轴“u”进行第二次旋转时，根据设置时获得的定义：\tdplotsetrotatedcoords{40}{0}{40}因为该命令的第一个参数是绕 z 轴的旋转，第二个参数是绕 y 轴的旋转，第三个参数是绕 x 轴的旋转，当我尝试这样做时没有任何变化，所以有没有什么方法可以表示这种旋转（请注意，我还没有完全阅读文档）。

有什么想法吗？提前致谢！

答案1

我正在使用3d和perspectiveTi钾为此，我创建了 Z 库。我还创建了三种样式：

  • axis，如果需要，可以更改轴样式。绘图的大部分都是轴，因此我们避免逐个更改它们。
  • my view，只需同时更改所有图像中的视图即可。
  • nutation，从而根据‘章动’角度改变轴。

这样，我们只需要几个scopes，每个图像一个，还有一个用于中心图像（“章动”部分）。

这是我的代码：

\usetikzlibrary{3d,perspective}

\tikzset
{
  axis/.style={thick,-latex},
  my view/.style={3d view={65}{20}},
  nutation/.style={rotate around x=\nut}
}
\colorlet{my cyan}{cyan!50}
\colorlet{my magenta}{magenta!50!pink}

\begin{document}
\begin{tikzpicture}[line cap=round]
\def\pre{-30} % précession
\def\nut{40}  % nutation
\def\rop{30}  % rotation propre
% left
\begin{scope}[shift={(-7,0)},my view]
\draw[fill=my cyan] (0,0) circle (2);
\draw[axis] (0,0,0) -- (4,0,0)     node[below] {$\vec x_1$};
\draw[axis] (0,0,0) -- (0,4,0)     node[right] {$\vec y_1$};
\draw[axis] (0,0,0) -- (0,0,4)     node[above] {$\vec z_f=\vec z_1$};
\draw[axis] (0,0,0) -- (\pre:4)    node[below] {$\vec x_f$};
\draw[axis] (0,0,0) -- (90+\pre:4) node[below] {$\vec y_f$};
\foreach\i in {0,90}
  \draw[-latex] (\i+\pre:2.5) arc (\i+\pre:\i:2.5)
        node at (\i+0.5*\pre:3) {$\psi$};
\draw[canvas is xy plane at z=2,->] (90:0.5) arc (90:360:0.5) node[pos=0,right] {Précession $\psi$};
\end{scope}
% center
\begin{scope}[my view]
\draw[fill=my magenta,nutation] (2,0) arc (0:-180:2) -- cycle;
\draw[fill=my cyan] (0,0) circle (2);
\draw[axis]   (0,0,0) -- (0,4,0) node[right] {$\vec y_1$};
\begin{scope}[nutation]
  \draw[fill=my magenta] (2,0) arc (0:180:2) -- cycle;
  \draw[axis] (0,0,0) -- (0,4,0) node[above] {$\vec y_2$};
  \draw[axis] (0,0,0) -- (0,0,4) node[above] {$\vec z_2$};
\end{scope}
\foreach\i in {0,90}
  \draw[my view,canvas is yz plane at x=0,-latex] (\i:2.5) arc (\i:\i+\nut:2.5)
                                          node at (\i+0.5*\nut:3) {$\theta$};
\draw[axis] (0,0,0) -- (4,0,0) node[below] {$\vec x_1=\vec x_2$};
\draw[axis] (0,0,0) -- (0,0,4) node[above] {$\vec z_1$};
\draw[canvas is yz plane at x=2,->] (-90:0.5) arc (-90:170:0.5) node[pos=0.3,right] {Nutation $\theta$};
\end{scope}
% right
\begin{scope}[shift={(7,0)},my view,nutation]
\draw[fill=my magenta] (0,0) circle (2);
\draw[axis] (0,0,0) -- (4,0,0)     node[right] {$\vec x_2$};
\draw[axis] (0,0,0) -- (0,4,0)     node[above] {$\vec y_2$};
\draw[axis] (0,0,0) -- (0,0,4)     node[above] {$\vec z_2=\vec z_3$};
\draw[axis] (0,0,0) -- (\rop:4)    node[right] {$\vec x_3$};
\draw[axis] (0,0,0) -- (90+\rop:4) node[above] {$\vec y_3$};
\foreach\i in {0,90}
  \draw[-latex] (\i:2.5) arc (\i:\i+\rop:2.5)
        node at (\i+0.5*\rop:3) {$\varphi$};
\draw[canvas is xy plane at z=2,->] (-90:0.5) arc (-90:160:0.5) node[yshift=-4mm,pos=0,text width=2cm] {Rotation propre $\varphi$};
\end{scope}
\end{tikzpicture}
\end{document}

输出结果如下： 在此处输入图片描述

更新 1：第二张图：

\documentclass[tikz,border=2.718mm]{standalone}

\begin{document}
\begin{tikzpicture}[line cap=round]
% axis
\foreach\i in {1,2,3}
{
  \begin{scope}[shift={(6*\i,0)}]
    \foreach\j in {0,1}
    {
      \draw[thick,latex-latex,rotate=20*\j] (0,4) coordinate (Y\i\j) |- (4,0) coordinate (X\i\j);
      \draw[->] (90*\j:3) arc (90*\j:90*\j+20:3) coordinate[midway] (A\i\j);
    }
    \draw[fill=white] (0,0) circle (0.2);
    \fill (0,0) coordinate (O\i) circle (0.1);
    \coordinate (P\i) at (2,3);
  \end{scope}
}
% left
\node[yshift=-5mm] at (O1) {\strut$\vec z_f=\vec z_1$};
\node[right] at (X10) {\strut$\vec x_f$};
\node[above] at (Y10) {\strut$\vec y_f$};
\node[right] at (X11) {\strut$\vec x_1$};
\node[above] at (Y11) {\strut$\vec y_1$};
\node[right] at (A10) {\strut$\psi$};
\node[above] at (A11) {\strut$\psi$};
\node        at (P1)  {\strut Précession};
% center
\node[yshift=-5mm] at (O2) {\strut$\vec x_1=\vec x_2$};
\node[right] at (X20) {\strut$\vec y_1$};
\node[above] at (Y20) {\strut$\vec z_1$};
\node[right] at (X21) {\strut$\vec y_2$};
\node[above] at (Y21) {\strut$\vec z_2$};
\node[right] at (A20) {\strut$\theta$};
\node[above] at (A21) {\strut$\theta$};
\node        at (P2)  {\strut Nutation};
% right
\node[yshift=-5mm] at (O3) {\strut$\vec z_2=\vec z_1$};
\node[right] at (X30) {\strut$\vec x_2$};
\node[above] at (Y30) {\strut$\vec y_2$};
\node[right] at (X31) {\strut$\vec x_3$};
\node[above] at (Y31) {\strut$\vec y_3$};
\node[right] at (A30) {\strut$\varphi$};
\node[above] at (A31) {\strut$\varphi$};
\node        at (P3)  {\strut Rotation propre};
\end{tikzpicture}
\end{document}

更新 2：第二张图的第二个版本，使用\pic（几乎相同的输出）：

\tikzset
{%
   pics/axis/.style n args={7}{
   % #1 = x axis label (without subscript): x,y,z
   % #2 = y axis label (without subscript): x,y,z
   % #3 = z axis label (without subscript): x,y,z
   % #4 = original axis label  (subscript)
   % #5 = rotated  axis label  (subscript)
   % #6 = angle
   % #7 = figure label
     code={%
       \draw[thick,latex-latex]           (0,4) node[above] {\strut$\vec#2_#4$} |- (4,0) node[right] {\strut$\vec#1_#4$};
       \draw[thick,latex-latex,rotate=20] (0,4) node[above] {\strut$\vec#2_#5$} |- (4,0) node[right] {\strut$\vec#1_#5$};
       \foreach\j in {0,1}
         \draw[->] (90*\j:3) arc (90*\j:90*\j+20:3) node at (90*\j+10:3.25) {$#6$};
       \draw[fill=white] (0,0) circle (0.2);
       \fill (0,0) circle (0.1);
       \node at (0,-0.5) {\strut$\vec#3_#4=\vec#3_#5$};
       \node at (2,3)    {\strut#7};
    }}
}

\begin{document}
\begin{tikzpicture}[line cap=round]
\pic at  (0,0) {axis={x}{y}{z}{f}{1}{\psi}{Precéssion}};
\pic at  (6,0) {axis={y}{z}{x}{1}{2}{\theta}{Nutation}};
\pic at (12,0) {axis={x}{y}{z}{2}{3}{\varphi}{Rotation propre}};
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

使用“蛮力”的方法在构造上缺乏优雅和灵活性，但却能让你得到你想要的东西。

\documentclass{standalone}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\def\radius{2}
\def\rA{0.3}
\def\addAx{1}
\def\nutation{45}
\def\precession{-30}

\begin{scope}[shift={(-3.2*\radius,0)}]
\begin{scope}[rotate around y =-50, rotate around x = -90,rotate around y = 5]
\draw[fill=cyan!50] (0,0) circle (\radius);
\draw[thick, -latex] (0,0,0) -- (0,\radius+\addAx,0) node[above] {$\vec{y_1}$};
\draw[thick, -latex] (0,0)  ++(90:\radius+0.4) arc (90:90+\precession:\radius+0.4);
\path (0,0)  ++(90:\radius+0.4) arc (90:90+0.5*\precession:\radius+0.4) node[right]{$\psi$};
\draw[thick, -latex] (0,0,0) -- (90+\precession:\radius+\addAx) node[right] {$\vec{y_f}$};
\draw[thick, -latex] (0,0,0) -- (0,0,\radius+\addAx) node[above] {$\vec{z_1}$};
\begin{scope}[shift={(0,0,0.9*\radius)}]
\draw[-latex] (0,0) ++(-150:\rA) arc(-150:150:\rA);
\path (0,0) ++(-150:\rA) arc(-150:90:\rA) node[right]{Precession $\psi$};
\end{scope}
\draw[thick, -latex] (0,0,0) -- (\radius+\addAx,0,0) node[below right] {$\vec{x_1}$};
\begin{scope}[rotate around z = \precession]
\draw[thick, -latex] (0,0,0) -- (\radius+\addAx,0,0) node[below right] {$\vec{x_f}$};
\end{scope}
\draw[thick,latex-] (0,0) ++(\radius+0.4,0,0) arc (0:\precession:\radius+0.4);
\path (0,0) ++(\radius+0.4,0,0) arc (0:0.5*\precession:\radius+0.4) node[below] {$\psi$};
\end{scope}
\end{scope}


\begin{scope}[rotate around y =-50, rotate around x = -90,rotate around y = 5]
\begin{scope}[rotate around x = \nutation]
\draw[fill=magenta!50] (0,0,0) -- (-\radius,0,0 ) arc (180:360:\radius);
\end{scope}
\draw[fill=cyan!50] (0,0) circle (\radius);
\draw[thick, -latex] (0,0,0) -- (0,\radius+0.4,0) node[above] {$\vec{y_1}$};
\begin{scope}[rotate around x = \nutation]
\draw[fill=magenta!50] (0,0,0) -- (\radius,0,0 ) arc (0:180:\radius);
\end{scope}
\draw[thick, -latex] (0,0,0) -- (0,0,\radius+0.4) node[above] {$\vec{z_1}$};
\draw[thick, -latex] (0,0,0) -- (\radius+2.5,0,0) node[below right] {$\vec{x_1} = \vec{x_2}$};
\begin{scope}[shift={(\radius+1,0,0)}]
\begin{scope}[rotate around y=90]
\draw[-latex] (0,0) ++(-90:\rA) arc(-90:180:\rA) -- ++(0,-0.075,0);
\node[right] at (0,\rA,0) {Nutation $\theta$};
\end{scope}
\end{scope}
\begin{scope}[rotate around y=90]
\draw[thick,-latex] (0,0,0) ++(90:\radius+0.1)  arc (90:90+\nutation:\radius+0.1);
\path (0,0,0) ++(90:\radius+0.1)  arc (90:90+0.5*\nutation:\radius+0.1) node[right] {$\theta$};
\draw[thick,-latex] (0,0,0) ++(180:\radius-0.2)  arc (180:180+\nutation:\radius-0.2);
\path (0,0,0) ++(180:\radius-0.2)  arc (180:180+0.5*\nutation:\radius-0.2) node[above] {$\theta$};
\draw[thick,-latex] (0,0) -- (180+\nutation:\radius+0.4) node[above] {$\vec{z_2}$};
\draw[thick,-latex] (0,0) -- (90+\nutation:\radius+0.4) node[above] {$\vec{y_2}$};
\end{scope}
\end{scope}


\begin{scope}[shift={(3.2*\radius,0)}]
\begin{scope}[rotate around y =-50, rotate around x = -90,rotate around y = 5]
\begin{scope}[rotate around x = \nutation]
\draw[fill=magenta!50] (0,0) circle (\radius);
\draw[thick, -latex] (0,0,0) -- (0,\radius+1,0) node[above] {$\vec{y_2}$};
\draw[thick, -latex] (0,0)  ++(90:\radius+0.4) arc (90:90-\precession:\radius+0.4);
\path (0,0)  ++(90:\radius+0.4) arc (90:90-0.5*\precession:\radius+0.4) node[above]{$\varphi$};
\draw[thick, -latex] (0,0,0) -- (90-\precession:\radius+1) node[left] {$\vec{y_f}$};
\draw[thick, -latex] (0,0,0) -- (0,0,\radius+0.4) node[above] {$\vec{z_2}=\vec{z_1}$};
\begin{scope}[shift={(0,0,0.9*\radius)}]
\draw[-latex] (0,0) ++(-150:\rA) arc(-150:150:\rA);
\path (0,0) ++(-90:\rA) node[align=left,below]{Rotation\\propre $\phi$};
\end{scope}
\draw[thick, -latex] (0,0,0) -- (\radius+1,0,0) node[below right] {$\vec{x_2}$};
\begin{scope}[rotate around z = -\precession]
\draw[thick, -latex] (0,0,0) -- (\radius+1,0,0) node[below right] {$\vec{x_f}$};
\end{scope}
\draw[thick,-latex] (0,0) ++(\radius+0.4,0,0) arc (0:-\precession:\radius+0.4);
\path (0,0) ++(\radius+0.4,0,0) arc (0:-0.5*\precession:\radius+0.4) node[right] {$\varphi$};
\end{scope}
\end{scope}
\end{scope}
\end{tikzpicture}
\end{document}

在此处输入图片描述

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