tikz-3dplot：繞特定軸旋轉圓弧

Question

    \documentclass[tikz]{standalone}
    \usepackage{tikz-3dplot}
    \begin{document}
    \begin{tikzpicture}[scale=2]
        % draw arcs
        \draw[canvas is zx plane at y = 1, line width = 1pt] (2,1) arc (-90:-180:1);
        \draw[canvas is zx plane at y = 1, opacity = 0.2, line width = 1pt] (2,1) arc (90:180:1);
        \draw[canvas is zy plane at x = 1, opacity = 0.2, line width = 1pt] (2,1) arc (-90:-180:1);
        \draw[canvas is zy plane at x = 1, opacity = 0.2, line width = 1pt] (2,1) arc (90:180:1);   

        %draw the axes
        \draw[red,->] (1,1,2) -- (1, 1, -1.1) node[anchor=north west]{$x$};
        \draw[blue,->] (1,1,2) -- (3.5,1,2) node[anchor=west]{$z$};
        \draw[blue,->] (1,1,2) -- (1,-1.2,2) node[anchor=north]{$y$};
    \end{tikzpicture}
    \end{document}

你好，

我有以下問題。我希望 xz 平面中的黑色圓弧圍繞繪製的 x 軸旋轉。我只達到了 90° 旋轉步長，但我希望旋轉步長為 5°。誰能幫我解決這個問題嗎？

謝謝，尼科

Answer 1

我透過將原點放在 來簡化程式碼(0,0,0)。

可以使用以下方式設定視角：

\tdplotsetmaincoords{70}{110} % rotation about the x and y axis

可使用以下指令設定黑色圓弧旋轉：

\tdplotsetrotatedcoords{0}{0}{-5} % rotation about the x, y and z axis

\documentclass[tikz,border=10pt]{standalone}
\usepackage{tikz-3dplot}
\begin{document}

\tdplotsetmaincoords{70}{110}     % point of view
\tdplotsetrotatedcoords{0}{0}{-5} % black arc rotation (x,y,z)

\begin{tikzpicture}[tdplot_main_coords,scale=1]
  %draw the axes
  \draw[blue,->] (0,0,0) -- (2,0,0) node[anchor=south]{$x$};
  \draw[blue,->] (0,0,0) -- (0,2,0) node[anchor=north]{$y$};
  \draw[red,->]  (0,0,0) -- (0,0,2) node[anchor=west]{$z$};

  % draw arcs  
  \draw[canvas is yz plane at x = 0, opacity = 0.2, line width = 1pt]
    (0,0) arc (0:90:1);
  \draw[canvas is yz plane at x = 0, opacity = 0.2, line width = 1pt]
    (0,0) arc (0:-90:-1);
  \draw[canvas is xz plane at y = 0, opacity = 0.2, line width = 1pt]
    (0,0) arc (0:-90:-1);

  \draw[tdplot_rotated_coords, canvas is zx plane at y = 0, line width = 1pt]
    (0,0) arc (90:0:1);

\end{tikzpicture}
\end{document}

動畫版（僅供娛樂）：

代碼：

\documentclass{beamer}
\usepackage{tikz,tikz-3dplot}
\setbeamertemplate{navigation symbols}{}

\tikzset{
  invisible/.style={opacity=0},
  visible on/.style={alt={#1{}{invisible}}},
  alt/.code args={<#1>#2#3}{%
    \alt<#1>{\pgfkeysalso{#2}}{\pgfkeysalso{#3}}
  },
}

\begin{document}

\tdplotsetmaincoords{70}{110}    % point of view
\tdplotsetrotatedcoords{0}{0}{0} % black arc rotation (x,y,z)

\begin{frame}
\centering
\begin{tikzpicture}[tdplot_main_coords]
    %draw the axes  
    \draw[blue,->] (0,0,0) -- (2,0,0) node[anchor=south]{$x$};
    \draw[blue,->] (0,0,0) -- (0,2,0) node[anchor=north]{$y$};
    \draw[red,->]  (0,0,0) -- (0,0,2) node[anchor=west]{$z$};

    % draw arcs  
    \draw[canvas is yz plane at x = 0, opacity = 0.2, line width = 1pt]
      (0,0) arc (0:90:1);
    \draw[canvas is yz plane at x = 0, opacity = 0.2, line width = 1pt]
      (0,0) arc (0:-90:-1);
    \draw[canvas is xz plane at y = 0, opacity = 0.2, line width = 1pt]
      (0,0) arc (0:-90:-1);

    \foreach \i in {0,...,10}
    \tdplotsetrotatedcoords{0}{0}{\i*36}
    \draw[tdplot_rotated_coords, thick,visible on=<\i>,
      canvas is zx plane at y = 0, line width = 1pt]
      (0,0) arc (90:0:1);

\end{tikzpicture}
\end{frame}

\end{document}

用於產生動畫 gif 的 ImageMagick 指令：

convert -verbose -delay 12 -loop 0 -density 300 i.pdf o.gif

Answer 2

\documentclass[tikz,border=10pt]{standalone}
\usepackage{tikz-3dplot}
\begin{document}

\tdplotsetmaincoords{70}{20}     % point of view

\begin{tikzpicture}[tdplot_main_coords,scale=1]

 %draw black arc
  \draw[canvas is xy plane at z = 0, line width = 1pt]
    (0,0) arc (0:-90:-1);

 %draw rotated gray arcs (5°-steps)
  \foreach \rotStep in {5,10,15,...,355}{
    \tdplotsetrotatedcoords{0}{\rotStep}{0} 
        \draw[tdplot_rotated_coords, canvas is xy plane at z = 0, line width = 1pt, opacity = 0.2]
          (0,0) arc (0:-90:-1);
   }

  %draw the axes
  \draw[red,->] (0,0,0) -- (0,4,0) node[anchor=north]{$x$};
  \draw[blue,->]  (0,0,0) -- (0,0,-2) node[anchor=west]{$y$};
  \draw[blue,->] (0,0,0) -- (2,0,0) node[anchor=south]{$z$};

\end{tikzpicture}
\end{document}

在 Sergej 的幫助下，我使用\tdplotsetrotatedcoords{}{}{}.順便說一句，動畫版本是一個很酷的功能。

感謝您的幫忙！尼可