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无法掌握函数 \tdplotsetrotatedcoords{}{}{}

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无法掌握函数 \tdplotsetrotatedcoords{}{}{}

我仍在尝试掌握函数 \tdplotsetrotatedcoords{}{}{}。我举一个例子：

\documentclass[a4paper,11pt]{article}
\usepackage{tikz, tkz-euclide}
\usepackage{tikz-3dplot}
\usepackage[margin=2.5cm, vmargin={2.5cm,1.5cm}]{geometry}

\begin{document}

\tdplotsetmaincoords{60}{40}
\begin{tikzpicture}[tdplot_main_coords,scale=4]
\draw[thick,dashed] (0,0,0) -- (-0.2,0,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0.2,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0,-0.2) ;
\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,-1,0) node[anchor=north west]{$y$}; % pas op y-as geinviteerd
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

\draw[very thick, blue] (0,0,0) -- (1,0,{2/3}) node[anchor=west]{$l$} ; % functie in x-z vlak

\tdplotsetrotatedcoords{0}{0}{0} % 

\begin{scope}[tdplot_rotated_coords]
    \foreach \p in {0,0.02,...,1}
            {\tdplotdrawarc[black, very thin]{(0,0,\p)}{\p*2/3}{0}{360}{}{}{}} 
\end{scope}

\end{tikzpicture}

围绕 z 轴画出漂亮的圆圈。当我将 \tdplotsetrotatedcoords{0}{0}{0} 更改为 \tdplotsetrotatedcoords{0}{90}{0} 时，圆圈围绕 x 轴，完美！

但是我怎样才能让它们围绕 y 轴？我想用 \tdplotsetrotatedcoords{90}{0}{0}，但是不行。我的答案是什么？

我仅使用 \tdplotsetrotatedcoords{}{}{}，因为函数 \tdplotdrawarc 仅在 xy 平面中绘制圆弧。是否有函数可以在 xz 平面或任何其他平面中绘制圆弧？

与 {0}{0}{0} 与 {0}{90}{0}

答案1

更新：我好像误读了你的问题。我把“如何让它们围绕 y 轴”理解为“如何围绕 y 轴旋转”，但你想要的是围绕 y 轴的圆，对吗？这可以通过以下方式实现

\documentclass[a4paper,11pt]{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\usepackage[margin=2.5cm, vmargin={2.5cm,1.5cm}]{geometry}
\begin{document}

\tdplotsetmaincoords{60}{40}
\begin{tikzpicture}[tdplot_main_coords,scale=4]
\draw[thick,dashed] (0,0,0) -- (-0.2,0,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0.2,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0,-0.2) ;
\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,-1,0) node[anchor=north west]{$y$}; % pas op y-as geinviteerd
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

\draw[very thick, blue] (0,0,0) -- (1,0,{2/3}) node[anchor=west]{$l$} ; % functie in x-z vlak
\foreach \p in {0,0.02,...,1}
{\begin{scope}[canvas is xz plane at y=-\p]
 \draw circle[radius=\p*2/3];  
\end{scope}}
\end{tikzpicture}
\end{document}

在此处输入图片描述

正如您所怀疑的，有一个更直接的选择：3d库，您可以使用它在任意平面上绘制物体。

或者，您可以使用\tdplotsetrotatedcoords{90}{-90}{0}

\documentclass[a4paper,11pt]{article}
\usepackage{tikz, tkz-euclide}
\usepackage{tikz-3dplot}
\usepackage[margin=2.5cm, vmargin={2.5cm,1.5cm}]{geometry}
\begin{document}

\tdplotsetmaincoords{60}{40}
\begin{tikzpicture}[tdplot_main_coords,scale=4]
\draw[thick,dashed] (0,0,0) -- (-0.2,0,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0.2,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0,-0.2) ;
\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,-1,0) node[anchor=north west]{$y$}; % pas op y-as geinviteerd
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

\draw[very thick, blue] (0,0,0) -- (1,0,{2/3}) node[anchor=west]{$l$} ; % functie in x-z vlak

\tdplotsetrotatedcoords{90}{-90}{0} % 

\begin{scope}[tdplot_rotated_coords]
    \foreach \p in {0,0.02,...,1}
            {\tdplotdrawarc[black, very thin]{(0,0,\p)}{\p*2/3}{0}{360}{}{}{}} 
\end{scope}

\end{tikzpicture}
\end{document}

得到的结果是一样的。为什么？一般来说，您可以通过查看手册找到所需的旋转角度，手册在第 7 页有说明

在此处输入图片描述

因此，如果希望旋转后的z轴指向原来的负y方向，我们希望矩阵 D 的最后一列为0,1,0，这意味着alpha=90和beta=-90。当然，旋转并不是唯一的。

请查看以下问题的答案这个问题可以更简单地采用这种方式来滚动、俯仰和偏航轴。

原始答案：（解释：您想绕 y 轴旋转东西。）

\documentclass[a4paper,11pt]{article}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\usetikzlibrary{3d}
\usepackage[margin=2.5cm, vmargin={2.5cm,1.5cm}]{geometry}
\begin{document}

\tdplotsetmaincoords{60}{40}
\begin{tikzpicture}[tdplot_main_coords,scale=4]
\draw[thick,dashed] (0,0,0) -- (-0.2,0,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0.2,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0,-0.2) ;
\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,-1,0) node[anchor=north west]{$y$}; % pas op y-as geinviteerd
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

\draw[very thick, blue] (0,0,0) -- (1,0,{2/3}) node[anchor=west]{$l$} ; % functie in x-z vlak
\foreach \p in {0,0.02,...,1}
{\begin{scope}[canvas is yz plane at x=\p]
 \draw circle[radius=\p*2/3];  
\end{scope}}
\end{tikzpicture}
\end{document}

在此处输入图片描述

如第节所述40.2.1 切换到任意平面在 pgfmanual 第 558 页上，您实际上可以切换到任意平面。但当然，您可能希望确保基向量正确归一化，这时您可以使用\draw[red,thick,circle in plane with normal={{\mynormal} with radius {\r} around (I)}];。

仅供记录，要绕y轴旋转只需使用\tdplotsetrotatedcoords{0}{90}{0}。

\documentclass[a4paper,11pt]{article}
\usepackage{tikz, tkz-euclide}
\usepackage{tikz-3dplot}
\usepackage[margin=2.5cm, vmargin={2.5cm,1.5cm}]{geometry}
\begin{document}

\tdplotsetmaincoords{60}{40}
\begin{tikzpicture}[tdplot_main_coords,scale=4]
\draw[thick,dashed] (0,0,0) -- (-0.2,0,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0.2,0) ;
\draw[thick,dashed] (0,0,0) -- (0,0,-0.2) ;
\draw[thick,->] (0,0,0) -- (1,0,0) node[anchor=north east]{$x$};
\draw[thick,->] (0,0,0) -- (0,-1,0) node[anchor=north west]{$y$}; % pas op y-as geinviteerd
\draw[thick,->] (0,0,0) -- (0,0,1) node[anchor=south]{$z$};

\draw[very thick, blue] (0,0,0) -- (1,0,{2/3}) node[anchor=west]{$l$} ; % functie in x-z vlak

\tdplotsetrotatedcoords{0}{90}{0} % 

\begin{scope}[tdplot_rotated_coords]
    \foreach \p in {0,0.02,...,1}
            {\tdplotdrawarc[black, very thin]{(0,0,\p)}{\p*2/3}{0}{360}{}{}{}} 
\end{scope}

\end{tikzpicture}
\end{document}

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