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在 TikZ-3d 中添加角度

tag-icon • tag-icon tikz-pgf tikz-3d
在 TikZ-3d 中添加角度

我已经在 TikZ 中完成了这个图形，但我不知道如何在 TikZ-3D 中添加和标记角度，我该怎么做？

原始数据如下：

在此处输入图片描述

这是我的以及代码：

\documentclass[tikz]{standalone}
\usepackage{tikz}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{60}{-30}
\begin{tikzpicture}[tdplot_main_coords, >=stealth, scale=2.5]
\draw[->, thick] (0,0,0)--(0,0,3) node[left] {$\vec{z}_{n-1}$};
\draw[->, thick] (0,0,0)--(3,0,0) node[below] {$\vec{x}_{n-1}$};
\draw[dashed] (0,0,0)--(0,0.53,0.47);
\draw[dashed] (1.75,0,0)--(1.75,0,1);
\draw[->, thick] (1.75,0,0)--(1.75,2,1.75) node[left] {$\vec{z}_{n}$};
\draw[dashed] (1.75,0.97,0.85)--(3,0.97,0.85);
\draw[->, thick] (1.75,0.97,0.85)--(3,0.97,1.5) node[below] {$\vec{x}_n$};
\draw[<->, thick] (0,0.32,0.25)--(1.75,0.32,0.25) node[above, midway] {$d_n$};
\draw[<->, thick] (2.75,0,0)--(2.75,0.97,0.85) node[right, midway] {$r_n$};
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案1

另一个选项是更换tikz-3dplot和3d库perspective。依我之见，这样我们可以更好地控制放置矢量的斜平面，而且绘图非常简单。此外，我只使用库来angles绘制直角。

像这样：

\documentclass[tikz,border=2mm]{standalone}
\usetikzlibrary{3d,angles,perspective}

\tikzset{ra/.style={red,draw,angle radius=0.5cm}} % right angle style

\begin{document}
\begin{tikzpicture}[3d view={-30}{30},>=stealth,scale=2.5,
                    line cap=round,line join=round]
% angles
\def\aa{48} % alpha angle
\def\ta{80} % theta angle
% some coordinates
\coordinate (O)  at (0,0);
\coordinate (X)  at (3,0,0);
\coordinate (Z)  at (0,0,3);
\coordinate (O') at (1.75,0,0);
% vertical stuff
\begin{scope}[canvas is xz plane at y=0]
  \draw[<->,thick] (X) node[below] {$\vec{x}_{n-1}$} -|
                   (Z) node[left]  {$\vec{z}_{n-1}$};
  \draw[dashed] (O') --++ (0,1);
  \pic [ra] {right angle=Z--O--X};
\end{scope}
%z_n x_{n-1} plane
\begin{scope}[rotate around x=90-\aa,canvas is xy plane at z=0]
  \draw[dashed]    (O)    --++ (0,0.7);
  \draw[thick,->]  (O')   --++ (0,2.6) coordinate (Z') node[left] {$\vec{z}_n$};
  \draw[thick,<->] (0,0.4)  -- (1.75,0.4) node[midway,above] {$d_n$};
  \draw[thick,<->] (2.75,0) -- (2.75,1.3) node[midway,right] {$r_n$};
  \draw[dashed]    (1.75,1.3) coordinate (P) --++ (1.25,0);
  \pic [ra] {right angle=Z'--O'--O};
\end{scope}
% x_n and theta angle
\begin{scope}[rotate around x=180-\aa,canvas is xy plane at z=0]
  \draw[thick,->] (P) --++ (\ta:2.3) coordinate (Q) node[below] {$\vec{x}_n$};
  \draw[red,->]   (P)   ++ (0.5,0)  arc (0:\ta:0.5) node[xshift=0.7cm,yshift=0.25cm] {$\theta_j$};
  \pic [ra] {right angle=Q--P--O'};
\end{scope}
% alpha angle
\draw[canvas is yz plane at x=0,red,->] (O') ++ (0,0.5) arc (90:90-\aa:0.5) node[midway,above] {$\alpha_j$};
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案2

我认为原图描绘了两个三维欧几里得变换。可以tikz-3dplot通过定义旋转轴和新原点来实现这些变换，例如

\path (1,0,0) coordinate (xj)
    (0,{cos(alphaj)},{-sin(alphaj)}) coordinate (yj) 
    (0,{sin(alphaj)},{cos(alphaj)}) coordinate (zj)
    (dj,0,0) coordinate (Oj);

然后切换到新框架，例如通过

\begin{scope}[x={(xj)},y={(yj)},z={(zj)},shift={(Oj)}]
  <code>
\end{scope}

可以在给定的平面中方便地绘制各种角度，例如

\scoped[canvas is xz plane at y=0] {\draw (0.5,0) |- (0,0.5);}

使用这些方法，可以用以下代码定性地再现原始图片，该代码将旋转角度和偏移定义为“函数”。

\documentclass[tikz,boder=3mm]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{arrows.meta,bending}
\begin{document}
\tdplotsetmaincoords{60}{-30}
\begin{tikzpicture}[tdplot_main_coords, >={Stealth[bend]}, 
    declare function={alphaj=50;thetaj=70;dj=5;rj=3;
        zj1=4;xj1=8;},
    pics/slash/.style={code={\draw[pic actions]
    foreach \i in {1,...,#1} {({-0.3+0.3*(\i-#1/2-0.5)},-0.5) -- ({0.3+0.3*(\i-#1/2-0.5)},0.5)};}},
    pics/slash/.default=1]
  \draw[<->,thick] (xj1,0,0) node[below right] {$x_{j-1}$}
   --  (0,0,0) coordinate[label=below:{$O_{j-1}$}] (Oj1)    
   --  (0,0,zj1) node[above]{$z_{j-1}$};
  \scoped[canvas is xz plane at y=0] {\draw (0.5,0) |- (0,0.5);} 
  % define rotated y and z coordinates 
  \path (1,0,0) coordinate (xj)
    (0,{cos(alphaj)},{-sin(alphaj)}) coordinate (yj) 
    (0,{sin(alphaj)},{cos(alphaj)}) coordinate (zj)
    (dj,0,0) coordinate (Oj);
  \begin{scope}[canvas is yz plane at x=dj]
    \draw (0,0) -- pic[transform shape,sloped]{slash} ++ (0,3);  
    \path (Oj1) -- pic[sloped,transform shape,thin,-]{slash} ++ (0,3);   
    \path (90-alphaj/2:2) node[above]{$\alpha_j$};
    \pgflowlevelsynccm
    \draw[->] (0,2) arc[start angle=90,end angle=90-alphaj,radius=2];
  \end{scope}
  % switch to first rotated plane
  \begin{scope}[x={(xj)},y={(yj)},z={(zj)},shift={(Oj)}]
    \draw[thick,->] (0,0,0) -- ++ (0,0,5) node[above]{$z_j$};
    \draw[dashed] (-dj,0,0) -- ++ (0,0,4);
    \draw[dashed,<->] (-dj,0,2.5) -- node[above]{$d_j$} (0,0,2.5);
    \draw[dashed,<->] (1.5,0,0) -- node[above right]{$r_j$} (1.5,0,rj);
    \scoped[canvas is xz plane at y=0] {\draw (-0.5,0) |- (0,0.5);} 
    % define rotated x and y coordinates 
    \path ({cos(thetaj)},{-sin(thetaj)},0) coordinate (xj')
        ({sin(thetaj)},{cos(thetaj)},0) coordinate (yj') 
        (0,0,1) coordinate (zj')
        (0,0,rj) coordinate (Oj');
    \draw (Oj') -- pic[pos=0.7]{slash=2} ++ (5,0,0);    
    \path (Oj1) -- pic{slash=2} (Oj);
    % switch to second rotated plane
    \begin{scope}[x={(xj')},y={(yj')},z={(zj')},shift={(Oj')}]
      \scoped[canvas is xz plane at y=0] {\draw (0.5,0) |- (0,0.5);}
      \draw[thick,->] (0,0,0) -- (3,0,0) node[right]{$x_j$};
      \begin{scope}[canvas is xy plane at z=0] 
        \path (thetaj/2:2) node[right]{$\theta_j$};
        \pgflowlevelsynccm
        \draw[->] (thetaj:2) arc[start angle=thetaj,end angle=0,radius=2];
      \end{scope}  
    \end{scope}  
  \end{scope}  
\end{tikzpicture}
\end{document}

在此处输入图片描述

答案3

默认情况下，所有圆和圆弧都绘制在 xy 平面上，但您可以使用 进行更改\tdplotsetthetaplanecoords{}。 tikzlibrary 应该可以做到这一点。

\documentclass[tikz]{standalone}
\usepackage{tikz}
\usetikzlibrary{angles}
\usepackage{tikz-3dplot}
\begin{document}
\tdplotsetmaincoords{60}{-30}
\begin{tikzpicture}[tdplot_main_coords, >=stealth, scale=2.5]
\draw[->, thick] (0,0,0) coordinate (O)--(0,0,3) coordinate(A) node[left] {$\vec{z}_{n-1}$};
\draw[->, thick] (O)--(3,0,0) coordinate(B) node[below] {$\vec{x}_{n-1}$};
\draw[dashed] (O)--(0,0.53,0.47);
\draw[dashed] (1.75,0,0)--(1.75,0,1);
\draw[->, thick] (1.75,0,0)  coordinate(C) --(1.75,2,1.75)  coordinate(D) node[left] {$\vec{z}_{n}$};
\draw[dashed] (1.75,0.97,0.85)--(3,0.97,0.85);
\draw[->, thick] (1.75,0.97,0.85)--(3,0.97,1.5) node[below] {$\vec{x}_n$};
\draw[<->, thick] (0,0.32,0.25)--(1.75,0.32,0.25) node[above, midway] {$d_n$};
\draw[<->, thick] (2.75,0,0)--(2.75,0.97,0.85) node[right, midway] {$r_n$};
\tdplotsetthetaplanecoords{90}
\draw[red] pic[draw] {right angle=B--O--A};
\tdplotsetthetaplanecoords{0}
\draw[red] pic[draw] {right angle=O--C--D};
\end{tikzpicture}
\end{document}

演示

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