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当我旋转矩形时，如何跟踪以获得圆柱体？

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当我旋转矩形时，如何跟踪以获得圆柱体？

我正在尝试旋转一个矩形来制作轨迹并得到一个圆柱体。我的代码

\documentclass[border=2mm,12pt,tikz]{standalone}
\usepackage{tikz-3dplot} 
\begin{document}
    \pgfmathsetmacro{\myr}{3}
    \pgfmathsetmacro{\h}{4}
    \foreach \X in {10,20,...,350}  
    {\tdplotsetmaincoords{70}{\X}
    \begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,line join=round]
    \begin{scope}[canvas is xy plane at z=0]
      \coordinate (O) at (0,0);
    \coordinate (A) at (0,\myr);

    \end{scope}
    \begin{scope}[canvas is xy plane at z=\h]
    \coordinate (O') at (0,0);
    \coordinate (B) at (0,\myr);
    \end{scope}
    \foreach \v/\position in { B/below,O/below,A/below,O'/above} {\draw[draw =black, fill=black] (\v) circle (1pt) node [\position=0.2mm] {$\v$};
    }
       \draw[thick]   (O) -- (A) --  (B) -- (O')  -- cycle; 
    \end{tikzpicture}}
\end{document}

如何得到结果？

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答案1

这利用了坐标是全局的这一特点。即使我们在每一帧中绘制一张新图片，坐标A-\Z和B-Z仍然是已知的。而且可以说在 yz 平面中绘制矩形并使用旋转坐标更简单。

\documentclass[border=2mm,12pt,tikz]{standalone}
\usepackage{tikz-3dplot} 
\begin{document}
    \pgfmathsetmacro{\myr}{3}
    \pgfmathsetmacro{\h}{4}
    \tdplotsetmaincoords{70}{0}
    \foreach \X [count=\Z] in {0,10,...,360}  
    {
    \begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,line join=round]
    \path[tdplot_screen_coords,use as bounding box] (-1.2*\myr,-2) rectangle (1.2*\myr,1.25*\h);
    \tdplotsetrotatedcoords{\X}{0}{0}
    \begin{scope}[tdplot_rotated_coords,canvas is yz plane at x=0]
      \path (0,0) coordinate (O) 
      (\myr,0) coordinate (A-\Z)(\myr,0) coordinate (A)
      (0,\h) coordinate (O') 
      (\myr,\h) coordinate (B-\Z) (\myr,\h) coordinate (B);
    \end{scope}
    \foreach \v/\position in {B/below,O/below,A/below,O'/above} 
    {\draw[draw =black, fill=black] (\v) circle (1pt) 
      node [\position=0.2mm] {$\v$};
    }
    \draw[thick]   (O) -- (A-\Z) --  (B-\Z) -- (O')  -- cycle; 
    \ifnum\Z>1
     \draw plot[smooth,samples at={1,...,\Z}] (B-\x); 
     \ifnum\Z>8
      \ifnum\Z>27
       \draw[dashed] plot[smooth,samples at={1,...,9}] (A-\x); 
       \draw[dashed] plot[smooth,samples at={28,...,\Z}] (A-\x); 
       \draw plot[smooth,samples at={9,...,28}] (A-\x); 
       \draw (-\myr,0,0) -- (-\myr,0,\h);
       \draw (\myr,0,0) -- (\myr,0,\h);
      \else
       \draw[dashed] plot[smooth,samples at={1,...,9}] (A-\x); 
       \draw plot[smooth,samples at={9,...,\Z}] (A-\x); 
       \draw (-\myr,0,0) -- (-\myr,0,\h);
      \fi
     \else
      \draw plot[smooth,samples at={1,...,\Z}] (A-\x); 
     \fi
    \fi
    \end{tikzpicture}}
\end{document}

在此处输入图片描述

附录：minthien_2016 的静态版本不适合评论。

\documentclass[border=2mm,12pt,tikz]{standalone}
\usepackage{tikz-3dplot} 
\begin{document}
 \tdplotsetmaincoords{70}{0}
 \begin{tikzpicture}[tdplot_main_coords,scale=1,line cap=butt,line join=round]
    \pgfmathsetmacro{\myr}{3}
    \pgfmathsetmacro{\h}{4}
    \begin{scope}[canvas is xy plane at z=0]
     \draw[dashed] (\myr,0) arc(0:180:\myr);
     \draw (\myr,0) arc(0:-180:\myr);
    \end{scope}
    \foreach \X [evaluate=\X as \mixture using {int(50+50*sin(\X))}] 
    in {-80,-70,...,270}  
    {\tdplotsetrotatedcoords{\X}{0}{0}
     \begin{scope}[tdplot_rotated_coords,canvas is yz plane at x=0]
       \draw[fill=blue!\mixture!red,fill opacity=0.1] (0,0) rectangle (\myr,\h);
     \end{scope}}
    \begin{scope}[canvas is xy plane at z=\h]
     \draw circle [radius=\myr];
    \end{scope}
    \end{tikzpicture}
\end{document}

在此处输入图片描述

附录 2：更多 Ti钾Zy 版本带有一个3d cylinder图片，其中高度和半径存储在 pgf 键中。它还绘制了一个“完整圆柱体”。

\documentclass[border=2mm,12pt,tikz]{standalone}
\usepackage{tikz-3dplot} 
\tikzset{pics/3d cylinder/.style={code={%
 \tikzset{3d cylinder/.cd,#1}
 \draw[left color=gray!90,right color=gray!60,middle color=gray!20] 
  plot[domain=\tdplotmainphi:\tdplotmainphi-180,variable=\t,smooth]
  ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
  {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},0)
  -- 
  plot[domain=\tdplotmainphi-180:\tdplotmainphi,variable=\t,smooth]
  ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
  {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},
  \pgfkeysvalueof{/tikz/3d cylinder/h}) 
  -- cycle;
 \draw[fill=gray!30] 
  plot[domain=0:360,variable=\t,smooth cycle]
    ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
  {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},
  \pgfkeysvalueof{/tikz/3d cylinder/h}); 
}},3d cylinder/.cd,r/.initial=1,h/.initial=1}
\begin{document}
\tdplotsetmaincoords{70}{0}
\foreach \X [count=\Z] in {0,10,...,360}  
{\begin{tikzpicture}[tdplot_main_coords,scale=1,
  line cap=butt,line join=round,3d cylinder/r=3,3d cylinder/h=4]
 \path[tdplot_screen_coords,use as bounding box]
  (-1.2*\pgfkeysvalueof{/tikz/3d cylinder/r},
   -0.33*\pgfkeysvalueof{/tikz/3d cylinder/h}) rectangle 
  (1.2*\pgfkeysvalueof{/tikz/3d cylinder/r},
  1.25*\pgfkeysvalueof{/tikz/3d cylinder/h});
 \draw[fill=gray!80] 
   plot[domain=\tdplotmainphi+90:\tdplotmainphi+90+\X,variable=\t,smooth]
  ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
  {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},0)
  -- (0,0,0) -- cycle; 
 \ifnum\X<190
  \draw[fill=gray!80] plot[domain=\tdplotmainphi+90:\tdplotmainphi+90+\X,variable=\t,smooth]
   ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
   {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},0)
   -- 
   plot[domain=\tdplotmainphi+90+\X:\tdplotmainphi+90,variable=\t,smooth]
   ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
   {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},
   \pgfkeysvalueof{/tikz/3d cylinder/h}) 
   -- cycle;
 \fi 
 \draw[fill=gray!30] 
   plot[domain=\tdplotmainphi+90:\tdplotmainphi+90+\X,variable=\t,smooth]
  ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
  {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},
  \pgfkeysvalueof{/tikz/3d cylinder/h})
   -- (0,0,\pgfkeysvalueof{/tikz/3d cylinder/h}) -- cycle; 
 \ifnum\X>90
  \ifnum\X<280
   \clip plot[domain=\tdplotmainphi+180:\tdplotmainphi+90+\X,variable=\t,smooth]
    ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
    {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},0)
    --({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\tdplotmainphi+90+\X)},
    {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\tdplotmainphi+90+\X)},
    \pgfkeysvalueof{/tikz/3d cylinder/h}) 
    -- (0,0,\pgfkeysvalueof{/tikz/3d cylinder/h}) 
    -- plot[domain=\tdplotmainphi+90:\tdplotmainphi+180,variable=\t,smooth]
    ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\t)},
    {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\t)},
    \pgfkeysvalueof{/tikz/3d cylinder/h}) 
    -- cycle;
   \pic{3d cylinder};
  \else
   \clip (0,0,\pgfkeysvalueof{/tikz/3d cylinder/h}) 
    -- ({\pgfkeysvalueof{/tikz/3d cylinder/r}*cos(\tdplotmainphi+90+\X)},
    {\pgfkeysvalueof{/tikz/3d cylinder/r}*sin(\tdplotmainphi+90+\X)},
    \pgfkeysvalueof{/tikz/3d cylinder/h})
    -| (current bounding box.south east) 
    -| (current bounding box.north west) 
    -| cycle;
   \pic{3d cylinder};
  \fi 
 \fi 
 \end{tikzpicture}}
\end{document}

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